Dirac operators on coset spaces
International Nuclear Information System (INIS)
Balachandran, A.P.; Immirzi, Giorgio; Lee, Joohan; Presnajder, Peter
2003-01-01
The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact connected Lie groups and G is simple. An elementary discussion of the differential geometric and bundle theoretic aspects of G/H, including its projective modules and complex, Kaehler and Riemannian structures, is presented for this purpose. An attractive feature of our approach is that it transparently shows obstructions to spin- and spin c -structures. When a manifold is spin c and not spin, U(1) gauge fields have to be introduced in a particular way to define spinors, as shown by Avis, Isham, Cahen, and Gutt. Likewise, for manifolds like SU(3)/SO(3), which are not even spin c , we show that SU(2) and higher rank gauge fields have to be introduced to define spinors. This result has potential consequences for string theories if such manifolds occur as D-branes. The spectra and eigenstates of the Dirac operator on spheres S n =SO(n+1)/SO(n), invariant under SO(n+1), are explicitly found. Aspects of our work overlap with the earlier research of Cahen et al
On the level order for Dirac operators
International Nuclear Information System (INIS)
Grosse, H.
1987-01-01
We start from the Dirac operator for the Coulomb potential and prove within first order perturbation theory that degenerate levels split in a definite way depending on the sign of the Laplacian of the perturbing potential. 9 refs. (Author)
Dirac operator on spaces with conical singularities
International Nuclear Information System (INIS)
Chou, A.W.
1982-01-01
The Dirac operator on compact spaces with conical singularities is studied via the separation of variables formula and the functional calculus of the Dirac Laplacian on the cone. A Bochner type vanishing theorem which gives topological obstructions to the existence of non-negative scalar curvature k greater than or equal to 0 in the singular case is proved. An index formula relating the index of the Dirac operator to the A-genus and Eta-invariant similar to that of Atiyah-Patodi-Singer is obtained. In an appendix, manifolds with boundary with non-negative scalar curvature k greater than or equal to 0 are studied, and several new results on constructing complete metrics with k greater than or equal to on them are obtained
The Dirac operator on the Fuzzy sphere
International Nuclear Information System (INIS)
Grosse, H.
1994-01-01
We introduce the Fuzzy analog of spinor bundles over the sphere on which the non-commutative analog of the Dirac operator acts. We construct the complete set of eigenstates including zero modes. In the commutative limit we recover known results. (authors)
Dirac operators and Killing spinors with torsion
International Nuclear Information System (INIS)
Becker-Bender, Julia
2012-01-01
On a Riemannian spin manifold with parallel skew torsion, we use the twistor operator to obtain an eigenvalue estimate for the Dirac operator with torsion. We consider the equality case in dimensions four and six. In odd dimensions we describe Sasaki manifolds on which equality in the estimate is realized by Killing spinors with torsion. In dimension five we characterize all Killing spinors with torsion and obtain certain naturally reductive spaces as exceptional cases.
On Huygens' principle for Dirac operators associated to electromagnetic fields
Directory of Open Access Journals (Sweden)
CHALUB FABIO A.C.C.
2001-01-01
Full Text Available We study the behavior of massless Dirac particles, i.e., solutions of the Dirac equation with m = 0 in the presence of an electromagnetic field. Our main result (Theorem 1 is that for purely real or imaginary fields any Huygens type (in Hadamard's sense Dirac operators is equivalent to the free Dirac operator, equivalence given by changes of variables and multiplication (right and left by nonzero functions.
Dirac operator, chirality and random matrix theory
International Nuclear Information System (INIS)
Pullirsch, R.
2001-05-01
Quantum Chromodynamics (QCD) is considered to be the correct theory which describes quarks and gluons and, thus, all strong interaction phenomena from the fundamental forces of nature. However, important properties of QCD such as the physical mechanism of color confinement and the spontaneous breaking of chiral symmetry are still not completely understood and under extensive discussion. Analytical calculations are limited, because in the low-energy regime where quarks are confined, application of perturbation theory is restricted due to the large gluon coupling. A powerful tool to investigate numerically and analytically the non-perturbative region is provided by the lattice formulation of QCD. From Monte Carlo simulations of lattice QCD we know that chiral symmetry is restored above a critical temperature. As the chiral condensate is connected to the spectral density of the Dirac operator via the Banks-Casher relation, the QCD Dirac spectrum is an interesting object for detailed studies. In search for an analytical expression of the infrared limit of the Dirac spectrum it has been realized that chiral random-matrix theory (chRMT) is a suitable tool to compare with the distribution and the correlations of the small Dirac eigenvalues. Further, it has been shown that the correlations of eigenvalues on the scale of mean level spacings are universal for complex physical systems and are given by random-matrix theory (Rm). This has been formulated as the Baghouse-Giannoni-Schmit conjecture which states that spectral correlations of a classically chaotic system are given by RMT on the quantum level. The aim of this work is to analyze the relationship between chiral phase transitions and chaos to order transitions in quantum field theories. We study the eigenvalues of the Dirac operator for Quantum Electrodynamics (QED) with compact gauge group U(1) on the lattice. This theory shows chiral symmetry breaking and confinement in the strong coupling region. Although being
Spectrum of the Wilson Dirac operator at finite lattice spacings
DEFF Research Database (Denmark)
Akemann, G.; Damgaard, Poul Henrik; Splittorff, Kim
2011-01-01
We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral Perturbation Theory and chiral Random Matrix Theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac operator...... as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac operator. It is shown that a chiral Random Matrix Theory for the Wilson Dirac operator reproduces the leading zero-momentum terms of Wilson chiral Perturbation Theory. All results are obtained for fixed index...... of the Wilson Dirac operator. The low-energy constants of Wilson chiral Perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac operator....
Particles and Dirac-type operators on curved spaces
International Nuclear Information System (INIS)
Visinescu, Mihai
2003-01-01
We review the geodesic motion of pseudo-classical particles in curved spaces. Investigating the generalized Killing equations for spinning spaces, we express the constants of motion in terms of Killing-Yano tensors. Passing from the spinning spaces to the Dirac equation in curved backgrounds we point out the role of the Killing-Yano tensors in the construction of the Dirac-type operators. The general results are applied to the case of the four-dimensional Euclidean Taub-Newman-Unti-Tamburino space. From the covariantly constant Killing-Yano tensors of this space we construct three new Dirac-type operators which are equivalent with the standard Dirac operator. Finally the Runge-Lenz operator for the Dirac equation in this background is expressed in terms of the fourth Killing-Yano tensor which is not covariantly constant. As a rule the covariantly constant Killing-Yano tensors realize certain square roots of the metric tensor. Such a Killing-Yano tensor produces simultaneously a Dirac-type operator and the generator of a one-parameter Lie group connecting this operator with the standard Dirac one. On the other hand, the not covariantly constant Killing-Yano tensors are important in generating hidden symmetries. The presence of not covariantly constant Killing-Yano tensors implies the existence of non-standard supersymmetries in point particle theories on curved background. (author)
Dirac operators and Killing spinors with torsion; Dirac-Operatoren und Killing-Spinoren mit Torsion
Energy Technology Data Exchange (ETDEWEB)
Becker-Bender, Julia
2012-12-17
On a Riemannian spin manifold with parallel skew torsion, we use the twistor operator to obtain an eigenvalue estimate for the Dirac operator with torsion. We consider the equality case in dimensions four and six. In odd dimensions we describe Sasaki manifolds on which equality in the estimate is realized by Killing spinors with torsion. In dimension five we characterize all Killing spinors with torsion and obtain certain naturally reductive spaces as exceptional cases.
Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator
International Nuclear Information System (INIS)
Babich, R.; Brower, R. C.; Rebbi, C.; Brannick, J.; Clark, M. A.; Manteuffel, T. A.; McCormick, S. F.; Osborn, J. C.
2010-01-01
We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called γ 5 -Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume.
Dispersive estimates for massive Dirac operators in dimension two
Erdoğan, M. Burak; Green, William R.; Toprak, Ebru
2018-05-01
We study the massive two dimensional Dirac operator with an electric potential. In particular, we show that the t-1 decay rate holds in the L1 →L∞ setting if the threshold energies are regular. We also show these bounds hold in the presence of s-wave resonances at the threshold. We further show that, if the threshold energies are regular then a faster decay rate of t-1(log t) - 2 is attained for large t, at the cost of logarithmic spatial weights. The free Dirac equation does not satisfy this bound due to the s-wave resonances at the threshold energies.
A toy model for higher spin Dirac operators
International Nuclear Information System (INIS)
Eelbode, D.; Van de Voorde, L.
2010-01-01
This paper deals with the higher spin Dirac operator Q 2,1 acting on functions taking values in an irreducible representation space for so(m) with highest weight (5/2, 3/2, 1/2,..., 1/2). . This operator acts as a toy model for generalizations of the classical Rarita-Schwinger equations in Clifford analysis. Polynomial null solutions for this operator are studied in particular.
The overlap Dirac operator as a continued fraction
International Nuclear Information System (INIS)
Wenger, U.; Deutsches Elektronen-Synchrotron
2004-03-01
We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single Krylov space method and nested conjugate gradient procedures are avoided. We point out that the five dimensional linear system can be made well conditioned using equivalence transformations on the continued fractions. (orig.)
Spectral density and a family of Dirac operators
International Nuclear Information System (INIS)
Niemi, A.J.
1985-01-01
The spectral density for a class Dirac operators is investigated by relating its even and odd parts to the Riemann zeta-function and to the eta-invariant by Atiyah, Padoti and Singer. Asymptotic expansions are studied and a 'hidden' supersymmetry is revealed and used to relate the Dirac operator to a supersymmetric quantum mechanics. A general method for the computation of the odd spectral density is developed, and various applications are discussed. In particular the connection to the fermion number and a relation between the odd spectral density and some ratios of Jost functions and relative phase shifts are pointed out. Chiral symmetry breaking is investigated using methods analogous to those applied in the investigation of the fermion number, and related to supersymmetry breaking in the corresponding quantum mechanical model. (orig.)
Chiral condensate from the twisted mass Dirac operator spectrum
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krzysztof [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Garcia-Ramos, Elena [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany); Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Collaboration: European Twisted Mass Collaboration
2013-03-15
We present the results of our computation of the chiral condensate with N{sub f}=2 and N{sub f}=2+1+1 flavours of maximally twisted mass fermions. The condensate is determined from the Dirac operator spectrum, applying the spectral projector method proposed by Giusti and Luescher. We use 3 lattice spacings and several quark masses at each lattice spacing to reliably perform the chiral and continuum extrapolations. We study the effect of the dynamical strange and charm quarks by comparing our results for N{sub f}=2 and N{sub f}=2+1+1 dynamical flavours.
Chiral condensate from the twisted mass Dirac operator spectrum
International Nuclear Information System (INIS)
Cichy, Krzysztof; Jansen, Karl; Cyprus Univ., Nicosia
2013-03-01
We present the results of our computation of the chiral condensate with N f =2 and N f =2+1+1 flavours of maximally twisted mass fermions. The condensate is determined from the Dirac operator spectrum, applying the spectral projector method proposed by Giusti and Luescher. We use 3 lattice spacings and several quark masses at each lattice spacing to reliably perform the chiral and continuum extrapolations. We study the effect of the dynamical strange and charm quarks by comparing our results for N f =2 and N f =2+1+1 dynamical flavours.
Perturbation of self-adjoint operators by Dirac distributions
International Nuclear Information System (INIS)
Zorbas, J.
1980-01-01
The existence of a family of self-adjoint Hamiltonians H/sub theta/, theta element of [0, 2π), corresponding to the formal expression H 0 +νdelta (x) is shown for a general class of self-adjoint operators H 0 . Expressions for the Green's function and wavefunction corresponding to H/sub theta/ are obtained in terms of the Green's function and wavefunction corresponding to H 0 . Similar results are shown for the perturbation of H 0 by a finite sum of Dirac distributions. A prescription is given for obtaining H/sub theta/ as the strong resolvent limit of a family of momentum cutoff Hamiltonians H/sup N/. The relationship between the scattering theories corresponding to H/sup N/ and H/sub theta/ is examined
Uniform bounds of the spectrum of Dirac operators
International Nuclear Information System (INIS)
Ezin, J.P.; Rigoli, M.
1988-06-01
Let (M,g) be a compact, connected Riemannian manifold of dimension n ≥ 3. We denote with Ric g , S g and γ the Ricci curvature, the scalar curvature and conformal class of g, respectively. Then using techniques introduced by A. Lichnerowicz we present a proof of Hijazi's following result. If S g ≥ 0 and (M,g) is a spin manifold, there is a constant μ ≥ 0, depending only on n and γ, such that every eigenvalue λ of the Dirac operator acting on spinor fields over M satisfies λ 2 vol(M,g) 2/n ≥μ. In an appendix we prove that if S g is constant and (M,g) is not conformally diffeomorphic to a standard n-sphere, then if γ contains another metric with constant scalar curvature, there is a positive function ρ on M such that (Ric - Sg / n g) (∇ρ, ∇ρ) is negative somewhere on M. (author). 12 refs
Marshman, Emily; Singh, Chandralekha
2018-01-01
In quantum mechanics, for every physical observable, there is a corresponding Hermitian operator. According to the most common interpretation of quantum mechanics, measurement of an observable collapses the quantum state into one of the possible eigenstates of the operator and the corresponding eigenvalue is measured. Since Dirac notation is an elegant notation that is commonly used in upper-level quantum mechanics, it is important that students learn to express quantum operators corresponding to observables in Dirac notation in order to apply the quantum formalism effectively in diverse situations. Here we focus on an investigation that suggests that, even though Dirac notation is used extensively, many advanced undergraduate and PhD students in physics have difficulty expressing the identity operator and other Hermitian operators corresponding to physical observables in Dirac notation. We first describe the difficulties students have with expressing the identity operator and a generic Hermitian operator corresponding to an observable in Dirac notation. We then discuss how the difficulties found via written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of these concepts. The QuILT strives to help students become proficient in expressing the identity operator and a generic Hermitian operator corresponding to an observable in Dirac notation. We also discuss the effectiveness of the QuILT based on in-class evaluations.
Operator ordering in quantum optics theory and the development of Dirac's symbolic method
International Nuclear Information System (INIS)
Fan Hongyi
2003-01-01
We present a general unified approach for arranging quantum operators of optical fields into ordered products (normal ordering, antinormal ordering, Weyl ordering (or symmetric ordering)) by fashioning Dirac's symbolic method and representation theory. We propose the technique of integration within an ordered product (IWOP) of operators to realize our goal. The IWOP makes Dirac's representation theory and the symbolic method more transparent and consequently more easily understood. The beauty of Dirac's symbolic method is further revealed. Various applications of the IWOP technique, such as in developing the entangled state representation theory, nonlinear coherent state theory, Wigner function theory, etc, are presented. (review article)
Asymptotic analysis of fundamental solutions of Dirac operators on even dimensional Euclidean spaces
International Nuclear Information System (INIS)
Arai, A.
1985-01-01
We analyze the short distance asymptotic behavior of some quantities formed out of fundamental solutions of Dirac operators on even dimensional Euclidean spaces with finite dimensional matrix-valued potentials. (orig.)
Generalized ladder operators for the Dirac-Coulomb problem via SUSY QM
International Nuclear Information System (INIS)
Rodrigues, R. de Lima; Universidade Federal de Campina Grande, PB
2003-12-01
The supersymmetry in quantum mechanics and shape invariance condition are applied as an algebraic method to solving the Dirac-Coulomb problem. The ground state and the excited states are investigated via new generalized ladder operators. (author)
Chiral measurements with the Fixed-Point Dirac operator and construction of chiral currents
International Nuclear Information System (INIS)
Hasenfratz, P.; Hauswirth, S.; Holland, K.; Joerg, T.; Niedermayer, F.
2002-01-01
In this preliminary study, we examine the chiral properties of the parametrized Fixed-Point Dirac operator D FP , see how to improve its chirality via the Overlap construction, measure the renormalized quark condensate Σ-circumflex and the topological susceptibility χ t , and investigate local chirality of near zero modes of the Dirac operator. We also give a general construction of chiral currents and densities for chiral lattice actions
Spectral correlations of the massive QCD Dirac operator at finite temperature
International Nuclear Information System (INIS)
Seif, Burkhard; Wettig, Tilo; Guhr, Thomas
1999-01-01
We use the graded eigenvalue method, a variant of the supersymmetry technique, to compute the universal spectral correlations of the QCD Dirac operator in the presence of massive dynamical quarks. The calculation is done for the chiral Gaussian unitary ensemble of random matrix theory with an arbitrary Hermitian matrix added to the Dirac matrix. This case is of interest for schematic models of OCD at finite temperature
The spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking
International Nuclear Information System (INIS)
Toublan, D.; Verbaarschot, J.J.M.
1999-01-01
We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For N f flavors, the chiral flavor symmetry of these theories is spontaneously broken according to SU (2N f → Sp (2N f ) and SU (N f → O (N f ), respectively, rather than the symmetry breaking pattern SU (N f ) x SU (N f ) → SU (N f ) for QCD with three or more colors and fundamental fermions. In this paper we study the Dirac spectrum for the first two symmetry breaking patterns. Following previous work for the third case we find the Dirac spectrum in the domain λ QCD by means of partially quenched chiral perturbation theory. In particular, this result allows us to calculate the slope of the Dirac spectrum at λ = 0. We also show that for λ 2 Λ QCD (wing L the linear size of the system) the Dirac spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator
The spectrum of a Dirac-like operator class and the topology in two dimensions
International Nuclear Information System (INIS)
Botelho, Luiz C.L.
1998-05-01
It is shown, in a relatively simple way and based on Seeley pseudo-differential operator theory, that the main result of Atiyah-Singer in which the trace of the evolution operator associated to a Dirac-like operator class defined in two-dimensional manifolds and coming out of Quantum Physics has a deep topological meaning
Dai, Jian; Song, Xing-Chang
2001-07-01
One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as `natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices.
Huygens' Principle, Dirac Operators, and Rational Solutions of the AKNS Hierarchy
International Nuclear Information System (INIS)
Chalub, Fabio A. C. C.; Zubelli, Jorge P.
2005-01-01
We prove that rational solutions of the AKNS hierarchy of the form q=σ/τ and r=ρ/τ, where (σ,τ,ρ) are certain Schur functions, naturally yield Dirac operators of strict Huygens' type, i.e., the support of their fundamental solutions is the surface of the light-cone. This strengthens the connection between the theory of completely integrable systems and Huygens' principle by extending to the Dirac operators and the rational solutions of the AKNS hierarchy a classical result of Lagnese and Stellmacher concerning perturbations of wave operators
Self-adjointness and spectral properties of Dirac operators with magnetic links
DEFF Research Database (Denmark)
Portmann, Fabian; Sok, Jérémy; Solovej, Jan Philip
2018-01-01
We define Dirac operators on $\\mathbb{S}^3$ (and $\\mathbb{R}^3$) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among other things, that these operators have discrete spectrum...
The Dirac operator on a finite domain and the R-matrix method
International Nuclear Information System (INIS)
Grant, I P
2008-01-01
Relativistic effects in electron-atom collisions and photo-excitation and -ionization processes increase in importance as the atomic number of the target atom grows and spin-dependent effects increase. A relativistic treatment in which electron motion is described using the Dirac Hamiltonian is then desirable. A version of the popular nonrelativistic R-matrix package incorporating terms from the Breit-Pauli Hamiltonian has been used for modelling such processes for some years. The fully relativistic Dirac R-matrix method has been less popular, but is becoming increasingly relevant for applications to heavy ion targets, where the need to use relativistic wavefunctions is more obvious. The Dirac R-matrix method has been controversial ever since it was first proposed by Goertzel (1948 Phys. Rev. 73 1463-6), and it is therefore important to confirm that recent elaborate and costly applications of the method, such as, Badnell et al (2004 J. Phys. B: At. Mol. Phys. 37 4589) and Ballance and Griffin (2007 J. Phys. B: At. Mol. Opt. Phys. 40 247-58), rest on secure foundations. The first part of this paper analyses the structure of the two-point boundary-value problem for the Dirac operator on a finite domain, from which we construct a unified derivation of the Schroedinger (nonrelativistic) and Dirac (relativistic) R-matrix methods. Suggestions that the usual relativistic theory is not well founded are shown to be without foundation
On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk
International Nuclear Information System (INIS)
Lisovyy, O.
2008-01-01
Dirac Hamiltonian on the Poincare disk in the presence of an Aharonov-Bohm flux and a uniform magnetic field admits a one-parameter family of self-adjoint extensions. We determine the spectrum and calculate the resolvent for each element of this family. Explicit expressions for Green's functions are then used to find Fredholm determinant representations for the tau function of the Dirac operator with two branch points on the Poincare disk. Isomonodromic deformation theory for the Dirac equation relates this tau function to a one-parameter class of solutions of the Painleve VI equation with γ=0. We analyze long-distance behavior of the tau function, as well as the asymptotics of the corresponding Painleve VI transcendents as s→1. Considering the limit of flat space, we also obtain a class of solutions of the Painleve V equation with β=0
String structures and the index of the Dirac-Ramond operator on orbifolds
International Nuclear Information System (INIS)
Pilch, K.; Warner, N.P.
1988-01-01
We discuss the relationship between 'string structures' and the topological class λ element of H 4 (M,Z) on non-simply connected manifolds. We also investigate to what extent the index formula for the Dirac-Ramond operator detects the class, λ. (orig.)
Dirac-like operators on the Hilbert space of differential forms on manifolds with boundaries
Pérez-Pardo, Juan Manuel
The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analyzed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like potentials, in manifolds of dimension higher than one. Self-adjoint boundary conditions for the case of dimension 2 are obtained explicitly.
Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets
International Nuclear Information System (INIS)
Cariglia, Marco; Krtous, Pavel; Kubiznak, David
2011-01-01
In this paper we derive the most general first-order symmetry operator commuting with the Dirac operator in all dimensions and signatures. Such an operator splits into Clifford even and Clifford odd parts which are given in terms of odd Killing-Yano and even closed conformal Killing-Yano inhomogeneous forms, respectively. We study commutators of these symmetry operators and give necessary and sufficient conditions under which they remain of the first-order. In this specific setting we can introduce a Killing-Yano bracket, a bilinear operation acting on odd Killing-Yano and even closed conformal Killing-Yano forms, and demonstrate that it is closely related to the Schouten-Nijenhuis bracket. An important nontrivial example of vanishing Killing-Yano brackets is given by Dirac symmetry operators generated from the principal conformal Killing-Yano tensor [hep-th/0612029]. We show that among these operators one can find a complete subset of mutually commuting operators. These operators underlie separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all dimensions [arXiv:0711.0078].
Directory of Open Access Journals (Sweden)
Brian Jonathan Wolk
2017-01-01
Full Text Available This paper introduces an alternative formalism for deriving the Dirac operator and equation. The use of this formalism concomitantly generates a separate operator coupled to the Dirac operator. When operating on a Clifford field, this coupled operator produces field components which are formally equivalent to the field components of Maxwell's electromagnetic field tensor. Consequently, the Lagrangian of the associated coupled field exhibits internal local gauge symmetry. The coupled field Lagrangian is seen to be equivalent to the Lagrangian of Quantum Electrodynamics. Received: 8 November 2016, Accepted: 4 January 2017; Edited by: D. Gomez Dumm; DOI: http://dx.doi.org/10.4279/PIP.090002 Cite as: B J Wolk, Papers in Physics 9, 090002 (2017
Spectral asymmetry of the massless Dirac operator on a 3-torus
International Nuclear Information System (INIS)
Downes, Robert J.; Vassiliev, Dmitri; Levitin, Michael
2013-01-01
Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant
On the discrete spectrum of the Dirac operator on bent chain quantum graph
Directory of Open Access Journals (Sweden)
Belov Michail
2017-01-01
Full Text Available We study Dirac operators on an infinite quantum graph of a bent chain form which consists of identical rings connected at the touching points by δ-couplings with a parameter α ∈ ℝ. We are interested in the discrete spectrum of the corresponding Hamiltonian. It can be non-empty due to a local (geometrical perturbation of the corresponding infinite chain of rings. The quantum graph of analogous geometry with the Schrodinger operator on the edges was considered by Duclos, Exner and Turek in 2008. They showed that the absence of δ-couplings at vertices (i.e. the Kirchhoff condition at the vertices lead to the absence of eigenvalues. We consider the relativistic particle (the Dirac operator instead of the Schrodinger one but the result is analogous. Quantum graphs of such type are suitable for description of grapheme-based nanostructures. It is established that the negativity of α is the necessary and sufficient condition for the existence of eigenvalues of the Dirac operator (i.e. the discrete spectrum of the Hamiltonian in this case is not empty. The continuous spectrum of the Hamiltonian for bent chain graph coincides with that for the corresponding straight infinite chain. Conditions for appearance of more than one eigenvalue are obtained. It is related to the bending angle. The investigation is based on the transfer-matrix approach. It allows one to reduce the problem to an algebraic task. δ-couplings was introduced by the operator extensions theory method.
On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential
Hulko, Artem
2018-03-01
In this paper we define a one-dimensional discrete Dirac operator on Z . We study the eigenvalues of the Dirac operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity. We also estimate the number of eigenvalues for the discrete Schrödinger operator with complex potential on Z . That is we extend the result obtained by Hulko (Bull Math Sci, to appear) to the whole Z.
On the spectrum of the staggered Dirac operator at finite chemical potential
International Nuclear Information System (INIS)
Vink, J.C.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica
1988-12-01
The spectrum of the staggered Dirac operator in two-dimensional QEDF is investigated at finite chemical potential. In the quenced model, it is shown that lattice artefacts cause a spurious scattering of eigenvalues. This scattering disappears when lattice distance is taken to zero. In the unquenced model, a new approach is used to show that similar effects are absent. (author). 17 refs.; 6 figs
On the spectral properties of Dirac operators with electrostatic delta-shell interactions
Czech Academy of Sciences Publication Activity Database
Behrndt, J.; Exner, Pavel; Holzmann, M.; Lotoreichik, Vladimir
2018-01-01
Roč. 111, č. 3 (2018), s. 47-78 ISSN 0021-7824 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Dirac operator * self-adjoint extension * shell interaction * spectral properties Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.802, year: 2016
A comparative study of numerical methods for the overlap Dirac operator--a status report
International Nuclear Information System (INIS)
Eshof, J. van den; Frommer, A.; Lippert, Th.; Schilling, K.; Vorst, H. van der
2002-01-01
Improvements of various methods to compute the sign function of the hermitian Wilson-Dirac matrix within the overlap operator are presented. An optimal partial fraction expansion (PFE) based on a theorem of Zolotarev is given. Benchmarks show that this PFE together with removal of converged systems within a multi-shift CG appears to approximate the sign function times a vector most efficiently. A posteriori error bounds are given
ζ-function regularization of chiral Jacobians for singular Dirac operators
International Nuclear Information System (INIS)
Carneiro, C.E.I.; Dias, S.A.; Thomaz, M.T.
1989-01-01
We propose a definition of the chiral Jacobian which uses the invariance of the generating functional under chiral rotations. This definition takes into account the contributions of all terms which, after rotation, depend on the chiral parameter α. We show that when the Dirac operator has zero eigenvalues the presence of fermionic sources gives an additional dependence on α. Our definition, by considering this α dependence, reconciles the ζ-function method of calculating chiral Jacobians with Fujikawa's
Characterization and uniqueness of distinguished self-adjoint extensions of dirac operators
International Nuclear Information System (INIS)
Klaus, M.; Wuest, R.; Princeton Univ., NJ
1979-01-01
Distinguished self-adjoint extensions of Dirac operators are characterized by Nenciu and constructed by means of cut-off potentials by Wuest. In this paper it is shown that the existence and a more explicit characterization of Nenciu's self-adjoint extensions can be obtained as a consequence from results of the cut-off method, that these extensions are the same as the extensions constructed with cut-off potentials and that they are unique in some sense. (orig.) [de
Dirac operators and spectral triples for some fractal sets built on curves
DEFF Research Database (Denmark)
Christensen, Erik; Ivan, Cristina; Lapidus, Michel L.
2008-01-01
A spectral triple is an object which is described using an algebra of operators on a Hilbert space and an unbounded self-adjoint operator, called a Dirac operator. This model may be applied to the study of classical geometrical objects .The article contains a construction of a spectral triple ass...... associated to some classical fractal subsets of the plane, and it is demonstrated that you can read of many classical geometrical structures, such as distance, measure and Hausdorff dimension from the spectral triple....
Low-lying eigenmodes of the Wilson-Dirac operator and correlations with topological objects
International Nuclear Information System (INIS)
Kusterer, Daniel-Jens; Hedditch, John; Kamleh, Waseem; Leinweber, D.B.; Williams, Anthony G.
2002-01-01
The probability density of low-lying eigenvectors of the hermitian Wilson-Dirac operator H(κ)=γ 5 D W (κ) is examined. Comparisons in position and size between eigenvectors, topological charge and action density are made. We do this for standard Monte-Carlo generated SU(3) background fields and for single instanton background fields. Both hot and cooled SU(3) background fields are considered. An instanton model is fitted to eigenmodes and topological charge density and the sizes and positions of these are compared
Energy Technology Data Exchange (ETDEWEB)
Dai Jian [Theory Group, Department of Physics, Peking University, Beijing (China)]. E-mail: jdai@mail.phy.pku.edu.cn; Song Xingchang [Theory Group, Department of Physics, Peking University, Beijing (China)]. E-mail: songxc@ibm320h.phy.pku.edu.cn
2001-07-13
One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as 'natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices. (author)
FFT-split-operator code for solving the Dirac equation in 2+1 dimensions
Mocken, Guido R.; Keitel, Christoph H.
2008-06-01
The main part of the code presented in this work represents an implementation of the split-operator method [J.A. Fleck, J.R. Morris, M.D. Feit, Appl. Phys. 10 (1976) 129-160; R. Heather, Comput. Phys. Comm. 63 (1991) 446] for calculating the time-evolution of Dirac wave functions. It allows to study the dynamics of electronic Dirac wave packets under the influence of any number of laser pulses and its interaction with any number of charged ion potentials. The initial wave function can be either a free Gaussian wave packet or an arbitrary discretized spinor function that is loaded from a file provided by the user. The latter option includes Dirac bound state wave functions. The code itself contains the necessary tools for constructing such wave functions for a single-electron ion. With the help of self-adaptive numerical grids, we are able to study the electron dynamics for various problems in 2+1 dimensions at high spatial and temporal resolutions that are otherwise unachievable. Along with the position and momentum space probability density distributions, various physical observables, such as the expectation values of position and momentum, can be recorded in a time-dependent way. The electromagnetic spectrum that is emitted by the evolving particle can also be calculated with this code. Finally, for planning and comparison purposes, both the time-evolution and the emission spectrum can also be treated in an entirely classical relativistic way. Besides the implementation of the above-mentioned algorithms, the program also contains a large C++ class library to model the geometric algebra representation of spinors that we use for representing the Dirac wave function. This is why the code is called "Dirac++". Program summaryProgram title: Dirac++ or (abbreviated) d++ Catalogue identifier: AEAS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing
Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator
Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi
2018-03-01
Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.
Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator
Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi
2017-12-01
The Atiyah-Patodi-Singer (APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. The mathematical setup for this theorem is, however, not directly related to the physical fermion system, as it imposes on the fermion fields a nonlocal boundary condition known as the "APS boundary condition" by hand, which is unlikely to be realized in the materials. In this work, we attempt to reformulate the APS index in a "physicist-friendly" way for a simple setup with U (1 ) or S U (N ) gauge group on a flat four-dimensional Euclidean space. We find that the same index as APS is obtained from the domain-wall fermion Dirac operator with a local boundary condition, which is naturally given by the kink structure in the mass term. As the boundary condition does not depend on the gauge fields, our new definition of the index is easy to compute with the standard Fujikawa method.
Pais, Abraham; Jacob, Maurice; Olive, David I.; Atiyah, Michael F.
2005-09-01
Preface Peter Goddard; Dirac memorial address Stephen Hawking; 1. Paul Dirac: aspects of his life and work Abraham Pais; 2. Antimatter Maurice Jacob; 3. The monopole David Olive; 4. The Dirac equation and geometry Michael F. Atiyah.
The square root of the Dirac operator on superspace and the Maxwell equations
International Nuclear Information System (INIS)
Bzdak, Adam; Hadasz, Leszek
2004-01-01
We re-consider the procedure of 'taking a square root of the Dirac equation' on superspace and show that it leads to the well-known superfield W α and to the proper equations of motion for the components, i.e., the Maxwell equations and the massless Dirac equation
The square root of the Dirac operator on superspace and the Maxwell equations
Bzdak, Adam; Hadasz, Leszek
2004-02-01
We re-consider the procedure of "taking a square root of the Dirac equation" on superspace and show that it leads to the well-known superfield Wα and to the proper equations of motion for the components, i.e., the Maxwell equations and the massless Dirac equation.
The square root of the Dirac operator on the superspace and the Maxwell equations
Bzdak, Adam; Hadasz, Leszek
2003-01-01
We re-consider the procedure of ``taking a square root of the Dirac equation'' on the superspace and show that it leads to the well known superfield W_\\alpha and to the proper equations of motion for the components, i.e. the Maxwell equations and the massless Dirac equation.
The square root of the Dirac operator on superspace and the Maxwell equations
Energy Technology Data Exchange (ETDEWEB)
Bzdak, Adam; Hadasz, Leszek
2004-02-26
We re-consider the procedure of 'taking a square root of the Dirac equation' on superspace and show that it leads to the well-known superfield W{sub {alpha}} and to the proper equations of motion for the components, i.e., the Maxwell equations and the massless Dirac equation.
Energy Technology Data Exchange (ETDEWEB)
Botelho, Luiz C.L
1998-05-01
It is shown, in a relatively simple way and based on Seeley pseudo-differential operator theory, that the main result of Atiyah-Singer in which the trace of the evolution operator associated to a Dirac-like operator class defined in two-dimensional manifolds and coming out of Quantum Physics has a deep topological meaning 5 refs.
Quark mass anomalous dimension from the twisted mass Dirac operator spectrum
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krzysztof [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics
2013-12-15
We investigate whether it is possible to extract the quark mass anomalous dimension and its scale dependence from the spectrum of the twisted mass Dirac operator in Lattice QCD. The answer to this question appears to be positive, provided that one goes to large enough eigenvalues, sufficiently above the non-perturbative regime. The obtained results are compared to continuum perturbation theory. By analyzing possible sources of systematic effects, we find the domain of applicability of the approach, extending from an energy scale of around 1.5 to 4 GeV. The lower limit is dictated by physics (non-perturbative effects at low energies), while the upper bound is set by the ultraviolet cut-off of present-day lattice simulations. We use gauge field configuration ensembles generated by the European Twisted Mass Collaboration (ETMC) with 2 flavours of dynamical twisted mass quarks, at 4 lattice spacings in the range between around 0.04 and 0.08 fm.
Quark mass anomalous dimension from the twisted mass Dirac operator spectrum
International Nuclear Information System (INIS)
Cichy, Krzysztof; Poznan Univ.
2013-12-01
We investigate whether it is possible to extract the quark mass anomalous dimension and its scale dependence from the spectrum of the twisted mass Dirac operator in Lattice QCD. The answer to this question appears to be positive, provided that one goes to large enough eigenvalues, sufficiently above the non-perturbative regime. The obtained results are compared to continuum perturbation theory. By analyzing possible sources of systematic effects, we find the domain of applicability of the approach, extending from an energy scale of around 1.5 to 4 GeV. The lower limit is dictated by physics (non-perturbative effects at low energies), while the upper bound is set by the ultraviolet cut-off of present-day lattice simulations. We use gauge field configuration ensembles generated by the European Twisted Mass Collaboration (ETMC) with 2 flavours of dynamical twisted mass quarks, at 4 lattice spacings in the range between around 0.04 and 0.08 fm.
Schrödinger and Dirac operators with the Aharonov-Bohm and magnetic-solenoid fields
International Nuclear Information System (INIS)
Gitman, D M; Tyutin, I V; Voronov, B L
2012-01-01
We construct all self-adjoint Schrödinger and Dirac operators (Hamiltonians) with both the pure Aharonov-Bohm (AB) field and the so-called magnetic-solenoid field (a collinear superposition of the AB field and a constant magnetic field). We perform a spectral analysis for these operators, which includes finding spectra and spectral decompositions, or inversion formulae. In constructing the Hamiltonians and performing their spectral analysis, we follow, respectively, the von Neumann theory of self-adjoint extensions of symmetric operators and the Krein method of guiding functionals. (paper)
Wehling, T. O.; Black-Schaffer, A. M.; Balatsky, A. V.
2014-01-01
A wide range of materials, like d-wave superconductors, graphene, and topological insulators, share a fundamental similarity: their low-energy fermionic excitations behave as massless Dirac particles rather than fermions obeying the usual Schrodinger Hamiltonian. This emergent behavior of Dirac fermions in condensed matter systems defines the unifying framework for a class of materials we call "Dirac materials''. In order to establish this class of materials, we illustrate how Dirac fermions ...
Rivasseau, Vincent; Fuchs, Jean-Nöel
2017-01-01
This fifteenth volume of the Poincare Seminar Series, Dirac Matter, describes the surprising resurgence, as a low-energy effective theory of conducting electrons in many condensed matter systems, including graphene and topological insulators, of the famous equation originally invented by P.A.M. Dirac for relativistic quantum mechanics. In five highly pedagogical articles, as befits their origin in lectures to a broad scientific audience, this book explains why Dirac matters. Highlights include the detailed "Graphene and Relativistic Quantum Physics", written by the experimental pioneer, Philip Kim, and devoted to graphene, a form of carbon crystallized in a two-dimensional hexagonal lattice, from its discovery in 2004-2005 by the future Nobel prize winners Kostya Novoselov and Andre Geim to the so-called relativistic quantum Hall effect; the review entitled "Dirac Fermions in Condensed Matter and Beyond", written by two prominent theoreticians, Mark Goerbig and Gilles Montambaux, who consider many other mater...
Casajús Ramo, A
2006-01-01
DIRAC is the LHCb Workload and Data Management System. Based on a service-oriented architecture, it enables generic distributed computing with lightweight Agents and Clients for job execution and data transfers. DIRAC implements a client-server architecture exposing server methods through XML Remote Procedure Call (XML-RPC) protocol. DIRAC is mostly coded in python. DIRAC security infrastructure has been designed to be a completely generic XML-RPC transport over a SSL tunnel. This new security layer is able to handle standard X509 certificates as well as grid-proxies to authenticate both sides of the connection. Serve and client authentication relies over OpenSSL and py-Open SSL, but to be able to handle grid proxies some modifications have been added to those libraries. DIRAC security infrastructure handles authorization and authorization as well as provides extended capabilities like secure connection tunneling and file transfer. Using this new security infrastructure all LHCb users can safely make use o...
International Nuclear Information System (INIS)
Gomez, F.; Adeva, B.; Afanasev, L.; Benayoun, M.; Brekhovskikh, V.; Caragheorgheopol, G.; Cechak, T.; Chiba, M.; Constantinescu, S.; Doudarev, A.; Dreossi, D.; Drijard, D.; Ferro-Luzzi, M.; Gallas, M.V.; Gerndt, J.; Giacomich, R.; Gianotti, P.; Goldin, D.; Gorin, A.; Gortchakov, O.; Guaraldo, C.; Hansroul, M.; Hosek, R.; Iliescu, M.; Jabitski, M.; Kalinina, N.; Karpoukhine, V.; Kluson, J.; Kobayashi, M.; Kokkas, P.; Komarov, V.; Koulikov, A.; Kouptsov, A.; Krouglov, V.; Krouglova, L.; Kuroda, K.-I.; Lanaro, A.; Lapshine, V.; Lednicky, R.; Leruste, P.; Levisandri, P.; Lopez Aguera, A.; Lucherini, V.; Maki, T.; Manuilov, I.; Montanet, L.; Narjoux, J.-L.; Nemenov, L.; Nikitin, M.; Nunez Pardo, T.; Okada, K.; Olchevskii, V.; Pazos, A.; Pentia, M.; Penzo, A.; Perreau, J.-M.; Petrascu, C.; Plo, M.; Ponta, T.; Pop, D.; Riazantsev, A.; Rodriguez, J.M.; Rodriguez Fernandez, A.; Rykaline, V.; Santamarina, C.; Saborido, J.; Schacher, J.; Sidorov, A.; Smolik, J.; Takeutchi, F.; Tarasov, A.; Tauscher, L.; Tobar, M.J.; Trusov, S.; Vazquez, P.; Vlachos, S.; Yazkov, V.; Yoshimura, Y.; Zrelov, P.
2001-01-01
The main objective of DIRAC experiment is the measurement of the lifetime τ of the exotic hadronic atom consisting of π + and π - mesons. The lifetime of this atom is determined by the decay mode π + π - → π 0 π 0 due to the strong interaction. Through the precise relationship between the lifetime and the S-wave pion-pion scattering length difference |a 0 - a 2 | for isospin 0 and 2 (respectively), a measurement of τ with an accuracy of 10% will allow a determination of |a 0 - a 2 | at a 5% precision level. Pion-pion scattering lengths have been calculated in the framework of chiral perturbation theory with an accuracy below 5%. In this way DIRAC experiment will provide a crucial test of the chiral symmetry breaking scheme in QCD effective theories at low energies
Energy Technology Data Exchange (ETDEWEB)
Gomez, F.; Adeva, B.; Afanasev, L.; Benayoun, M.; Brekhovskikh, V.; Caragheorgheopol, G.; Cechak, T.; Chiba, M.; Constantinescu, S.; Doudarev, A.; Dreossi, D.; Drijard, D.; Ferro-Luzzi, M.; Gallas, M.V.; Gerndt, J.; Giacomich, R.; Gianotti, P.; Goldin, D.; Gorin, A.; Gortchakov, O.; Guaraldo, C.; Hansroul, M.; Hosek, R.; Iliescu, M.; Jabitski, M.; Kalinina, N.; Karpoukhine, V.; Kluson, J.; Kobayashi, M.; Kokkas, P.; Komarov, V.; Koulikov, A.; Kouptsov, A.; Krouglov, V.; Krouglova, L.; Kuroda, K.-I.; Lanaro, A.; Lapshine, V.; Lednicky, R.; Leruste, P.; Levisandri, P.; Lopez Aguera, A.; Lucherini, V.; Maki, T.; Manuilov, I.; Montanet, L.; Narjoux, J.-L.; Nemenov, L.; Nikitin, M.; Nunez Pardo, T.; Okada, K.; Olchevskii, V.; Pazos, A.; Pentia, M.; Penzo, A.; Perreau, J.-M.; Petrascu, C.; Plo, M.; Ponta, T.; Pop, D.; Riazantsev, A.; Rodriguez, J.M.; Rodriguez Fernandez, A.; Rykaline, V.; Santamarina, C.; Saborido, J.; Schacher, J.; Sidorov, A.; Smolik, J.; Takeutchi, F.; Tarasov, A.; Tauscher, L.; Tobar, M.J.; Trusov, S.; Vazquez, P.; Vlachos, S.; Yazkov, V.; Yoshimura, Y.; Zrelov, P
2001-04-01
The main objective of DIRAC experiment is the measurement of the lifetime {tau} of the exotic hadronic atom consisting of {pi}{sup +} and {pi}{sup -} mesons. The lifetime of this atom is determined by the decay mode {pi}{sup +} {pi}{sup -} {yields} {pi}{sup 0} {pi}{sup 0} due to the strong interaction. Through the precise relationship between the lifetime and the S-wave pion-pion scattering length difference |a{sub 0} - a{sub 2}| for isospin 0 and 2 (respectively), a measurement of {tau} with an accuracy of 10% will allow a determination of |a{sub 0} - a{sub 2}| at a 5% precision level. Pion-pion scattering lengths have been calculated in the framework of chiral perturbation theory with an accuracy below 5%. In this way DIRAC experiment will provide a crucial test of the chiral symmetry breaking scheme in QCD effective theories at low energies.
International Nuclear Information System (INIS)
Thaller, B.
1992-01-01
This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics
Resolvent convergence in norm for Dirac operator with Aharonov-Bohm field
International Nuclear Information System (INIS)
Tamura, Hideo
2003-01-01
We consider the Hamiltonian for relativistic particles moving in the Aharonov-Bohm magnetic field in two dimensions. The field has δ-like singularity at the origin, and the Hamiltonian is not necessarily essentially self-adjoint. The self-adjoint realization requires one parameter family of boundary conditions at the origin. We approximate the point-like field by smooth ones and study the problem of norm resolvent convergence to see which boundary condition is physically reasonable among admissible boundary conditions. We also study the effect of perturbations by scalar potentials. Roughly speaking, the obtained result is that the limit self-adjoint realization is different even for small perturbation of scalar potentials according to the values of magnetic fluxes. It changes at half-integer fluxes. The method is based on the resolvent analysis at low energy on magnetic Schroedinger operators with resonance at zero energy and the resonance plays an important role from a mathematical point of view. However it has been neglected in earlier physical works. The emphasis here is placed on this natural aspect
Data Management System of the DIRAC Project
Haen, Christophe; Tsaregorodtsev, Andrei
2015-01-01
The DIRAC Interware provides a development framework and a complete set of components for building distributed computing systems. The DIRAC Data Management System (DMS) offers all the necessary tools to ensure data handling operations for small and large user communities. It supports transparent access to storage resources based on multiple technologies, and is easily expandable. The information on data files and replicas is kept in a File Catalog of which DIRAC offers a powerful and versatile implementation (DFC). Data movement can be performed using third party services including FTS3. Bulk data operations are resilient with respect to failures due to the use of the Request Management System (RMS) that keeps track of ongoing tasks. In this contribution we will present an overview of the DIRAC DMS capabilities and its connection with other DIRAC subsystems such as the Transformation System. The DIRAC DMS is in use by several user communities now. The contribution will present the experience of the LHCb exper...
The DIRAC Data Management System (poster)
Haen, Christophe
2015-01-01
The DIRAC Interware provides a development framework and a complete set of components for building distributed computing systems. The DIRAC Data Management System (DMS) offers all the necessary tools to ensure data handling operations for small and large user communities. It supports transparent access to storage resources based on multiple technologies, and is easily expandable. The information on data files and replicas is kept in a File Catalog of which DIRAC offers a powerful and versatile implementation (DFC). Data movement can be performed using third party services including FTS3. Bulk data operations are resilient with respect to failures due to the use of the Request Management System (RMS) that keeps track of ongoing tasks. In this contribution we will present an overview of the DIRAC DMS capabilities and its connection with other DIRAC subsystems such as the Transformation System. The DIRAC DMS is in use by several user communities now. The contribution will present the experience of the LHCb exper...
DIRAC in Large Particle Physics Experiments
Stagni, F.; Tsaregorodtsev, A.; Arrabito, L.; Sailer, A.; Hara, T.; Zhang, X.; Consortium, DIRAC
2017-10-01
The DIRAC project is developing interware to build and operate distributed computing systems. It provides a development framework and a rich set of services for both Workload and Data Management tasks of large scientific communities. A number of High Energy Physics and Astrophysics collaborations have adopted DIRAC as the base for their computing models. DIRAC was initially developed for the LHCb experiment at LHC, CERN. Later, the Belle II, BES III and CTA experiments as well as the linear collider detector collaborations started using DIRAC for their computing systems. Some of the experiments built their DIRAC-based systems from scratch, others migrated from previous solutions, ad-hoc or based on different middlewares. Adaptation of DIRAC for a particular experiment was enabled through the creation of extensions to meet their specific requirements. Each experiment has a heterogeneous set of computing and storage resources at their disposal that were aggregated through DIRAC into a coherent pool. Users from different experiments can interact with the system in different ways depending on their specific tasks, expertise level and previous experience using command line tools, python APIs or Web Portals. In this contribution we will summarize the experience of using DIRAC in particle physics collaborations. The problems of migration to DIRAC from previous systems and their solutions will be presented. An overview of specific DIRAC extensions will be given. We hope that this review will be useful for experiments considering an update, or for those designing their computing models.
Akemann, G; Bittner, E; Lombardo, M; Markum, H; Pullirsch, R
2004-01-01
We investigate the eigenvalue spectrum of the staggered Dirac matrix in two color QCD at finite chemical potential. The profiles of complex eigenvalues close to the origin are compared to a complex generalization of the chiral Gaussian Symplectic Ensemble, confirming its predictions for weak and strong non-Hermiticity. They differ from the QCD symmetry class with three colors by a level repulsion from both the real and imaginary axis.
International Nuclear Information System (INIS)
Akemann, Gernot; Bittner, Elmar; Lombardo, Maria-Paola; Markum, Harald; Pullirsch, Rainer
2005-01-01
We investigate the eigenvalue spectrum of the staggered Dirac matrix in two color QCD at finite chemical potential. The profiles of complex eigenvalues close to the origin are compared to a complex generalization of the chiral Gaussian Symplectic Ensemble, confirming its predictions for weak and strong non-Hermiticity. They differ from the QCD symmetry class with three colors by a level repulsion from both the real and imaginary axis
International Nuclear Information System (INIS)
Kalkreuter, T.; Simma, H.
1995-07-01
The low-lying eigenvalues of a (sparse) hermitian matrix can be computed with controlled numerical errors by a conjugate gradient (CG) method. This CG algorithm is accelerated by alternating it with exact diagonalizations in the subspace spanned by the numerically computed eigenvectors. We study this combined algorithm in case of the Dirac operator with (dynamical) Wilson fermions in four-dimensional SU(2) gauge fields. The algorithm is numerically very stable and can be parallelized in an efficient way. On lattices of sizes 4 4 - 16 4 an acceleration of the pure CG method by a factor of 4 - 8 is found. (orig.)
New solitons connected to the Dirac equation
International Nuclear Information System (INIS)
Grosse, H.
1984-01-01
Imposing isospectral invariance for the one dimensional Dirac operator leads to systems of nonlinear partial differential equations. By constructing reflectionless potentials of the Dirac equation we obtain a new type of solitons for a system of modified Korteweg-de Vries equations. (Author)
DIRAC - The Distributed MC Production and Analysis for LHCb
Tsaregorodtsev, A
2004-01-01
DIRAC is the LHCb distributed computing grid infrastructure for MC production and analysis. Its architecture is based on a set of distributed collaborating services. The service decomposition broadly follows the ARDA project proposal, allowing for the possibility of interchanging the EGEE/ARDA and DIRAC components in the future. Some components developed outside the DIRAC project are already in use as services, for example the File Catalog developed by the AliEn project. An overview of the DIRAC architecture will be given, in particular the recent developments to support user analysis. The main design choices will be presented. One of the main design goals of DIRAC is the simplicity of installation, configuring and operation of various services. This allows all the DIRAC resources to be easily managed by a single Production Manager. The modular design of the DIRAC components allows its functionality to be easily extended to include new computing and storage elements or to handle new tasks. The DIRAC system al...
DIRAC distributed secure framework
International Nuclear Information System (INIS)
Casajus, A; Graciani, R
2010-01-01
DIRAC, the LHCb community Grid solution, provides access to a vast amount of computing and storage resources to a large number of users. In DIRAC users are organized in groups with different needs and permissions. In order to ensure that only allowed users can access the resources and to enforce that there are no abuses, security is mandatory. All DIRAC services and clients use secure connections that are authenticated using certificates and grid proxies. Once a client has been authenticated, authorization rules are applied to the requested action based on the presented credentials. These authorization rules and the list of users and groups are centrally managed in the DIRAC Configuration Service. Users submit jobs to DIRAC using their local credentials. From then on, DIRAC has to interact with different Grid services on behalf of this user. DIRAC has a proxy management service where users upload short-lived proxies to be used when DIRAC needs to act on behalf of them. Long duration proxies are uploaded by users to a MyProxy service, and DIRAC retrieves new short delegated proxies when necessary. This contribution discusses the details of the implementation of this security infrastructure in DIRAC.
International Nuclear Information System (INIS)
Casajus Ramo, A; Graciani Diaz, R; Tsaregorodtsev, A
2012-01-01
The DIRAC framework for distributed computing has been designed as a flexible and modular solution that can be adapted to the requirements of any community. Users interact with DIRAC via command line, using the web portal or accessing resources via the DIRAC python API. The current DIRAC API requires users to use a python version valid for DIRAC. Some communities have developed their own software solutions for handling their specific workload, and would like to use DIRAC as their back-end to access distributed computing resources easily. Many of these solutions are not coded in python or depend on a specific python version. To solve this gap DIRAC provides a new language agnostic API that any software solution can use. This new API has been designed following the RESTful principles. Any language with libraries to issue standard HTTP queries may use it. GSI proxies can still be used to authenticate against the API services. However GSI proxies are not a widely adopted standard. The new DIRAC API also allows clients to use OAuth for delegating the user credentials to a third party solution. These delegated credentials allow the third party software to query to DIRAC on behalf of the users. This new API will further expand the possibilities communities have to integrate DIRAC into their distributed computing models.
Photoconductivity in Dirac materials
International Nuclear Information System (INIS)
Shao, J. M.; Yang, G. W.
2015-01-01
Two-dimensional (2D) Dirac materials including graphene and the surface of a three-dimensional (3D) topological insulator, and 3D Dirac materials including 3D Dirac semimetal and Weyl semimetal have attracted great attention due to their linear Dirac nodes and exotic properties. Here, we use the Fermi’s golden rule and Boltzmann equation within the relaxation time approximation to study and compare the photoconductivity of Dirac materials under different far- or mid-infrared irradiation. Theoretical results show that the photoconductivity exhibits the anisotropic property under the polarized irradiation, but the anisotropic strength is different between 2D and 3D Dirac materials. The photoconductivity depends strongly on the relaxation time for different scattering mechanism, just like the dark conductivity
Dirac, Weyl, Majorana, a review
International Nuclear Information System (INIS)
Uschersohn, J.
1982-05-01
The Dirac equation and the properties of Dirac matrices are presented and discussed. A large number of representations of the Dirac matrices is identified. Special emphasis is put on aspects rarely treated or neglected in textbooks
Indian Academy of Sciences (India)
IAS Admin
Pauli exclusion principle, Fermi–. Dirac statistics, identical and in- distinguishable particles, Fermi gas. Fermi–Dirac Statistics. Derivation and Consequences. S Chaturvedi and Shyamal Biswas. (left) Subhash Chaturvedi is at University of. Hyderabad. His current research interests include phase space descriptions.
Dimock, J.
2010-01-01
We give an alternate definition of the free Dirac field featuring an explicit construction of the Dirac sea. The treatment employs a semi-infinite wedge product of Hilbert spaces. We also show that the construction is equivalent to the standard Fock space construction.
Indian Academy of Sciences (India)
IAS Admin
We present an account of the work of Niels Bohr and Paul Dirac, their interactions and personal- ities. 1. Introduction. In this essay I would like to convey to my readers some- thing about the personalities and work of Niels Bohr and Paul Dirac, juxtaposed against one another. Let me hope that the portraits I will paint of these ...
International Nuclear Information System (INIS)
Rodrigues, R. de Lima
2007-01-01
In the present work we obtain a new representation for the Dirac oscillator based on the Clifford algebra C 7. The symmetry breaking and the energy eigenvalues for our model of the Dirac oscillator are studied in the non-relativistic limit. (author)
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education. P A M Dirac. Articles written in Resonance – Journal of Science Education. Volume 8 Issue 8 August 2003 pp 102-110 Classics. XI. The Relation between Mathematics and Physics · P A M Dirac · More Details Fulltext PDF ...
Three Dimensional Dirac Semimetals
Zaheer, Saad
2014-03-01
Dirac points on the Fermi surface of two dimensional graphene are responsible for its unique electronic behavior. One can ask whether any three dimensional materials support similar pseudorelativistic physics in their bulk electronic spectra. This possibility has been investigated theoretically and is now supported by two successful experimental demonstrations reported during the last year. In this talk, I will summarize the various ways in which Dirac semimetals can be realized in three dimensions with primary focus on a specific theory developed on the basis of representations of crystal spacegroups. A three dimensional Dirac (Weyl) semimetal can appear in the presence (absence) of inversion symmetry by tuning parameters to the phase boundary separating a bulk insulating and a topological insulating phase. More generally, we find that specific rules governing crystal symmetry representations of electrons with spin lead to robust Dirac points at high symmetry points in the Brillouin zone. Combining these rules with microscopic considerations identifies six candidate Dirac semimetals. Another method towards engineering Dirac semimetals involves combining crystal symmetry and band inversion. Several candidate materials have been proposed utilizing this mechanism and one of the candidates has been successfully demonstrated as a Dirac semimetal in two independent experiments. Work carried out in collaboration with: Julia A. Steinberg, Steve M. Young, J.C.Y. Teo, C.L. Kane, E.J. Mele and Andrew M. Rappe.
Monti, Dalida
1996-01-01
Relativamente poco noto al gran pubblico, il premio Nobel Paul Adrien Maurice Dirac appartiene a quel gruppo di uomini di ingegno che nei primi decenni del secolo contribuirono a dare alla nostra concezione del mondo fisico la sua impronta attuale. Assolutamente cruciali, per una valutazione dell'opera di Dirac, sono gli anni compresi tra il 1925 e il 1931: un periodo in cui il fisico fornisce la prima spiegazione chiara e coerente delle proprietà di spin dell'elettrone (equazione di Dirac) e perviene, in forza della pura deduzione matematica, alla scoperta dell'esistenza dell'elettrone positivo o positrone.
Energy Technology Data Exchange (ETDEWEB)
Anon.
1988-04-15
It was Paul Dirac who cast quantum mechanics into the form we now use, and many generations of theoreticians openly acknowledge his influence on their thinking. When Dirac died in 1984, St. John's College, Cambridge, his base for most of his lifetime, instituted an annual lecture in his memory at Cambridge. The first lecture, in 1986, attracted two heavyweights - Richard Feynman and Steven Weinberg. Far from using the lectures as a platform for their own work, in the Dirac tradition they presented stimulating material on deep underlying questions.
International Nuclear Information System (INIS)
Anon.
1988-01-01
It was Paul Dirac who cast quantum mechanics into the form we now use, and many generations of theoreticians openly acknowledge his influence on their thinking. When Dirac died in 1984, St. John's College, Cambridge, his base for most of his lifetime, instituted an annual lecture in his memory at Cambridge. The first lecture, in 1986, attracted two heavyweights - Richard Feynman and Steven Weinberg. Far from using the lectures as a platform for their own work, in the Dirac tradition they presented stimulating material on deep underlying questions
DIRAC distributed computing services
International Nuclear Information System (INIS)
Tsaregorodtsev, A
2014-01-01
DIRAC Project provides a general-purpose framework for building distributed computing systems. It is used now in several HEP and astrophysics experiments as well as for user communities in other scientific domains. There is a large interest from smaller user communities to have a simple tool like DIRAC for accessing grid and other types of distributed computing resources. However, small experiments cannot afford to install and maintain dedicated services. Therefore, several grid infrastructure projects are providing DIRAC services for their respective user communities. These services are used for user tutorials as well as to help porting the applications to the grid for a practical day-to-day work. The services are giving access typically to several grid infrastructures as well as to standalone computing clusters accessible by the target user communities. In the paper we will present the experience of running DIRAC services provided by the France-Grilles NGI and other national grid infrastructure projects.
Casajus Ramo, A.; Graciani Diaz, R.
2012-12-01
DIRAC framework for distributed computing has been designed as a group of collaborating components, agents and servers, with persistent database back-end. Components communicate with each other using DISET, an in-house protocol that provides Remote Procedure Call (RPC) and file transfer capabilities. This approach has provided DIRAC with a modular and stable design by enforcing stable interfaces across releases. But it made complicated to scale further with commodity hardware. To further scale DIRAC, components needed to send more queries between them. Using RPC to do so requires a lot of processing power just to handle the secure handshake required to establish the connection. DISET now provides a way to keep stable connections and send and receive queries between components. Only one handshake is required to send and receive any number of queries. Using this new communication mechanism DIRAC now provides a new type of component called Executor. Executors process any task (such as resolving the input data of a job) sent to them by a task dispatcher. This task dispatcher takes care of persisting the state of the tasks to the storage backend and distributing them among all the Executors based on the requirements of each task. In case of a high load, several Executors can be started to process the extra load and stop them once the tasks have been processed. This new approach of handling tasks in DIRAC makes Executors easy to replace and replicate, thus enabling DIRAC to further scale beyond the current approach based on polling agents.
International Nuclear Information System (INIS)
Casajus Ramo, A; Graciani Diaz, R
2012-01-01
DIRAC framework for distributed computing has been designed as a group of collaborating components, agents and servers, with persistent database back-end. Components communicate with each other using DISET, an in-house protocol that provides Remote Procedure Call (RPC) and file transfer capabilities. This approach has provided DIRAC with a modular and stable design by enforcing stable interfaces across releases. But it made complicated to scale further with commodity hardware. To further scale DIRAC, components needed to send more queries between them. Using RPC to do so requires a lot of processing power just to handle the secure handshake required to establish the connection. DISET now provides a way to keep stable connections and send and receive queries between components. Only one handshake is required to send and receive any number of queries. Using this new communication mechanism DIRAC now provides a new type of component called Executor. Executors process any task (such as resolving the input data of a job) sent to them by a task dispatcher. This task dispatcher takes care of persisting the state of the tasks to the storage backend and distributing them among all the Executors based on the requirements of each task. In case of a high load, several Executors can be started to process the extra load and stop them once the tasks have been processed. This new approach of handling tasks in DIRAC makes Executors easy to replace and replicate, thus enabling DIRAC to further scale beyond the current approach based on polling agents.
Relativistic Spinning Particle without Grassmann Variables and the Dirac Equation
Directory of Open Access Journals (Sweden)
A. A. Deriglazov
2011-01-01
Full Text Available We present the relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Classical dynamics of the model is in correspondence with the dynamics of mean values of the corresponding operators in the Dirac theory. Classical equations for the spin tensor are the same as those of the Barut-Zanghi model of spinning particle.
DIRAC optimized workload management
Paterson, S K
2008-01-01
The LHCb DIRAC Workload and Data Management System employs advanced optimization techniques in order to dynamically allocate resources. The paradigms realized by DIRAC, such as late binding through the Pilot Agent approach, have proven to be highly successful. For example, this has allowed the principles of workload management to be applied not only at the time of user job submission to the Grid but also to optimize the use of computing resources once jobs have been acquired. Along with the central application of job priorities, DIRAC minimizes the system response time for high priority tasks. This paper will describe the recent developments to support Monte Carlo simulation, data processing and distributed user analysis in a consistent way across disparate compute resources including individual PCs, local batch systems, and the Worldwide LHC Computing Grid. The Grid environment is inherently unpredictable and whilst short-term studies have proven to deliver high job efficiencies, the system performance over ...
Energy Technology Data Exchange (ETDEWEB)
Abel, Steven [Durham Univ. (United Kingdom). Inst. for Particle Physics Phenomenology; CERN, Geneva (Switzerland); Goodsell, Mark [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2011-02-15
A simple and natural model is presented that gives Dirac gauginos. The configuration is related to ''deconstructed gaugino mediation''. A high energy completion is provided based on existing ISS-like models of deconstructed gaugino mediation. This provides a complete picture of Dirac gauginos that includes the necessary extra adjoint fermions (generated as magnetic quarks of the ISS theory) and supersymmetry breaking (via the ISS mechanism). Moreover the screening of the scalar masses means that they can similar to or less than the gaugino masses, even though the supersymmetry breaking is driven by F-terms. (orig.)
International Nuclear Information System (INIS)
Abel, Steven; Goodsell, Mark
2011-02-01
A simple and natural model is presented that gives Dirac gauginos. The configuration is related to ''deconstructed gaugino mediation''. A high energy completion is provided based on existing ISS-like models of deconstructed gaugino mediation. This provides a complete picture of Dirac gauginos that includes the necessary extra adjoint fermions (generated as magnetic quarks of the ISS theory) and supersymmetry breaking (via the ISS mechanism). Moreover the screening of the scalar masses means that they can similar to or less than the gaugino masses, even though the supersymmetry breaking is driven by F-terms. (orig.)
LHCb: Monitoring the DIRAC Distribution System
Nandakumar, R; Santinelli, R
2009-01-01
DIRAC is the LHCb gateway to any computing grid infrastructure (currently supporting WLCG) and is intended to reliably run large data mining activities. The DIRAC system consists of various services (which wait to be contacted to perform actions) and agents (which carry out periodic activities) to direct jobs as required. An important part of ensuring the reliability of the infrastructure is the monitoring and logging of these DIRAC distributed systems. The monitoring is done collecting information from two sources - one is from pinging the services or by keeping track of the regular heartbeats of the agents, and the other from the analysis of the error messages generated by both agents and services and collected by the logging system. This allows us to ensure that he components are running properly and to collect useful information regarding their operations. The process status monitoring is displayed using the SLS sensor mechanism which also automatically allows one to plot various quantities and also keep ...
From a world-sheet supersymmetry to the Dirac equation
International Nuclear Information System (INIS)
Mankoc Borstnik, N.
1991-10-01
Starting from a classical action for a point particle with a local world-sheet supersymmetry, the Dirac equation follows with operators α-vector, β-vector γ-vector being defined in the Grassmann space as differential operators and having all the properties of the corresponding Dirac matrices except that α-vector and β-vector are anti-Hermitian rather than Hermitian. Such a particle interacts with an external field as expected. (author). 7 refs
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
International Nuclear Information System (INIS)
Joshipura, A.S.; Rindani, S.D.
1991-01-01
The consequences of imposing an exact L e +L τ -L μ symmetry on a 6x6 matrix describing neutrino masses are discussed. The presence of right-handed neutrinos avoids the need of introducing any SU(2) Higgs triplet. Hence the conflict with the CERN LEP data on the Z width found in earlier models with L e +L τ -L μ symmetry is avoided. The L e +L τ -L μ symmetry provides an interesting realization of a recent proposal of Glashow to accommodate the 17-keV Dirac neutrino in the SU(2)xU(1) theory. All the neutrinos in this model are Dirac particles. The solar-neutrino problem can be solved in an extension of the model which generates a large (∼10 -11 μ B ) magnetic moment for the electron neutrino
Sheka, Elena F.
2016-01-01
The paper presents the author view on spin-rooted properties of graphene supported by numerous experimental and calculation evidences. Dirac fermions of crystalline graphene and local spins of graphene molecules are suggested to meet a strict demand - different orbitals for different spins- which leads to a large spectrum of effects caused by spin polarization of electronic states. The consequent topological non-triviality, making graphene topological insulator, and local spins, imaging graph...
Dirac particle in a box, and relativistic quantum Zeno dynamics
International Nuclear Information System (INIS)
Menon, Govind; Belyi, Sergey
2004-01-01
After developing a complete set of eigenfunctions for a Dirac particle restricted to a box, the quantum Zeno dynamics of a relativistic system is considered. The evolution of a continuously observed quantum mechanical system is governed by the theorem put forth by Misra and Sudarshan. One of the conditions for quantum Zeno dynamics to be manifest is that the Hamiltonian is semi-bounded. This Letter analyzes the effects of continuous observation of a particle whose time evolution is generated by the Dirac Hamiltonian. The theorem by Misra and Sudarshan is not applicable here since the Dirac operator is not semi-bounded
Transversal Dirac families in Riemannian foliations
International Nuclear Information System (INIS)
Glazebrook, J.F.; Kamber, F.W.
1991-01-01
We describe a family of differential operators parametrized by the transversal vector potentials of a Riemannian foliation relative to the Clifford algebra of the foliation. This family is non-elliptic but in certain ways behaves like a standard Dirac family in the absolute case as a result of its elliptic-like regularity properties. The analytic and topological indices of this family are defined as elements of K-theory in the parameter space. We indicate how the cohomology of the parameter space is described via suitable maps to Fredholm operators. We outline the proof of a theorem of Vafa-Witten type on uniform bounds for the eigenvalues of this family using a spectral flow argument. A determinant operator is also defined with the appropriate zeta function regularization dependent on the codimension of the foliation. With respect to a generalized coupled Dirac-Yang-Mills system, we indicate how chiral anomalies are located relative to the foliation. (orig.)
Potential scattering of Dirac particles
International Nuclear Information System (INIS)
Thaller, B.
1981-01-01
A quantum mechanical interpretation of the Dirac equation for particles in external electromagnetic potentials is discussed. It is shown that a consequent development of the Stueckelberg-Feynman theory into a probabilistic interpretation of the Dirac equation corrects some prejudices concerning negative energy states, Zitterbewegung and bound states in repulsive potentials and yields the connection between propagator theory and scattering theory. Limits of the Dirac equation, considered as a wave mechanical equation, are considered. (U.K.)
Axial anomaly and index theorem for Dirac-Kaehler fermions
International Nuclear Information System (INIS)
Fonseca Junior, C.A.L. da.
1985-02-01
Some aspects of topological influence on gauge field theory are analysed, considering the geometry and differential topology methods. A review of concepts of differential forms, fibered spaces, connection and curvature, showing an interpretation of gauge theory in this context, is presented. The question of fermions, analysing in details the Dirac-Kaehler which fermionic particle is considered a general differential form, is studied. It is shown how the explicit expressions in function of the Dirac spinor components vary with the Dirac matrix representation. The Dirac-Kahler equation contains 4 times (in 4 dimensions) the Dirac equation, each particle being associated an ideal at left of the algebra of general differential forms. These ideals and the SU(4) symmetry among them are also studied on the point of view of spinors and, the group of reduction to one of the ideals is identified as the Cartan subalgebra of this SU(4). Finally, the axial anomaly is calculated through the functional determinant given by the Dirac-Kaehler operator. The regularization method is the Seeley's coefficients. From that results a comparison of the index theorems for the twisted complexes of signature and spin, which proportionality is given by the number of the algebra ideals contained in the Dirac-Kaehler equation and which also manifests in the respective axial anomaly equations. (L.C.) [pt
Dirac and Weyl fermion dynamics on two-dimensional surface
International Nuclear Information System (INIS)
Kavalov, A.R.; Sedrakyan, A.G.; Kostov, I.K.
1986-01-01
Fermions on 2-dimensional surface, embedded into a 3-dimensional space are investigated. The determinant of induced Dirac operator for the Dirac and Weyl fermions is calculated. The reparametrization-invariant effective action is determined by conformal anomaly (giving Liouville action) and also by Lorentz anomaly leading to Wess-Zumino term, the structure of which at d=3 is determined by the Hopf topological invariant of the S 3 → S 2 map
International Nuclear Information System (INIS)
Leo, Stefano de; Rotelli, Pietro
2009-01-01
We present the results of the planar diffusion of a Dirac particle by step and barrier potentials, when the incoming wave impinges at an arbitrary angle with the potential. Except for right-angle incidence this process is characterized by the appearance of spin flip terms. For the step potential, spin flip occurs for both transmitted and reflected waves. However, we find no spin flip in the transmitted barrier result. This is surprising because the barrier result may be derived directly from a two-step calculation. We demonstrate that the spin flip cancellation indeed occurs for each ''particle'' (wave packet) contribution. (orig.)
Dirac monopole without strings: monopole harmonics
International Nuclear Information System (INIS)
Wu, T.T.; Yang, C.N.
1983-01-01
Using the ideas developed in a previous paper which are borrowed from the mathematics of fiber bundles, it is shown that the wave function psi of a particle of charge Ze around a Dirac monopole of strength g should be regarded as a section. The section is without discontinuities. Thus the monopole does not possess strings of singularities in the field around it. The eigensections of the angular momentum operators are monopole harmonics which are explicitly exhibited. 7 references, 2 figures, 1 table
Dispersionless wave packets in Dirac materials
International Nuclear Information System (INIS)
Jakubský, Vít; Tušek, Matěj
2017-01-01
We show that a wide class of quantum systems with translational invariance can host dispersionless, soliton-like, wave packets. We focus on the setting where the effective, two-dimensional Hamiltonian acquires the form of the Dirac operator. The proposed framework for construction of the dispersionless wave packets is illustrated on silicene-like systems with topologically nontrivial effective mass. Our analytical predictions are accompanied by a numerical analysis and possible experimental realizations are discussed.
International Nuclear Information System (INIS)
Ferreira, P.L.; Palladino, B.E.
1985-01-01
The problem of a Dirac particle in stationary motion on S 2 - a two dimensional sphere embedded in Euclidean space E 3 - is discussed. It provides a particularly simple case of an exactly solvable constrained Dirac particle whose properties are here studied, with emphasis on its magnetic moment. (Author) [pt
LHCb: DIRAC Secure Distributed Platform
Casajus, A
2009-01-01
DIRAC, the LHCb community grid solution, provides access to a vast amount of computing and storage resources to a large number of users. In DIRAC users are organized in groups with different needs and permissions. In order to ensure that only allowed users can access the resources and to enforce that there are no abuses, security is mandatory. All DIRAC services and clients use secure connections that are authenticated using certificates and grid proxies. Once a client has been authenticated, authorization rules are applied to the requested action based on the presented credentials. These authorization rules and the list of users and groups are centrally managed in the DIRAC Configuration Service. Users submit jobs to DIRAC using their local credentials. From then on, DIRAC has to interact with different Grid services on behalf of this user. DIRAC has a proxy management service where users upload short-lived proxies to be used when DIRAC needs to act on behalf of them. Long duration proxies are uploaded by us...
DIRAC: data production management
International Nuclear Information System (INIS)
Smith, A C; Tsaregorodtsev, A
2008-01-01
The LHCb Computing Model describes the dataflow for all stages in the processing of real and simulated events, and defines the role of LHCb associated Tier-1 and Tier-2 computing centers. The WLCG 'Dress Rehearsal' exercise aims to allow LHC experiments to deploy the full chain of their Computing Models, making use of all underlying WLCG services and resources, in preparation for real data taking. During this exercise simulated RAW physics data, matching the properties of eventual real data, will be uploaded from the LHCb Online storage system to Grid enabled storage. This data will then be replicated to LHCb Tier-1 centers and subsequently processed (reconstructed and stripped). The product of this processing is user analysis data that are distributed to all LHCb Tier-1 centers. DIRAC, LHCbs Workload and Data Management System, supports the implementation of the Computing Model in a data driven, real time and coordinated fashion. In this paper the LHCb Computing Model will be reviewed and the DIRAC components providing the needed functionality to support the Computing Model will be detailed. An evaluation of the preparedness for real data taking will also be given
DIRAC: data production management
Energy Technology Data Exchange (ETDEWEB)
Smith, A C [CERN, CH-1211, Geneva (Switzerland); Tsaregorodtsev, A [CPPM, Marseille (France)], E-mail: a.smith@cern.ch, E-mail: atsareg@in2p3.fr
2008-07-15
The LHCb Computing Model describes the dataflow for all stages in the processing of real and simulated events, and defines the role of LHCb associated Tier-1 and Tier-2 computing centers. The WLCG 'Dress Rehearsal' exercise aims to allow LHC experiments to deploy the full chain of their Computing Models, making use of all underlying WLCG services and resources, in preparation for real data taking. During this exercise simulated RAW physics data, matching the properties of eventual real data, will be uploaded from the LHCb Online storage system to Grid enabled storage. This data will then be replicated to LHCb Tier-1 centers and subsequently processed (reconstructed and stripped). The product of this processing is user analysis data that are distributed to all LHCb Tier-1 centers. DIRAC, LHCbs Workload and Data Management System, supports the implementation of the Computing Model in a data driven, real time and coordinated fashion. In this paper the LHCb Computing Model will be reviewed and the DIRAC components providing the needed functionality to support the Computing Model will be detailed. An evaluation of the preparedness for real data taking will also be given.
International Nuclear Information System (INIS)
Casajus, A; Ciba, K; Fernandez, V; Graciani, R; Hamar, V; Mendez, V; Poss, S; Sapunov, M; Stagni, F; Tsaregorodtsev, A; Ubeda, M
2012-01-01
The DIRAC Project was initiated to provide a data processing system for the LHCb Experiment at CERN. It provides all the necessary functionality and performance to satisfy the current and projected future requirements of the LHCb Computing Model. A considerable restructuring of the DIRAC software was undertaken in order to turn it into a general purpose framework for building distributed computing systems that can be used by various user communities in High Energy Physics and other scientific application domains. The CLIC and ILC-SID detector projects started to use DIRAC for their data production system. The Belle Collaboration at KEK, Japan, has adopted the Computing Model based on the DIRAC system for its second phase starting in 2015. The CTA Collaboration uses DIRAC for the data analysis tasks. A large number of other experiments are starting to use DIRAC or are evaluating this solution for their data processing tasks. DIRAC services are included as part of the production infrastructure of the GISELA Latin America grid. Similar services are provided for the users of the France-Grilles and IBERGrid National Grid Initiatives in France and Spain respectively. The new communities using DIRAC started to provide important contributions to its functionality. Among recent additions can be mentioned the support of the Amazon EC2 computing resources as well as other Cloud management systems; a versatile File Replica Catalog with File Metadata capabilities; support for running MPI jobs in the pilot based Workload Management System. Integration with existing application Web Portals, like WS-PGRADE, is demonstrated. In this paper we will describe the current status of the DIRAC Project, recent developments of its framework and functionality as well as the status of the rapidly evolving community of the DIRAC users.
The DIRAC Data Management System and the Gaudi dataset federation
Haen, Christophe; Frank, Markus; Tsaregorodtsev, Andrei
2015-01-01
The DIRAC Interware provides a development framework and a complete set of components for building distributed computing systems. The DIRAC Data Management System (DMS) offers all the necessary tools to ensure data handling operations for small and large user communities. It supports transparent access to storage resources based on multiple technologies, and is easily expandable. The information on data files and replicas is kept in a File Catalog of which DIRAC offers a powerful and versatile implementation (DFC). Data movement can be performed using third party services including FTS3. Bulk data operations are resilient with respect to failures due to the use of the Request Management System (RMS) that keeps track of ongoing tasks.In this contribution we will present an overview of the DIRAC DMS capabilities and its connection with other DIRAC subsystems such as the Transformation System. This paper also focuses on the DIRAC File Catalog, for which a lot of new developments have been carried out, so that LH...
Dirac neutrino masses from generalized supersymmetry breaking
International Nuclear Information System (INIS)
Demir, D.A.; Everett, L.L.; Langacker, P.
2007-12-01
We demonstrate that Dirac neutrino masses in the experimentally preferred range are generated within supersymmetric gauge extensions of the Standard Model with a generalized supersymmetry breaking sector. If the usual superpotential Yukawa couplings are forbidden by the additional gauge symmetry (such as a U(1) ' ), effective Dirac mass terms involving the ''wrong Higgs'' field can arise either at tree level due to hard supersymmetry breaking fermion Yukawa couplings, or at one-loop due to nonanalytic or ''nonholomorphic'' soft supersymmetry breaking trilinear scalar couplings. As both of these operators are naturally suppressed in generic models of supersymmetry breaking, the resulting neutrino masses are naturally in the sub-eV range. The neutrino magnetic and electric dipole moments resulting from the radiative mechanism also vanish at one-loop order. (orig.)
On an uninterpretated tensor in Dirac's theory
International Nuclear Information System (INIS)
Costa de Beauregard, O.
1989-01-01
Franz, in 1935, deduced systematically from the Dirac equation 10 tensorial equations, 5 with a mechanical interpretation, 5 with an electromagnetic interpretation, which are also consequences of Kemmer's formalism for spins 1 and 0; Durand, in 1944, operating similarly with the second order Dirac equation, obtained, 10 equations, 5 of which expressing the divergences of the Gordon type tensors. Of these equations, together with the tensors they imply, some are easily interpreted by reference to the classical theories, some other remain uniterpreted. Recently (1988) we proposed a theory of the coupling between Einstein's gravity field and the 5 Franz mechanical equations, yielding as a bonus the complete interpretation of the 5 Franz mechanical equations. This is an incitation to reexamine the 5 electromagnetic equations. We show here that two of these, together with one of the Durand equations, implying the same tensor, remain uninterpreted. This is proposed as a challenge to the reader's sagacity [fr
DIRAC data production management
Smith, A C
2008-01-01
The LHCb Computing Model describes the dataflow for all stages in the processing of real and simulated events, and defines the role of LHCb associated Tier-1 and Tier-2 computing centers. The WLCG 'Dress Rehearsal' exercise aims to allow LHC experiments to deploy the full chain of their Computing Models, making use of all underlying WLCG services and resources, in preparation for real data taking. During this exercise simulated RAW physics data, matching the properties of eventual real data, will be uploaded from the LHCb Online storage system to Grid enabled storage. This data will then be replicated to LHCb Tier-1 centers and subsequently processed (reconstructed and stripped). The product of this processing is user analysis data that are distributed to all LHCb Tier-1 centers. DIRAC, LHCbs Workload and Data Management System, supports the implementation of the Computing Model in a data driven, real time and coordinated fashion.
Smith, A C
2007-01-01
The LHCb experiment being built to utilize CERN’s flagship Large Hadron Collider will generate data to be analysed by a community of over 600 physicists worldwide. DIRAC, LHCb’s Workload and Data Management System, facilitates the use of underlying EGEE Grid resources to generate, process and analyse this data in the distributed environment. The Data Management System, presented here, provides real-time, data-driven distribution in accordance with LHCb’s Computing Model. The data volumes produced by the LHC experiments are unprecedented, rendering individual institutes and even countries, unable to provide the computing and storage resources required to make full use of the produced data. EGEE Grid resources allow the processing of LHCb data possible in a distributed fashion and LHCb’s Computing Model is based on this approach. Data Management in this environment requires reliable and high-throughput transfer of data, homogeneous access to storage resources and the cataloguing of data replicas, all of...
Stagni, F.; McNab, A.; Luzzi, C.; Krzemien, W.; Consortium, DIRAC
2017-10-01
In the last few years, new types of computing models, such as IAAS (Infrastructure as a Service) and IAAC (Infrastructure as a Client), gained popularity. New resources may come as part of pledged resources, while others are in the form of opportunistic ones. Most but not all of these new infrastructures are based on virtualization techniques. In addition, some of them, present opportunities for multi-processor computing slots to the users. Virtual Organizations are therefore facing heterogeneity of the available resources and the use of an Interware software like DIRAC to provide the transparent, uniform interface has become essential. The transparent access to the underlying resources is realized by implementing the pilot model. DIRAC’s newest generation of generic pilots (the so-called Pilots 2.0) are the “pilots for all the skies”, and have been successfully released in production more than a year ago. They use a plugin mechanism that makes them easily adaptable. Pilots 2.0 have been used for fetching and running jobs on every type of resource, being it a Worker Node (WN) behind a CREAM/ARC/HTCondor/DIRAC Computing element, a Virtual Machine running on IaaC infrastructures like Vac or BOINC, on IaaS cloud resources managed by Vcycle, the LHCb High Level Trigger farm nodes, and any type of opportunistic computing resource. Make a machine a “Pilot Machine”, and all diversities between them will disappear. This contribution describes how pilots are made suitable for different resources, and the recent steps taken towards a fully unified framework, including monitoring. Also, the cases of multi-processor computing slots either on real or virtual machines, with the whole node or a partition of it, is discussed.
The Dirac equation for accountants
International Nuclear Information System (INIS)
Ord, G.N.
2006-01-01
In the context of relativistic quantum mechanics, derivations of the Dirac equation usually take the form of plausibility arguments based on experience with the Schroedinger equation. The primary reason for this is that we do not know what wavefunctions physically represent, so derivations have to rely on formal arguments. There is however a context in which the Dirac equation in one dimension is directly related to a classical generating function. In that context, the derivation of the Dirac equation is an exercise in counting. We provide this derivation here and discuss its relationship to quantum mechanics
International Nuclear Information System (INIS)
Skyrme, T.H.R.
1994-01-01
In a model quantum theory of interacting mesons, the motion of certain conserved particle-like structures is discussed. It is shown how collective coordinates may be introduced to describe them, leading, in lowest approximation, to a Dirac equation. (author)
Alternatives to the Dirac equation
International Nuclear Information System (INIS)
Girvin, S.M.; Brownstein, K.R.
1975-01-01
Recent work by Biedenharn, Han, and van Dam (BHvD) has questioned the uniqueness of the Dirac equation. BHvD have obtained a two-component equation as an alternate to the Dirac equation. Although they later show their alternative to be unitarily equivalent to the Dirac equation, certain physical differences were claimed. BHvD attribute the existence of this alternate equation to the fact that their factorizing matrices were position-dependent. To investigate this, we factor the Klein-Gordon equation in spherical coordinates allowing the factorizing matrices to depend arbitrarily upon theta and phi. It is shown that despite this additional freedom, and without involving any relativistic covariance, the conventional four-component Dirac equation is the only possibility
CERN Bulletin
2010-01-01
When a group of physicists entered the Main Auditorium, during the evening of 29 June, they felt they had opened a time portal. Paul Dirac in front of a blackboard showing his formula. ©Sandra Hoogeboom An attentive audience, dressed in early 1900 costumes, were watching a lecture by the elusive Paul Dirac, presenting for the first time his famous formula on the blackboard. Paul Adrien Maurice Dirac (1902-1984) was a British mathematical physicist at Cambridge, and one of the "fathers" of quantum mechanics. When he first wrote it, in 1928, Dirac was not sure what his formula really meant. As demonstrated by Andersson four year later, what Dirac had written on the blackboard was the first definition of a positron, hence he is credited with having anticipated the existence of antimatter. The actor John Kohl performs as Paul Dirac. ©Sandra Hoogeboom What the group of puzzled physicists were really observing when they entered the CERN Auditorium was the shoo...
Analytical Expressions of Matrix Elements of Physical Quantities for Dirac Oscillator
Institute of Scientific and Technical Information of China (English)
LI Ning; JU Guo-Xing; REN Zhong-Zhou
2004-01-01
The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case of operator's square is discussed in details. The twodimensional Dirac oscillator has similar behavior to that for three-dimensional one.
LHCb: LHCbDirac is a DIRAC extension to support LHCb specific workflows
Stagni, Federico
2012-01-01
We present LHCbDIRAC, an extension of the DIRAC community Grid solution to handle the LHCb specificities. The DIRAC software has been developed for many years within LHCb only. Nowadays it is a generic software, used by many scientific communities worldwide. Each community wanting to take advantage of DIRAC has to develop an extension, containing all the necessary code for handling their specific cases. LHCbDIRAC is an actively developed extension, implementing the LHCb computing model and workflows. LHCbDIRAC extends DIRAC to handle all the distributed computing activities of LHCb. Such activities include real data processing (reconstruction, stripping and streaming), Monte-Carlo simulation and data replication. Other activities are groups and user analysis, data management, resources management and monitoring, data provenance, accounting for user and production jobs. LHCbDIRAC also provides extensions of the DIRAC interfaces, including a secure web client, python APIs and CLIs. While DIRAC and LHCbDIRAC f...
Total angular momentum from Dirac eigenspinors
International Nuclear Information System (INIS)
Szabados, Laszlo B
2008-01-01
The eigenvalue problem for Dirac operators, constructed from two connections on the spinor bundle over closed spacelike 2-surfaces, is investigated. A class of divergence-free vector fields, built from the eigenspinors, are found, which, for the lowest eigenvalue, reproduce the rotation Killing vectors of metric spheres, and provide rotation BMS vector fields at future null infinity. This makes it possible to introduce a well-defined, gauge invariant spatial angular momentum at null infinity, which reduces to the standard expression in stationary spacetimes. The general formula for the angular momentum flux carried away by the gravitational radiation is also derived
Quasi-Dirac neutrino oscillations
Anamiati, Gaetana; Fonseca, Renato M.; Hirsch, Martin
2018-05-01
Dirac neutrino masses require two distinct neutral Weyl spinors per generation, with a special arrangement of masses and interactions with charged leptons. Once this arrangement is perturbed, lepton number is no longer conserved and neutrinos become Majorana particles. If these lepton number violating perturbations are small compared to the Dirac mass terms, neutrinos are quasi-Dirac particles. Alternatively, this scenario can be characterized by the existence of pairs of neutrinos with almost degenerate masses, and a lepton mixing matrix which has 12 angles and 12 phases. In this work we discuss the phenomenology of quasi-Dirac neutrino oscillations and derive limits on the relevant parameter space from various experiments. In one parameter perturbations of the Dirac limit, very stringent bounds can be derived on the mass splittings between the almost degenerate pairs of neutrinos. However, we also demonstrate that with suitable changes to the lepton mixing matrix, limits on such mass splittings are much weaker, or even completely absent. Finally, we consider the possibility that the mass splittings are too small to be measured and discuss bounds on the new, nonstandard lepton mixing angles from current experiments for this case.
The Dirac medals of the ICTP. 1993
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-12-31
The Dirac Medals of the International Centre for Theoretical Physics (ICTP) were instituted in 1985. These are awarded yearly to outstanding physicists, on Dirac`s birthday - 8th August- for contributions to theoretical physics. The document includes the lectures of the three Dirac Medalists for 1993: Professor Sergio Ferrara, Professor Daniel Z. Freedman, and Professor Peter van Nieuwenhuizen. A separate abstract was prepared for each lecture
Zero-energy eigenstates for the Dirac boundary problem
International Nuclear Information System (INIS)
Hortacsu, M.; Rothe, K.D.; Schroer, B.
1980-01-01
As an alternative to the method of spherical compactification for the Dirac operator in instanton background fields we study the correct method of 'box-quantization': the Atiyah-Patodi-Singer spectral boundary condition. This is the only self-adjoint boundary condition which respects the charge conjugation property and the γ 5 symmetry, apart form the usual breaking due to zero modes. We point out the relevance of this approach to the computation of instanton determinants and other problems involving Dirac spinors. (orig.)
Inverse scattering scheme for the Dirac equation at fixed energy
International Nuclear Information System (INIS)
Leeb, H.; Lehninger, H.; Schilder, C.
2001-01-01
Full text: Based on the concept of generalized transformation operators a new hierarchy of Dirac equations with spherical symmetric scalar and fourth component vector potentials is presented. Within this hierarchy closed form expressions for the solutions, the potentials and the S-matrix can be given in terms of solutions of the original Dirac equation. Using these transformations an inverse scattering scheme has been constructed for the Dirac equation which is the analog to the rational scheme in the non-relativistic case. The given method provides for the first time an inversion scheme with closed form expressions for the S-matrix for non-relativistic scattering problems with central and spin-orbit potentials. (author)
A Dirac algebraic approach to supersymmetry
International Nuclear Information System (INIS)
Guersey, F.
1984-01-01
The power of the Dirac algebra is illustrated through the Kaehler correspondence between a pair of Dirac spinors and a 16-component bosonic field. The SO(5,1) group acts on both the fermion and boson fields, leading to a supersymmetric equation of the Dirac type involving all these fields. (author)
Axial anomaly and index theorem for Dirac-Kaehler fermions
International Nuclear Information System (INIS)
Linhares, C.A.; Mignaco, J.A.; Monteiro, M.A.R.
1985-01-01
We present the calculation of the axial anomaly for Dirac-Kaehler fermions in two and four dimensions applying the procedure developed by Seeley to the signature operator in the twisted complex. The result is equal to the one for the twisted spin complex times 2 n/2 (n:number of dimensions) and agrees with the expressions from the index theorem. (author) [pt
Axial anomaly and index theorem for Dirac-Kaehler fermions
International Nuclear Information System (INIS)
Linhares, C.A.; Mignaco, J.A.; Rego Monteiro, M.A.
1985-01-01
We present a calculation of the axial anomaly for Dirac-Kaehler fermions in two and four dimensions applying the procedure developed by Seeley to the signature operator in the twisted complex. The result is equal to the one for the twisted spin complex times 2sup(π/2) (n: number of dimensions) and agrees with the expressions from the index theorem. (orig.)
Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones
Assili, Mohamed; Haddad, Sonia
2013-01-01
We theoretically study the effect of the motion and the merging of Dirac cone on the interlayer magnetoresistance in multilayer graphene like systems. This merging, which could be induced by a uniaxial strain, gives rise in monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase where Dirac points disappear. Based on a universal Hamiltonian proposed to describe the motion and the merging of Dirac points in two dimensional Dirac electron cr...
Dirac, Prof. Paul Adrien Maurice
Indian Academy of Sciences (India)
Home; Fellowship. Fellow Profile. Elected: 1935 Honorary. Dirac, Prof. Paul Adrien Maurice Nobel Laureate (Physics) - 1933. Date of birth: 8 August 1902. Date of death: 20 October 1984. YouTube; Twitter; Facebook; Blog. Academy News. IAS Logo. 29th Mid-year meeting. Posted on 19 January 2018. The 29th Mid-year ...
Dirac, Jordan and quantum fields
International Nuclear Information System (INIS)
Darrigol, O.
1985-01-01
The case of two principal physicists of quantum mechanics is specially chose: Paul Dirac and Pascual Jordan. They gave a signification and an importance very different to the notion of quantum field, and in particular to the quantized matter wave one. Through their formation and motivation differences, such as they are expressed in their writings, this deep difference is tentatively understood [fr
about the Dirac Delta Function(?)
Indian Academy of Sciences (India)
V Balakrishnan is in the. Department of ... and sweet as befits this impatient age. It said (in its en- ... to get down to real work by shutting down the system and reverting to ... the Dirac delta function" - but do note the all-important question mark in ...
Superconductivity in doped Dirac semimetals
Hashimoto, Tatsuki; Kobayashi, Shingo; Tanaka, Yukio; Sato, Masatoshi
2016-07-01
We theoretically study intrinsic superconductivity in doped Dirac semimetals. Dirac semimetals host bulk Dirac points, which are formed by doubly degenerate bands, so the Hamiltonian is described by a 4 ×4 matrix and six types of k -independent pair potentials are allowed by the Fermi-Dirac statistics. We show that the unique spin-orbit coupling leads to characteristic superconducting gap structures and d vectors on the Fermi surface and the electron-electron interaction between intra and interorbitals gives a novel phase diagram of superconductivity. It is found that when the interorbital attraction is dominant, an unconventional superconducting state with point nodes appears. To verify the experimental signature of possible superconducting states, we calculate the temperature dependence of bulk physical properties such as electronic specific heat and spin susceptibility and surface state. In the unconventional superconducting phase, either dispersive or flat Andreev bound states appear between point nodes, which leads to double peaks or a single peak in the surface density of states, respectively. As a result, possible superconducting states can be distinguished by combining bulk and surface measurements.
Dirac Magnons in Honeycomb Ferromagnets
Directory of Open Access Journals (Sweden)
Sergey S. Pershoguba
2018-01-01
Full Text Available The discovery of the Dirac electron dispersion in graphene [A. H. Castro Neto, et al., The Electronic Properties of Graphene, Rev. Mod. Phys. 81, 109 (2009RMPHAT0034-686110.1103/RevModPhys.81.109] led to the question of the Dirac cone stability with respect to interactions. Coulomb interactions between electrons were shown to induce a logarithmic renormalization of the Dirac dispersion. With a rapid expansion of the list of compounds and quasiparticle bands with linear band touching [T. O. Wehling, et al., Dirac Materials, Adv. Phys. 63, 1 (2014ADPHAH0001-873210.1080/00018732.2014.927109], the concept of bosonic Dirac materials has emerged. We consider a specific case of ferromagnets consisting of van der Waals-bonded stacks of honeycomb layers, e.g., chromium trihalides CrX_{3} (X=F, Cl, Br and I, that display two spin wave modes with energy dispersion similar to that for the electrons in graphene. At the single-particle level, these materials resemble their fermionic counterparts. However, how different particle statistics and interactions affect the stability of Dirac cones has yet to be determined. To address the role of interacting Dirac magnons, we expand the theory of ferromagnets beyond the standard Dyson theory [F. J. Dyson, General Theory of Spin-Wave Interactions, Phys. Rev. 102, 1217 (1956PHRVAO0031-899X10.1103/PhysRev.102.1217, F. J. Dyson, Thermodynamic Behavior of an Ideal Ferromagnet, Phys. Rev. 102, 1230 (1956PHRVAO0031-899X10.1103/PhysRev.102.1230] to the case of non-Bravais honeycomb layers. We demonstrate that magnon-magnon interactions lead to a significant momentum-dependent renormalization of the bare band structure in addition to strongly momentum-dependent magnon lifetimes. We show that our theory qualitatively accounts for hitherto unexplained anomalies in nearly half-century-old magnetic neutron-scattering data for CrBr_{3} [W. B. Yelon and R. Silberglitt, Renormalization of Large-Wave-Vector Magnons in
Dirac Magnons in Honeycomb Ferromagnets
Pershoguba, Sergey S.; Banerjee, Saikat; Lashley, J. C.; Park, Jihwey; Ågren, Hans; Aeppli, Gabriel; Balatsky, Alexander V.
2018-01-01
The discovery of the Dirac electron dispersion in graphene [A. H. Castro Neto, et al., The Electronic Properties of Graphene, Rev. Mod. Phys. 81, 109 (2009), 10.1103/RevModPhys.81.109] led to the question of the Dirac cone stability with respect to interactions. Coulomb interactions between electrons were shown to induce a logarithmic renormalization of the Dirac dispersion. With a rapid expansion of the list of compounds and quasiparticle bands with linear band touching [T. O. Wehling, et al., Dirac Materials, Adv. Phys. 63, 1 (2014), 10.1080/00018732.2014.927109], the concept of bosonic Dirac materials has emerged. We consider a specific case of ferromagnets consisting of van der Waals-bonded stacks of honeycomb layers, e.g., chromium trihalides CrX3 (X =F , Cl, Br and I), that display two spin wave modes with energy dispersion similar to that for the electrons in graphene. At the single-particle level, these materials resemble their fermionic counterparts. However, how different particle statistics and interactions affect the stability of Dirac cones has yet to be determined. To address the role of interacting Dirac magnons, we expand the theory of ferromagnets beyond the standard Dyson theory [F. J. Dyson, General Theory of Spin-Wave Interactions, Phys. Rev. 102, 1217 (1956), 10.1103/PhysRev.102.1217, F. J. Dyson, Thermodynamic Behavior of an Ideal Ferromagnet, Phys. Rev. 102, 1230 (1956), 10.1103/PhysRev.102.1230] to the case of non-Bravais honeycomb layers. We demonstrate that magnon-magnon interactions lead to a significant momentum-dependent renormalization of the bare band structure in addition to strongly momentum-dependent magnon lifetimes. We show that our theory qualitatively accounts for hitherto unexplained anomalies in nearly half-century-old magnetic neutron-scattering data for CrBr3 [W. B. Yelon and R. Silberglitt, Renormalization of Large-Wave-Vector Magnons in Ferromagnetic CrBr3 Studied by Inelastic Neutron Scattering: Spin-Wave Correlation
Cloud flexibility using DIRAC interware
International Nuclear Information System (INIS)
Albor, Víctor Fernandez; Miguelez, Marcos Seco; Silva, Juan Jose Saborido; Pena, Tomas Fernandez; Muñoz, Victor Mendez; Diaz, Ricardo Graciani
2014-01-01
Communities of different locations are running their computing jobs on dedicated infrastructures without the need to worry about software, hardware or even the site where their programs are going to be executed. Nevertheless, this usually implies that they are restricted to use certain types or versions of an Operating System because either their software needs an definite version of a system library or a specific platform is required by the collaboration to which they belong. On this scenario, if a data center wants to service software to incompatible communities, it has to split its physical resources among those communities. This splitting will inevitably lead to an underuse of resources because the data centers are bound to have periods where one or more of its subclusters are idle. It is, in this situation, where Cloud Computing provides the flexibility and reduction in computational cost that data centers are searching for. This paper describes a set of realistic tests that we ran on one of such implementations. The test comprise software from three different HEP communities (Auger, LHCb and QCD phenomelogists) and the Parsec Benchmark Suite running on one or more of three Linux flavors (SL5, Ubuntu 10.04 and Fedora 13). The implemented infrastructure has, at the cloud level, CloudStack that manages the virtual machines (VM) and the hosts on which they run, and, at the user level, the DIRAC framework along with a VM extension that will submit, monitorize and keep track of the user jobs and also requests CloudStack to start or stop the necessary VM's. In this infrastructure, the community software is distributed via the CernVM-FS, which has been proven to be a reliable and scalable software distribution system. With the resulting infrastructure, users are allowed to send their jobs transparently to the Data Center. The main purpose of this system is the creation of flexible cluster, multiplatform with an scalable method for software distribution for
Cloud flexibility using DIRAC interware
Fernandez Albor, Víctor; Seco Miguelez, Marcos; Fernandez Pena, Tomas; Mendez Muñoz, Victor; Saborido Silva, Juan Jose; Graciani Diaz, Ricardo
2014-06-01
Communities of different locations are running their computing jobs on dedicated infrastructures without the need to worry about software, hardware or even the site where their programs are going to be executed. Nevertheless, this usually implies that they are restricted to use certain types or versions of an Operating System because either their software needs an definite version of a system library or a specific platform is required by the collaboration to which they belong. On this scenario, if a data center wants to service software to incompatible communities, it has to split its physical resources among those communities. This splitting will inevitably lead to an underuse of resources because the data centers are bound to have periods where one or more of its subclusters are idle. It is, in this situation, where Cloud Computing provides the flexibility and reduction in computational cost that data centers are searching for. This paper describes a set of realistic tests that we ran on one of such implementations. The test comprise software from three different HEP communities (Auger, LHCb and QCD phenomelogists) and the Parsec Benchmark Suite running on one or more of three Linux flavors (SL5, Ubuntu 10.04 and Fedora 13). The implemented infrastructure has, at the cloud level, CloudStack that manages the virtual machines (VM) and the hosts on which they run, and, at the user level, the DIRAC framework along with a VM extension that will submit, monitorize and keep track of the user jobs and also requests CloudStack to start or stop the necessary VM's. In this infrastructure, the community software is distributed via the CernVM-FS, which has been proven to be a reliable and scalable software distribution system. With the resulting infrastructure, users are allowed to send their jobs transparently to the Data Center. The main purpose of this system is the creation of flexible cluster, multiplatform with an scalable method for software distribution for several
Graphene based d-character Dirac Systems
Li, Yuanchang; Zhang, S. B.; Duan, Wenhui
From graphene to topological insulators, Dirac material continues to be the hot topics in condensed matter physics. So far, almost all of the theoretically predicted or experimentally observed Dirac materials are composed of sp -electrons. By using first-principles calculations, we find the new Dirac system of transition-metal intercalated epitaxial graphene on SiC(0001). Intrinsically different from the conventional sp Dirac system, here the Dirac-fermions are dominantly contributed by the transition-metal d-electrons, which paves the way to incorporate correlation effect with Dirac-cone physics. Many intriguing quantum phenomena are proposed based on this system, including quantum spin Hall effect with large spin-orbital gap, quantum anomalous Hall effect, 100% spin-polarized Dirac fermions and ferromagnet-to-topological insulator transition.
DIRAC pilot framework and the DIRAC Workload Management System
International Nuclear Information System (INIS)
Casajus, Adrian; Graciani, Ricardo; Paterson, Stuart; Tsaregorodtsev, Andrei
2010-01-01
DIRAC, the LHCb community Grid solution, has pioneered the use of pilot jobs in the Grid. Pilot Jobs provide a homogeneous interface to an heterogeneous set of computing resources. At the same time, Pilot Jobs allow to delay the scheduling decision to the last moment, thus taking into account the precise running conditions at the resource and last moment requests to the system. The DIRAC Workload Management System provides one single scheduling mechanism for jobs with very different profiles. To achieve an overall optimisation, it organizes pending jobs in task queues, both for individual users and production activities. Task queues are created with jobs having similar requirements. Following the VO policy a priority is assigned to each task queue. Pilot submission and subsequent job matching are based on these priorities following a statistical approach.
DIRAC pilot framework and the DIRAC Workload Management System
Energy Technology Data Exchange (ETDEWEB)
Casajus, Adrian; Graciani, Ricardo [Universitat de Barcelona (Spain); Paterson, Stuart [CERN (Switzerland); Tsaregorodtsev, Andrei, E-mail: adria@ecm.ub.e, E-mail: graciani@ecm.ub.e, E-mail: stuart.paterson@cern.c, E-mail: atsareg@in2p3.f [CPPM Marseille (France)
2010-04-01
DIRAC, the LHCb community Grid solution, has pioneered the use of pilot jobs in the Grid. Pilot Jobs provide a homogeneous interface to an heterogeneous set of computing resources. At the same time, Pilot Jobs allow to delay the scheduling decision to the last moment, thus taking into account the precise running conditions at the resource and last moment requests to the system. The DIRAC Workload Management System provides one single scheduling mechanism for jobs with very different profiles. To achieve an overall optimisation, it organizes pending jobs in task queues, both for individual users and production activities. Task queues are created with jobs having similar requirements. Following the VO policy a priority is assigned to each task queue. Pilot submission and subsequent job matching are based on these priorities following a statistical approach.
P A M Dirac meets M G Krein: matrix orthogonal polynomials and Dirac's equation
International Nuclear Information System (INIS)
Duran, Antonio J; Gruenbaum, F Alberto
2006-01-01
The solution of several instances of the Schroedinger equation (1926) is made possible by using the well-known orthogonal polynomials associated with the names of Hermite, Legendre and Laguerre. A relativistic alternative to this equation was proposed by Dirac (1928) involving differential operators with matrix coefficients. In 1949 Krein developed a theory of matrix-valued orthogonal polynomials without any reference to differential equations. In Duran A J (1997 Matrix inner product having a matrix symmetric second order differential operator Rocky Mt. J. Math. 27 585-600), one of us raised the question of determining instances of these matrix-valued polynomials going along with second order differential operators with matrix coefficients. In Duran A J and Gruenbaum F A (2004 Orthogonal matrix polynomials satisfying second order differential equations Int. Math. Res. Not. 10 461-84), we developed a method to produce such examples and observed that in certain cases there is a connection with the instance of Dirac's equation with a central potential. We observe that the case of the central Coulomb potential discussed in the physics literature in Darwin C G (1928 Proc. R. Soc. A 118 654), Nikiforov A F and Uvarov V B (1988 Special Functions of Mathematical Physics (Basle: Birkhauser) and Rose M E 1961 Relativistic Electron Theory (New York: Wiley)), and its solution, gives rise to a matrix weight function whose orthogonal polynomials solve a second order differential equation. To the best of our knowledge this is the first instance of a connection between the solution of the first order matrix equation of Dirac and the theory of matrix-valued orthogonal polynomials initiated by M G Krein
Halogenated arsenenes as Dirac materials
International Nuclear Information System (INIS)
Tang, Wencheng; Sun, Minglei; Ren, Qingqiang; Wang, Sake; Yu, Jin
2016-01-01
Highlights: • We have revealed the presence of Dirac cone in fully-halogenated arsenene compounds. • All fully-halogenated arsenene except As_2I_2 would spontaneously form and stable in defending the thermal fluctuation in room temperature. - Abstract: Arsenene is the graphene-like arsenic nanosheet, which has been predicted very recently [S. Zhang, Z. Yan, Y. Li, Z. Chen, and H. Zeng, Angewandte Chemie, 127 (2015) 3155–3158]. Using first-principles calculations, we systematically investigate the structures and electronic properties of fully-halogenated arsenenes. Formation energy analysis reveals that all the fully-halogenated arsenenes except iodinated arsenene are energetically favorable and could be synthesized. We have revealed the presence of Dirac cone in fully-halogenated arsenene compounds. They may have great potential applications in next generation of high-performance devices.
On Charge Conjugation, Chirality and Helicity of the Dirac and Majorana Equation for Massive Leptons
Directory of Open Access Journals (Sweden)
Eckart Marsch
2015-04-01
Full Text Available We revisit the charge-conjugation operation for the Dirac equation in its chiral representation. A new decomposition of the Dirac spinor field is suggested and achieved by means of projection operators based on charge conjugation, which is discussed here in a non-standard way. Thus, two separate two-component Majorana-type field equations for the eigenfields of the charge-conjugation operator are obtained. The corresponding free fields are entirely separated without a gauge field, but remain mixed and coupled together through an electromagnetic field term. For fermions that are charged and, thus, subjected to the gauge field of electrodynamics, these two Majorana fields can be reassembled into a doublet, which is equivalent to a standard four-component Dirac spinor field. In this way, the Dirac equation is retained in a new guise, which is fully equivalent to that equation in its chiral form.
Basic quantum mechanics for three Dirac equations in a curved spacetime
International Nuclear Information System (INIS)
Arminjon, Mayeul
2010-01-01
We study the basic quantum mechanics for a fully general set of Dirac matrices in a curved spacetime by extending Pauli's method. We further extend this study to three versions of the Dirac equation: the standard (Dirac-Fock-Weyl or DFW) equation, and two alternative versions, both of which are based on the recently proposed linear tensor representations of the Dirac field (TRD). We begin with the current conservation: we show that the latter applies to any solution of the Dirac equation, if the field of Dirac matrices γμ satisfies a specific PDE. This equation is always satisfied for DFW with its restricted choice for the γμ matrices. It similarly restricts the choice of the γμ matrices for TRD. However, this restriction can be achieved. The frame dependence of a general Hamiltonian operator is studied. We show that in any given reference frame with minor restrictions on the spacetime metric, the axioms of quantum mechanics impose a unique form for the Hilbert space scalar product. Finally, the condition for the general Dirac Hamiltonian operator to be Hermitian is derived in a general curved spacetime. For DFW, the validity of this hermeticity condition depends on the choice of the γμ matrices. (author)
DIRAC: Secure web user interface
International Nuclear Information System (INIS)
Casajus Ramo, A; Sapunov, M
2010-01-01
Traditionally the interaction between users and the Grid is done with command line tools. However, these tools are difficult to use by non-expert users providing minimal help and generating outputs not always easy to understand especially in case of errors. Graphical User Interfaces are typically limited to providing access to the monitoring or accounting information and concentrate on some particular aspects failing to cover the full spectrum of grid control tasks. To make the Grid more user friendly more complete graphical interfaces are needed. Within the DIRAC project we have attempted to construct a Web based User Interface that provides means not only for monitoring the system behavior but also allows to steer the main user activities on the grid. Using DIRAC's web interface a user can easily track jobs and data. It provides access to job information and allows performing actions on jobs such as killing or deleting. Data managers can define and monitor file transfer activity as well as check requests set by jobs. Production managers can define and follow large data productions and react if necessary by stopping or starting them. The Web Portal is build following all the grid security standards and using modern Web 2.0 technologies which allow to achieve the user experience similar to the desktop applications. Details of the DIRAC Web Portal architecture and User Interface will be presented and discussed.
Double Dirac cones in phononic crystals
Li, Yan
2014-07-07
A double Dirac cone is realized at the center of the Brillouin zone of a two-dimensional phononic crystal (PC) consisting of a triangular array of core-shell-structure cylinders in water. The double Dirac cone is induced by the accidental degeneracy of two double-degenerate Bloch states. Using a perturbation method, we demonstrate that the double Dirac cone is composed of two identical and overlapping Dirac cones whose linear slopes can also be accurately predicted from the method. Because the double Dirac cone occurs at a relatively low frequency, a slab of the PC can be mapped onto a slab of zero refractive index material by using a standard retrieval method. Total transmission without phase change and energy tunneling at the double Dirac point frequency are unambiguously demonstrated by two examples. Potential applications can be expected in diverse fields such as acoustic wave manipulations and energy flow control.
Double Dirac cones in phononic crystals
Li, Yan; Wu, Ying; Mei, Jun
2014-01-01
A double Dirac cone is realized at the center of the Brillouin zone of a two-dimensional phononic crystal (PC) consisting of a triangular array of core-shell-structure cylinders in water. The double Dirac cone is induced by the accidental degeneracy of two double-degenerate Bloch states. Using a perturbation method, we demonstrate that the double Dirac cone is composed of two identical and overlapping Dirac cones whose linear slopes can also be accurately predicted from the method. Because the double Dirac cone occurs at a relatively low frequency, a slab of the PC can be mapped onto a slab of zero refractive index material by using a standard retrieval method. Total transmission without phase change and energy tunneling at the double Dirac point frequency are unambiguously demonstrated by two examples. Potential applications can be expected in diverse fields such as acoustic wave manipulations and energy flow control.
Local energy decay of massive Dirac fields in the 5D Myers-Perry metric
International Nuclear Information System (INIS)
Daudé, Thierry; Kamran, Niky
2012-01-01
We consider massive Dirac fields evolving in the exterior region of a five-dimensional Myers-Perry black hole and study their propagation properties. Our main result states that the local energy of such fields decays in a weak sense at late times. We obtain this result in two steps: first, using the separability of the Dirac equation, we prove the absence of a pure point spectrum for the corresponding Dirac operator; second, using a new form of the equation adapted to the local rotations of the black hole, we show by a Mourre theory argument that the spectrum is absolutely continuous. This leads directly to our main result. (paper)
Dirac fermions in nontrivial topology black hole backgrounds
International Nuclear Information System (INIS)
Gozdz, Marek; Nakonieczny, Lukasz; Rogatko, Marek
2010-01-01
We discuss the behavior of the Dirac fermions in a general spherically symmetric black hole background with a nontrivial topology of the event horizon. Both massive and massless cases are taken into account. We will conduct an analytical study of intermediate and late-time behavior of massive Dirac hair in the background of a black hole with a global monopole and dilaton black hole pierced by a cosmic string. In the case of a global monopole swallowed by a static black hole, the intermediate late-time behavior depends on the mass of the Dirac field, the multiple number of the wave mode, and the global monopole parameter. The late-time behavior is quite independent of these factors and has a decay rate proportional to t -5/6 . As far as the black hole pierced by a cosmic string is concerned, the intermediate late-time behavior depends only on the hair mass and the multipole number of the wave mode, while the late-time behavior dependence is the same as in the previous case. The main modification stems from the topology of the S 2 sphere pierced by a cosmic string. This factor modifies the eigenvalues of the Dirac operator acting on the transverse manifold.
The Dirac medals of the ICTP. 1993
International Nuclear Information System (INIS)
1995-01-01
The Dirac Medals of the International Centre for Theoretical Physics (ICTP) were instituted in 1985. These are awarded yearly to outstanding physicists, on Dirac's birthday - 8th August- for contributions to theoretical physics. The document includes the lectures of the three Dirac Medalists for 1993: Professor Sergio Ferrara, Professor Daniel Z. Freedman, and Professor Peter van Nieuwenhuizen. A separate abstract was prepared for each lecture
LHCbDIRAC as Apache Mesos microservices
Haen, Christophe; Couturier, Benjamin
2017-01-01
The LHCb experiment relies on LHCbDIRAC, an extension of DIRAC, to drive its offline computing. This middleware provides a development framework and a complete set of components for building distributed computing systems. These components are currently installed and run on virtual machines (VM) or bare metal hardware. Due to the increased workload, high availability is becoming more and more important for the LHCbDIRAC services, and the current installation model is showing its limitations. A...
LHCbDIRAC as Apache Mesos microservices
Haen, Christophe; Couturier, Benjamin
2017-10-01
The LHCb experiment relies on LHCbDIRAC, an extension of DIRAC, to drive its offline computing. This middleware provides a development framework and a complete set of components for building distributed computing systems. These components are currently installed and run on virtual machines (VM) or bare metal hardware. Due to the increased workload, high availability is becoming more and more important for the LHCbDIRAC services, and the current installation model is showing its limitations. Apache Mesos is a cluster manager which aims at abstracting heterogeneous physical resources on which various tasks can be distributed thanks to so called “frameworks” The Marathon framework is suitable for long running tasks such as the DIRAC services, while the Chronos framework meets the needs of cron-like tasks like the DIRAC agents. A combination of the service discovery tool Consul together with HAProxy allows to expose the running containers to the outside world while hiding their dynamic placements. Such an architecture brings a greater flexibility in the deployment of LHCbDirac services, allowing for easier deployment maintenance and scaling of services on demand (e..g LHCbDirac relies on 138 services and 116 agents). Higher reliability is also easier, as clustering is part of the toolset, which allows constraints on the location of the services. This paper describes the investigations carried out to package the LHCbDIRAC and DIRAC components into Docker containers and orchestrate them using the previously described set of tools.
International Nuclear Information System (INIS)
Karbstein, Felix
2009-01-01
We introduce a new method for dealing with fermionic quantum field theories amenable to a mean-field-type approximation. In this work we focus on the relativistic Hartree approximation. Our aim is to integrate out the Dirac sea and derive a no-sea effective theory'' with positive energy single particle states only. As the derivation of the no-sea effective theory involves only standard Feynman diagrams, our approach is quite general and not restricted to particular space-time dimensions. We develop and illustrate the approach in the ''large N'' limit of the Gross-Neveu model family in 1+1 dimensions. As the Gross-Neveu model has been intensely studied and several analytical solutions are known for this model, it is an ideal testing ground for our no-sea effective theory approach. The chiral Gross-Neveu model, also referred to as 1+1 dimensional Nambu-Jona-Lasinio model, turns out to be of particular interest. In this case, we explicitly derive a consistent effective theory featuring both elementary ''π meson'' fields and (positive energy) ''quark'' fields, starting from a purely fermionic quantum field theory. In the second part of this work, we apply our approach to the Walecka model in 1+1 and 3+1 dimensions. As the Dirac sea caused considerable difficulties in attempts to base nuclear physics on field theoretic models like the Walecka model, mean-field calculations were typically done without the sea. We confront several of these mean-field theory results with our no-sea effective theory approach. The potential of our approach is twofold. While the no-sea effective theory can be utilized to provide new analytical insights in particular parameter regimes, it also sheds new light on more fundamental issues as the explicit emergence of effective, Dirac-sea induced multi-fermion interactions in an effective theory with positive energy states only. (orig.)
The causal perturbation expansion revisited: Rescaling the interacting Dirac sea
International Nuclear Information System (INIS)
Finster, Felix; Grotz, Andreas
2010-01-01
The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.
The causal perturbation expansion revisited: Rescaling the interacting Dirac sea
Finster, Felix; Grotz, Andreas
2010-07-01
The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.
Dirac tensor with heavy photon
Energy Technology Data Exchange (ETDEWEB)
Bytev, V.V.; Kuraev, E.A. [Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Scherbakova, E.S. [Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik
2012-01-15
For the large-angles hard photon emission by initial leptons in process of high energy annihilation of e{sup +}e{sup -} {yields} to hadrons the Dirac tensor is obtained, taking into account the lowest order radiative corrections. The case of large-angles emission of two hard photons by initial leptons is considered. This result is being completed by the kinematics case of collinear hard photons emission as well as soft virtual and real photons and can be used for construction of Monte-Carlo generators. (orig.)
The Dirac equation in classical statistical mechanics
International Nuclear Information System (INIS)
Ord, G.N.
2002-01-01
The Dirac equation, usually obtained by 'quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic continuation, making the model 'self-quantizing'. This provides a new context for the Dirac equation, distinct from its usual context in relativistic quantum mechanics
Dirac and Weyl semimetals with holographic interactions
Jacobs, V.P.J.
2015-01-01
Dirac and Weyl semimetals are states of matter exhibiting the relativistic physics of, respectively, the Dirac and Weyl equation in a three-dimensional bulk material. These three-dimensional semimetals have recently been realized experimentally in various crystals. Theoretically, especially the
A fractional Dirac equation and its solution
International Nuclear Information System (INIS)
Muslih, Sami I; Agrawal, Om P; Baleanu, Dumitru
2010-01-01
This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit α → 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics.
Effects of acceleration through the Dirac sea
International Nuclear Information System (INIS)
Hacyan, S.
1986-01-01
The effects of acceleration through massive scalar and spin-1/2 fields are investigated. It is shown that the density-of-states factor in a uniformly accelerated frame takes a complicated form, but the energy spectrum exhibits a Bose-Einstein or Fermi-Dirac distribution function. In particular, the Dirac sea shows thermal-like effects
Semi-Dirac points in phononic crystals
Zhang, Xiujuan; Wu, Ying
2014-01-01
of rubber, in which the acoustic wave velocity is lower than that in water, the semi-Dirac dispersion can be characterized by an effective medium theory. The effective medium parameters link the semi-Dirac point to a topological transition in the iso
LHCbDIRAC as Apache Mesos microservices
Couturier, Ben
2016-01-01
The LHCb experiment relies on LHCbDIRAC, an extension of DIRAC, to drive its offline computing. This middleware provides a development framework and a complete set of components for building distributed computing systems. These components are currently installed and ran on virtual machines (VM) or bare metal hardware. Due to the increased load of work, high availability is becoming more and more important for the LHCbDIRAC services, and the current installation model is showing its limitations. Apache Mesos is a cluster manager which aims at abstracting heterogeneous physical resources on which various tasks can be distributed thanks to so called "framework". The Marathon framework is suitable for long running tasks such as the DIRAC services, while the Chronos framework meets the needs of cron-like tasks like the DIRAC agents. A combination of the service discovery tool Consul together with HAProxy allows to expose the running containers to the outside world while hiding their dynamic placements. Such an arc...
Fermi field and Dirac oscillator in a Som-Raychaudhuri space-time
de Montigny, Marc; Zare, Soroush; Hassanabadi, Hassan
2018-05-01
We investigate the relativistic dynamics of a Dirac field in the Som-Raychaudhuri space-time, which is described by a Gödel-type metric and a stationary cylindrical symmetric solution of Einstein field equations for a charged dust distribution in rigid rotation. In order to analyze the effect of various physical parameters of this space-time, we solve the Dirac equation in the Som-Raychaudhuri space-time and obtain the energy levels and eigenfunctions of the Dirac operator by using the Nikiforov-Uvarov method. We also examine the behaviour of the Dirac oscillator in the Som-Raychaudhuri space-time, in particular, the effect of its frequency and the vorticity parameter.
International Nuclear Information System (INIS)
Pierantozzi, T.; Vazquez, L.
2005-01-01
Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case
Energy Technology Data Exchange (ETDEWEB)
Karbstein, Felix
2009-07-08
We introduce a new method for dealing with fermionic quantum field theories amenable to a mean-field-type approximation. In this work we focus on the relativistic Hartree approximation. Our aim is to integrate out the Dirac sea and derive a no-sea effective theory'' with positive energy single particle states only. As the derivation of the no-sea effective theory involves only standard Feynman diagrams, our approach is quite general and not restricted to particular space-time dimensions. We develop and illustrate the approach in the ''large N'' limit of the Gross-Neveu model family in 1+1 dimensions. As the Gross-Neveu model has been intensely studied and several analytical solutions are known for this model, it is an ideal testing ground for our no-sea effective theory approach. The chiral Gross-Neveu model, also referred to as 1+1 dimensional Nambu-Jona-Lasinio model, turns out to be of particular interest. In this case, we explicitly derive a consistent effective theory featuring both elementary ''{pi} meson'' fields and (positive energy) ''quark'' fields, starting from a purely fermionic quantum field theory. In the second part of this work, we apply our approach to the Walecka model in 1+1 and 3+1 dimensions. As the Dirac sea caused considerable difficulties in attempts to base nuclear physics on field theoretic models like the Walecka model, mean-field calculations were typically done without the sea. We confront several of these mean-field theory results with our no-sea effective theory approach. The potential of our approach is twofold. While the no-sea effective theory can be utilized to provide new analytical insights in particular parameter regimes, it also sheds new light on more fundamental issues as the explicit emergence of effective, Dirac-sea induced multi-fermion interactions in an effective theory with positive energy states only. (orig.)
Paul Dirac: the purest soul in physics
International Nuclear Information System (INIS)
Berry, M.
1998-01-01
Paul Dirac published the first of his papers on ''The Quantum Theory of the Electron'' seventy years ago this month. Published in the Proceedings of the Royal Society (London) in February and March 1928, the papers contained one of the greatest leaps of imagination in 20th century physics. The Dirac equation, derived in those papers, is one of the most important equations in physics. Dirac showed that the simplest wave satisfying the requirements of quantum mechanics and relativity was not a simple number but had four components. He found that the logic that led to the theory was, although deeply sophisticated, in a sense beautifully simple. Much later, when someone asked him ''How did you find the Dirac equation?'' he is said to have replied: ''I found it beautiful''. In addition to explaining the magnetic and spin properties of the electron, the equation also predicts the existence of antimatter. Because Dirac was a quiet man - famously quiet, indeed - he is not well known outside physics, although this is slowly changing. In 1995 a plaque to Dirac was unveiled at Westminster Abbey in London and last year Institute of Physics Publishing, which is based in Bristol, named its new building Dirac House. In this article the author recalls the achievements of the greatest physicists of the 20th century. (UK)
Dirac fermions in blue-phosphorus
International Nuclear Information System (INIS)
Li, Yuanchang; Chen, Xiaobin
2014-01-01
We propose that Dirac cones can be engineered in phosphorene with fourfold-coordinated phosphorus atoms. The key is to separate the energy levels of the in-plane (s, p x , and p y ) and out-of-plane (p z ) oribtals through the sp 2 configuration, yielding respective σ- and π-character Dirac cones, and then quench the latter. As a proof-of-principle study, we create σ-character Dirac cones in hydrogenated and fluorinated phosphorene with a honeycomb lattice. The obtained Dirac cones are at K-points, slightly anisotropic, with Fermi velocities of 0.91 and 1.23 times that of graphene along the ΓK and KM direction, and maintain good linearity up to ∼2 eV for holes. A substantive advantage of a σ-character Dirac cone is its convenience in tuning the Dirac gap via in-plane strain. Our findings pave the way for development of high-performance electronic devices based on Dirac materials. (letter)
Dirac cones in isogonal hexagonal metallic structures
Wang, Kang
2018-03-01
A honeycomb hexagonal metallic lattice is equivalent to a triangular atomic one and cannot create Dirac cones in its electromagnetic wave spectrum. We study in this work the low-frequency electromagnetic band structures in isogonal hexagonal metallic lattices that are directly related to the honeycomb one and show that such structures can create Dirac cones. The band formation can be described by a tight-binding model that allows investigating, in terms of correlations between local resonance modes, the condition for the Dirac cones and the consequence of the third structure tile sustaining an extra resonance mode in the unit cell that induces band shifts and thus nonlinear deformation of the Dirac cones following the wave vectors departing from the Dirac points. We show further that, under structure deformation, the deformations of the Dirac cones result from two different correlation mechanisms, both reinforced by the lattice's metallic nature, which directly affects the resonance mode correlations. The isogonal structures provide new degrees of freedom for tuning the Dirac cones, allowing adjustment of the cone shape by modulating the structure tiles at the local scale without modifying the lattice periodicity and symmetry.
Benoit-Lévy, Aurélien; Chardin, Gabriel
2014-05-01
We study an unconventional cosmology, in which we investigate the consequences that antigravity would pose to cosmology. We present the main characteristics of the Dirac-Milne Universe, a cosmological model where antimatter has a negative active gravitational mass. In this non-standard Universe, separate domains of matter and antimatter coexist at our epoch without annihilation, separated by a gravitationally induced depletion zone. We show that this cosmology does not require a priori the Dark Matter and Dark Energy components of the standard model of cosmology. Additionally, inflation becomes an unnecessary ingredient. Investigating this model, we show that the classical cosmological tests such as primordial nucleosynthesis, Type Ia supernovæ and Cosmic Microwave Background are surprisingly concordant.
The Dirac equation and its solutions
Energy Technology Data Exchange (ETDEWEB)
Bagrov, Vladislav G. [Tomsk State Univ., Tomsk (Russian Federation). Dept. of Quantum Field Theroy; Gitman, Dmitry [Sao Paulo Univ. (Brazil). Inst. de Fisica; P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State Univ., Tomsk (Russian Federation). Faculty of Physics
2013-07-01
The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.
The Dirac equation and its solutions
Bagrov, Vladislav G
2014-01-01
Dirac equations are of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly.In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.
Counter-diabatic driving for Dirac dynamics
Fan, Qi-Zhen; Cheng, Xiao-Hang; Chen, Xi
2018-03-01
In this paper, we investigate the fast quantum control of Dirac equation dynamics by counter-diabatic driving, sharing the concept of shortcut to adiabaticity. We systematically calculate the counter-diabatic terms in different Dirac systems, like graphene and trapped ions. Specially, the fast and robust population inversion processes are achieved in Dirac system, taking into account the quantum simulation with trapped ions. In addition, the population transfer between two bands can be suppressed by counter-diabatic driving in graphene system, which might have potential applications in opt-electric devices.
Quantum geometry of the Dirac fermions
International Nuclear Information System (INIS)
Korchemskij, G.P.
1989-01-01
The bosonic path integral formalism is developed for Dirac fermions interacting with a nonabelian gauge field in the D-dimensional Euclidean space-time. The representation for the effective action and correlation functions of interacting fermions as sums over all bosonic paths on the complex projective space CP 2d-1 , (2d=2 [ D 2] is derived where all the spinor structure is absorbed by the one-dimensional Wess-Zumino term. It is the Wess-Zumino term that ensures all necessary properties of Dirac fermions under quantization. i.e., quantized values of the spin, Dirac equation, Fermi statistics. 19 refs
The Dirac equation and its solutions
International Nuclear Information System (INIS)
Bagrov, Vladislav G.; Gitman, Dmitry; P.N. Lebedev Physical Institute, Moscow; Tomsk State Univ., Tomsk
2013-01-01
The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.
Scalar potentials and the Dirac equation
International Nuclear Information System (INIS)
Bergerhoff, B.; Soff, G.
1994-01-01
The Dirac equation is solved for various types of scalar potentials. Energy eigenvalues and normalized bound-state wave functions are calculated analytically for a scalar 1/r-potential as well as for a mixed scalar and Coulomb 1/r-potential. Also continuum wave functions for positive and negative energies are derived. Similarly, we investigate the solutions of the Dirac equation for a scalar square-well potential. Relativistic wave functions for scalar Yukawa and exponential potentials are determined numerically. Finally, we also discuss solutions of the Dirac equation for scalar linear and quadratic potentials which are frequently used to simulate quark confinement. (orig.)
Wigner function for the Dirac oscillator in spinor space
International Nuclear Information System (INIS)
Ma Kai; Wang Jianhua; Yuan Yi
2011-01-01
The Wigner function for the Dirac oscillator in spinor space is studied in this paper. Firstly, since the Dirac equation is described as a matrix equation in phase space, it is necessary to define the Wigner function as a matrix function in spinor space. Secondly, the matrix form of the Wigner function is proven to support the Dirac equation. Thirdly, by solving the Dirac equation, energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained. (authors)
Dirac equation in magnetic-solenoid field
Energy Technology Data Exchange (ETDEWEB)
Gavrilov, S.P. [Dept. Fisica e Quimica, UNESP, Campus de Guaratingueta (Brazil); Gitman, D.M.; Smirnov, A.A. [Instituto de Fisica, Universidade de Sao Paulo (Brazil)
2004-07-01
We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid. (orig.)
SU(4) proprerties of the Dirac equation
International Nuclear Information System (INIS)
Linhares, C.A.; Mignaco, J.A.
1985-09-01
The Dirac equation in four dimensions has an intimate connection with the representations of the group SU(4). This connection is shown in detail and subsequent properties are displayed in the continuum as well as in the lattice description [pt
New symmetries for the Dirac equation
International Nuclear Information System (INIS)
Linhares, C.A.; Mignaco, J.A.
1990-01-01
The Dirac equation in four dimension is studied describing fermions, both as 4 x 4 matrices and differential forms. It is discussed in both formalisms its properties under transformations of the group SU(4). (A.C.A.S.) [pt
New and old symmetries of the Maxwell and Dirac equations
International Nuclear Information System (INIS)
Fushchich, V.I.; Nikitin, A.G.
1983-01-01
The symmetry properties of Maxwell's equations for the electromagnetic field and also of the Dirac and Kemmer-Duffin-Petiau equations are analyzed. In the framework of a ''non-Lie'' approach it is shown that, besides the well-known invariance with respect to the conformal group and the Heaviside-Larmor-Rainich transformations, Maxwell's equations have an additional symmetry with respect to the group U(2)xU(2) and with respect to the 23-dimensional Lie algebra A 23 . The transformations of the additional symmetry are given by nonlocal (integro-differential) operators. The symmetry of the Dirac equation in the class of differential and integro-differential transformations is investigated. It is shown that this equation is invariant with respect to an 18-parameter group, which includes the Poincare group as a subgroup. A 28-parameter invariance group of the Kemmer-Duffin-Petiau equation is found. Finite transformations of the conformal group for a massless field with arbitrary spin are obtained. The explicit form of conformal transformations for the electromagnetic field and also for the Dirac and Weyl fields is given
On new and old symmetries of Maxwell and Dirac equations
International Nuclear Information System (INIS)
Fushchich, V.I.; Nikitin, A.G.
1983-01-01
Symmetry properties of the Maxwell equation for the electromagnetic field are analysed as well as of the Dirac and Kemmer-Duffin-Petiau one. In the frame of the non-geometrical approach it is demonstrated, that besides to the well-known invariance under the conformal group and Heaviside-Larmor-Rainich transformation, Maxwell equation possess the additional symmetry under the group U(2)xU(2) and under the 23-dimensional Lie algebra A 23 . The additional symmetry transformations are realized by the non-local (integro-differential) operators. The symmetry of the Dirac. equation under the differential and integro-differential transformations is investio.ated. It is shown that this equation is invariant under the 18-parametrical group, which includes the Poincare group as a subgroup. The 28-parametrical invariance group of the Kemmer-Duffin-Petiau equation is found. The finite conformal group transformations for a massless field of any spin are obtained. The explicit form of the conformal transformations for the electromagnetic field as well as for the Dirac and Weyl fields is given
Drift chamber readout system of the DIRAC experiment
Afanasiev, L G
2002-01-01
A drift chamber readout system of the DIRAC experiment at CERN is presented. The system is intended to read out the signals from planar chambers operating in a high current mode. The sense wire signals are digitized in the 16-channel time-to-digital converter boards which are plugged in the signal plane connectors. This design results in a reduced number of modules, a small number of cables and high noise immunity. The system has been successfully operating in the experiment since 1999.
Quantized Dirac field interacting with a classical Maxwell field
International Nuclear Information System (INIS)
Kolsrud, M.
1987-10-01
The S operator for the quantized and the s matrix for the unquantized Dirac field, both fields interacting with an unquantized Maxwell field, are shown to be related in the following way: S=exp(-ic†kc) and s=exp(-ik). Here c is the column matrix of the particle operators, and k is a Hermitian matrix. With splitting of c into an electron and a positron part, a corresponding factorization of S is performed. Exact expressions for the probability amplitude for various electron and/or positron processes are then obtained
An asymptotic formula for Weyl solutions of the dirac equations
International Nuclear Information System (INIS)
Misyura, T.V.
1995-01-01
In the spectral analysis of differential operators and its applications an important role is played by the investigation of the behavior of the Weyl solutions of the corresponding equations when the spectral parameter tends to infinity. Elsewhere an exact asymptotic formula for the Weyl solutions of a large class of Sturm-Liouville equations has been obtained. A decisve role in the proof of this formula has been the semiboundedness property of the corresponding Sturm-Liouville operators. In this paper an analogous formula is obtained for the Weyl solutions of the Dirac equations
Data acquisition software for DIRAC experiment
International Nuclear Information System (INIS)
Ol'shevskij, V.G.; Trusov, S.V.
2000-01-01
The structure and basic processes of data acquisition software of DIRAC experiment for the measurement of π + π - atom life-time are described. The experiment is running on PS accelerator of CERN. The developed software allows one to accept, record and distribute to consumers up to 3 Mbytes of data in one accelerator supercycle of 14.4 s duration. The described system is used successfully in the DIRAC experiment starting from 1998 year
New exact solutions of the Dirac equation
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Lavrov, P.M.; Shapovalov, V.N.
1980-01-01
Search for new exact solutions of the Dirac and Klein-Gordon equations are in progress. Considered are general properties of the Dirac equation solutions for an electron in a purely magnetic field, in combination with a longitudinal magnetic and transverse electric fields. New solutions for the equations of charge motion in an electromagnetic field of axial symmetry and in a nonstationary field of a special form have been found for potentials selected concretely
Deuteron stripping reactions using dirac phenomenology
Hawk, E. A.; McNeil, J. A.
2001-04-01
In this work deuteron stripping reactions are studied using the distorted wave born approximation employing dirac phenomenological potentials. In 1982 Shepard and Rost performed zero-range dirac phenomenological stripping calculations and found a dramatic reduction in the predicted cross sections when compared with similar nonrelativistic calculations. We extend the earlier work by including full finite range effects as well as the deuteron's internal D-state. Results will be compared with traditional nonrelativistic approaches and experimental data at low energy.
Solvable linear potentials in the Dirac equation
International Nuclear Information System (INIS)
Dominguez-Adame, F.; Gonzalez, M.A.
1990-01-01
The Dirac equation for some linear potentials leading to Schroedinger-like oscillator equations for the upper and lower components of the Dirac spinor have been solved. Energy levels for the bound states appear in pairs, so that both particles and antiparticles may be bound with the same energy. For weak coupling, the spacing between levels is proportional to the coupling constant while in the strong limit those levels are depressed compared to the nonrelativistic ones
Leptons as systems of Dirac particles
International Nuclear Information System (INIS)
Borstnik, N.M.; Kaluza, M.
1988-03-01
Charged leptons are treated as systems of three equal independent Dirac particles in an external static effective potential which has a vector and a scalar term. The potential is constructed to reproduce the experimental mass spectrum of the charged leptons. The Dirac covariant equation for three interacting particles is discussed in order to comment on the magnetic moment of leptons. (author). 9 refs, 2 figs, 4 tabs
Dirac equation on a curved surface
Energy Technology Data Exchange (ETDEWEB)
Brandt, F.T., E-mail: fbrandt@usp.br; Sánchez-Monroy, J.A., E-mail: antosan@usp.br
2016-09-07
The dynamics of Dirac particles confined to a curved surface is examined employing the thin-layer method. We perform a perturbative expansion to first-order and split the Dirac field into normal and tangential components to the surface. In contrast to the known behavior of second order equations like Schrödinger, Maxwell and Klein–Gordon, we find that there is no geometric potential for the Dirac equation on a surface. This implies that the non-relativistic limit does not commute with the thin-layer method. Although this problem can be overcome when second-order terms are retained in the perturbative expansion, this would preclude the decoupling of the normal and tangential degrees of freedom. Therefore, we propose to introduce a first-order term which rescues the non-relativistic limit and also clarifies the effect of the intrinsic and extrinsic curvatures on the dynamics of the Dirac particles. - Highlights: • The thin-layer method is employed to derive the Dirac equation on a curved surface. • A geometric potential is absent at least to first-order in the perturbative expansion. • The effects of the extrinsic curvature are included to rescue the non-relativistic limit. • The resulting Dirac equation is consistent with the Heisenberg uncertainty principle.
Mathe, Z.; Casajus Ramo, A.; Lazovsky, N.; Stagni, F.
2015-12-01
For many years the DIRAC interware (Distributed Infrastructure with Remote Agent Control) has had a web interface, allowing the users to monitor DIRAC activities and also interact with the system. Since then many new web technologies have emerged, therefore a redesign and a new implementation of the DIRAC Web portal were necessary, taking into account the lessons learnt using the old portal. These new technologies allowed to build a more compact, robust and responsive web interface that enables users to have better control over the whole system while keeping a simple interface. The web framework provides a large set of “applications”, each of which can be used for interacting with various parts of the system. Communities can also create their own set of personalised web applications, and can easily extend already existing ones with a minimal effort. Each user can configure and personalise the view for each application and save it using the DIRAC User Profile service as RESTful state provider, instead of using cookies. The owner of a view can share it with other users or within a user community. Compatibility between different browsers is assured, as well as with mobile versions. In this paper, we present the new DIRAC Web framework as well as the LHCb extension of the DIRAC Web portal.
Dirac Fermions in an Antiferromagnetic Semimetal
Tang, Peizhe; Zhou, Quan; Xu, Gang; Zhang, Shou-Cheng; Shou-Cheng Zhang's Group Team, Prof.
Analogues of the elementary particles have been extensively searched for in condensed matter systems for both scientific interest and technological applications. Recently, massless Dirac fermions were found to emerge as low energy excitations in materials now known as Dirac semimetals. All the currently known Dirac semimetals are nonmagnetic with both time-reversal symmetry and inversion symmetry "". Here we show that Dirac fermions can exist in one type of antiferromagnetic systems, where both and "" are broken but their combination "" is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyze the robustness of the Dirac points under symmetry protections, and demonstrate its distinctive bulk dispersions as well as the corresponding surface states by ab initio calculations. Our results provide a possible platform to study the interplay of Dirac fermion physics and magnetism. We acknowledge the DOE, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract DE-AC02-76SF00515, NSF under Grant No.DMR-1305677 and FAME, one of six centers of STARnet.
The Dirac equation in external fields: Variable separation in Cartesian coordinates
International Nuclear Information System (INIS)
Shishkin, G.V.; Cabos, W.D.
1991-01-01
The method of separation of variables in the Dirac equation proposed in an earlier work by one of the present authors [J. Math. Phys. 30, 2132 (1989)] is developed for the complete set of interactions of the Dirac particle. The essence of the method consists of the separation of the first-order matrix differential operators that define the dependence of the Dirac bispinor on the related variables, but commutation of such operators with or between the operator of the equation is not assumed. This approach, which is perfectly justified in the presence of gravitational [Theor. Math. Phys. 70, 204 (1987)] or vector fields [J. Math. Phys. 30, 2132 (1989)], permits one to find all the possibilities of separation of variables in the Dirac equation in the case of the most general set of external fields. The complete set of interactions of the Dirac particle is determined by the symmetry group of equations, namely, viz. the SU(4) group. The interactions are scalar, vector, tensor, pseudovector and pseudoscalar. The analysis in this article is limited to Cartesian coordinates. The corresponding results for the general curvilinear coordinates will be presented in a future paper
Viability of Dirac phase leptogenesis
International Nuclear Information System (INIS)
Anisimov, Alexey; Blanchet, Steve; Di Bari, Pasquale
2008-01-01
We discuss the conditions for a non-vanishing Dirac phase δ and mixing angle θ 13 , sources of CP violation in neutrino oscillations, to be uniquely responsible for the observed matter–antimatter asymmetry of the Universe through leptogenesis. We show that this scenario, that we call δ-leptogenesis, is viable when the degenerate limit for the heavy right-handed (RH) neutrino spectrum is considered. We derive an interesting joint condition on sinθ 13 and the absolute neutrino mass scale that can be tested in future neutrino oscillation experiments. In the limit of the hierarchical heavy RH neutrino spectrum, we strengthen the previous result that δ-leptogenesis is only very marginally allowed, even when the production from the two heavier RH neutrinos is taken into account. An improved experimental upper bound on sinθ 13 and/or an account of quantum kinetic effects could completely rule out this option in the future. Therefore, δ-leptogenesis can be also regarded as motivation for models with degenerate heavy neutrino spectrum
First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals
Mei, Jun; Wu, Ying; Chan, C. T.; Zhang, Zhao-Qing
2012-01-01
By using the k•p method, we propose a first-principles theory to study the linear dispersions in phononic and photonic crystals. The theory reveals that only those linear dispersions created by doubly degenerate states can be described by a reduced Hamiltonian that can be mapped into the Dirac Hamiltonian and possess a Berry phase of -π. Linear dispersions created by triply degenerate states cannot be mapped into the Dirac Hamiltonian and carry no Berry phase, and, therefore should be called Dirac-like cones. Our theory is capable of predicting accurately the linear slopes of Dirac and Dirac-like cones at various symmetry points in a Brillouin zone, independent of frequency and lattice structure. © 2012 American Physical Society.
First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals
Mei, Jun
2012-07-24
By using the k•p method, we propose a first-principles theory to study the linear dispersions in phononic and photonic crystals. The theory reveals that only those linear dispersions created by doubly degenerate states can be described by a reduced Hamiltonian that can be mapped into the Dirac Hamiltonian and possess a Berry phase of -π. Linear dispersions created by triply degenerate states cannot be mapped into the Dirac Hamiltonian and carry no Berry phase, and, therefore should be called Dirac-like cones. Our theory is capable of predicting accurately the linear slopes of Dirac and Dirac-like cones at various symmetry points in a Brillouin zone, independent of frequency and lattice structure. © 2012 American Physical Society.
International Nuclear Information System (INIS)
Takane, Yoshitake
2016-01-01
An unbounded massless Dirac model with two nondegenerate Dirac cones is the simplest model for Weyl semimetals, which show the anomalous electromagnetic response of chiral magnetic effect (CME) and anomalous Hall effect (AHE). However, if this model is naively used to analyze the electromagnetic response within a linear response theory, it gives the result apparently inconsistent with the persuasive prediction based on a lattice model. We show that this serious difficulty is related to the breaking of current conservation in the Dirac model due to quantum anomaly and can be removed if current and charge operators are redefined to include the contribution from the anomaly. We demonstrate that the CME as well as the AHE can be properly described using newly defined operators, and clarify that the CME is determined by the competition between the contribution from the anomaly and that from low-energy electrons. (author)
Volfson, Boris
2013-09-01
The hypothesis of transition from a chaotic Dirac Sea, via highly unstable positronium, into a Simhony Model of stable face-centered cubic lattice structure of electrons and positrons securely bound in vacuum space, is considered. 13.75 Billion years ago, the new lattice, which, unlike a Dirac Sea, is permeable by photons and phonons, made the Universe detectable. Many electrons and positrons ended up annihilating each other producing energy quanta and neutrino-antineutrino pairs. The weak force of the electron-positron crystal lattice, bombarded by the chirality-changing neutrinos, may have started capturing these neutrinos thus transforming from cubic crystals into a quasicrystal lattice. Unlike cubic crystal lattice, clusters of quasicrystals are "slippery" allowing the formation of centers of local torsion, where gravity condenses matter into galaxies, stars and planets. In the presence of quanta, in a quasicrystal lattice, the Majorana neutrinos' rotation flips to the opposite direction causing natural transformations in a category comprised of three components; two others being positron and electron. In other words, each particle-antiparticle pair "e-" and "e+", in an individual crystal unit, could become either a quasi- component "e- ve e+", or a quasi- component "e+ - ve e-". Five-to-six six billion years ago, a continuous stimulation of the quasicrystal aetherial lattice by the same, similar, or different, astronomical events, could have triggered Hebbian and anti-Hebbian learning processes. The Universe may have started writing script into its own aether in a code most appropriate for the quasicrystal aether "hardware": Eight three-dimensional "alphabet" characters, each corresponding to the individual quasi-crystal unit shape. They could be expressed as quantum Turing machine qubits, or, alternatively, in a binary code. The code numerals could contain terminal and nonterminal symbols of the Chomsky's hierarchy, wherein, the showers of quanta, forming the
Semi-Dirac points in phononic crystals
Zhang, Xiujuan
2014-01-01
A semi-Dirac cone refers to a peculiar type of dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. It was originally discovered in electron systems, in which the associated quasi-particles are massless along one direction, like those in graphene, but effective-mass-like along the other. It was reported that a semi-Dirac point is associated with the topological phase transition between a semi-metallic phase and a band insulator. Very recently, the classical analogy of a semi-Dirac cone has been reported in an electromagnetic system. Here, we demonstrate that, by accidental degeneracy, two-dimensional phononic crystals consisting of square arrays of elliptical cylinders embedded in water are also able to produce the particular dispersion relation of a semi-Dirac cone in the center of the Brillouin zone. A perturbation method is used to evaluate the linear slope and to affirm that the dispersion relation is a semi-Dirac type. If the scatterers are made of rubber, in which the acoustic wave velocity is lower than that in water, the semi-Dirac dispersion can be characterized by an effective medium theory. The effective medium parameters link the semi-Dirac point to a topological transition in the iso-frequency surface of the phononic crystal, in which an open hyperbola is changed into a closed ellipse. This topological transition results in drastic change in wave manipulation. On the other hand, the theory also reveals that the phononic crystal is a double-zero-index material along the x-direction and photonic-band-edge material along the perpendicular direction (y-direction). If the scatterers are made of steel, in which the acoustic wave velocity is higher than that in water, the effective medium description fails, even though the semi-Dirac dispersion relation looks similar to that in the previous case. Therefore different wave transport behavior is expected. The semi-Dirac points in phononic crystals described in
Nonstandard Supersymmetry Breaking and Dirac Gaugino Masses without Supersoftness
Energy Technology Data Exchange (ETDEWEB)
Martin, Stephen P. [Northern Illinois U.
2015-08-05
I consider models in which nonstandard supersymmetry-breaking terms, including Dirac gaugino masses, arise from F-term breaking mediated by operators with a 1/M3 suppression. In these models, the supersoft properties found in the case of D-term breaking are absent in general, but can be obtained as a special case that is a fixed point of the renormalization group equations. The μ term is replaced by three distinct supersymmetry-breaking parameters, decoupling the Higgs scalar potential from the Higgsino masses. Both holomorphic and nonholomorphic scalar cubic interactions with minimal flavor violation are induced in the supersymmetric Standard Model Lagrangian.
Strain engineering of Dirac cones in graphyne
Energy Technology Data Exchange (ETDEWEB)
Wang, Gaoxue; Kumar, Ashok; Pandey, Ravindra, E-mail: pandey@mtu.edu [Department of Physics, Michigan Technological University, Houghton, Michigan 49931 (United States); Si, Mingsu [Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000 (China)
2014-05-26
6,6,12-graphyne, one of the two-dimensional carbon allotropes with the rectangular lattice structure, has two kinds of non-equivalent anisotropic Dirac cones in the first Brillouin zone. We show that Dirac cones can be tuned independently by the uniaxial compressive strain applied to graphyne, which induces n-type and p-type self-doping effect, by shifting the energy of the Dirac cones in the opposite directions. On the other hand, application of the tensile strain results into a transition from gapless to finite gap system for the monolayer. For the AB-stacked bilayer, the results predict tunability of Dirac-cones by in-plane strains as well as the strain applied perpendicular to the plane. The group velocities of the Dirac cones show enhancement in the resistance anisotropy for bilayer relative to the case of monolayer. Such tunable and direction-dependent electronic properties predicted for 6,6,12-graphyne make it to be competitive for the next-generation electronic devices at nanoscale.
P A M Dirac meets M G Krein: matrix orthogonal polynomials and Dirac's equation
Energy Technology Data Exchange (ETDEWEB)
Duran, Antonio J [Departamento de Analisis Matematico, Universidad de Sevilla, Apdo (PO BOX) 1160, 41080 Sevilla (Spain); Gruenbaum, F Alberto [Department of Mathematics, University of California, Berkeley, CA 94720 (United States)
2006-04-07
The solution of several instances of the Schroedinger equation (1926) is made possible by using the well-known orthogonal polynomials associated with the names of Hermite, Legendre and Laguerre. A relativistic alternative to this equation was proposed by Dirac (1928) involving differential operators with matrix coefficients. In 1949 Krein developed a theory of matrix-valued orthogonal polynomials without any reference to differential equations. In Duran A J (1997 Matrix inner product having a matrix symmetric second order differential operator Rocky Mt. J. Math. 27 585-600), one of us raised the question of determining instances of these matrix-valued polynomials going along with second order differential operators with matrix coefficients. In Duran A J and Gruenbaum F A (2004 Orthogonal matrix polynomials satisfying second order differential equations Int. Math. Res. Not. 10 461-84), we developed a method to produce such examples and observed that in certain cases there is a connection with the instance of Dirac's equation with a central potential. We observe that the case of the central Coulomb potential discussed in the physics literature in Darwin C G (1928 Proc. R. Soc. A 118 654), Nikiforov A F and Uvarov V B (1988 Special Functions of Mathematical Physics (Basle: Birkhauser) and Rose M E 1961 Relativistic Electron Theory (New York: Wiley)), and its solution, gives rise to a matrix weight function whose orthogonal polynomials solve a second order differential equation. To the best of our knowledge this is the first instance of a connection between the solution of the first order matrix equation of Dirac and the theory of matrix-valued orthogonal polynomials initiated by M G Krein.
Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones
International Nuclear Information System (INIS)
Assili, M; Haddad, S
2013-01-01
We theoretically study the effect of the motion and the merging of Dirac cones on the interlayer magnetoresistance in multilayer graphene-like systems. This merging, which can be induced by a uniaxial strain, gives rise in a monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase whereby Dirac points disappear. Based on a universal Hamiltonian, proposed to describe the motion and the merging of Dirac points in two-dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene-like layers using the Kubo formula in the quantum limit where only the contribution of the n = 0 Landau level is relevant. A crossover from a negative to a positive interlayer magnetoresistance is found to take place as the merging is approached. This sign change of the magnetoresistance can also result from a coupling between the Dirac valleys, which is enhanced as the magnetic field amplitude increases. Our results describe the behavior of the magnetotransport in the organic conductor α-(BEDT) 2 I 3 and in a stack of deformed graphene-like systems. The latter can be simulated by optical lattices or microwave experiments in which the merging of Dirac cones can be observed. (paper)
Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones
Assili, M.; Haddad, S.
2013-09-01
We theoretically study the effect of the motion and the merging of Dirac cones on the interlayer magnetoresistance in multilayer graphene-like systems. This merging, which can be induced by a uniaxial strain, gives rise in a monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase whereby Dirac points disappear. Based on a universal Hamiltonian, proposed to describe the motion and the merging of Dirac points in two-dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene-like layers using the Kubo formula in the quantum limit where only the contribution of the n = 0 Landau level is relevant. A crossover from a negative to a positive interlayer magnetoresistance is found to take place as the merging is approached. This sign change of the magnetoresistance can also result from a coupling between the Dirac valleys, which is enhanced as the magnetic field amplitude increases. Our results describe the behavior of the magnetotransport in the organic conductor α-(BEDT)2I3 and in a stack of deformed graphene-like systems. The latter can be simulated by optical lattices or microwave experiments in which the merging of Dirac cones can be observed.
Assili, M; Haddad, S
2013-09-11
We theoretically study the effect of the motion and the merging of Dirac cones on the interlayer magnetoresistance in multilayer graphene-like systems. This merging, which can be induced by a uniaxial strain, gives rise in a monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase whereby Dirac points disappear. Based on a universal Hamiltonian, proposed to describe the motion and the merging of Dirac points in two-dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene-like layers using the Kubo formula in the quantum limit where only the contribution of the n = 0 Landau level is relevant. A crossover from a negative to a positive interlayer magnetoresistance is found to take place as the merging is approached. This sign change of the magnetoresistance can also result from a coupling between the Dirac valleys, which is enhanced as the magnetic field amplitude increases. Our results describe the behavior of the magnetotransport in the organic conductor α-(BEDT)2I3 and in a stack of deformed graphene-like systems. The latter can be simulated by optical lattices or microwave experiments in which the merging of Dirac cones can be observed.
DIRAC - Distributed Infrastructure with Remote Agent Control
Tsaregorodtsev, A; Closier, J; Frank, M; Gaspar, C; van Herwijnen, E; Loverre, F; Ponce, S; Graciani Diaz, R.; Galli, D; Marconi, U; Vagnoni, V; Brook, N; Buckley, A; Harrison, K; Schmelling, M; Egede, U; Bogdanchikov, A; Korolko, I; Washbrook, A; Palacios, J P; Klous, S; Saborido, J J; Khan, A; Pickford, A; Soroko, A; Romanovski, V; Patrick, G N; Kuznetsov, G; Gandelman, M
2003-01-01
This paper describes DIRAC, the LHCb Monte Carlo production system. DIRAC has a client/server architecture based on: Compute elements distributed among the collaborating institutes; Databases for production management, bookkeeping (the metadata catalogue) and software configuration; Monitoring and cataloguing services for updating and accessing the databases. Locally installed software agents implemented in Python monitor the local batch queue, interrogate the production database for any outstanding production requests using the XML-RPC protocol and initiate the job submission. The agent checks and, if necessary, installs any required software automatically. After the job has processed the events, the agent transfers the output data and updates the metadata catalogue. DIRAC has been successfully installed at 18 collaborating institutes, including the DataGRID, and has been used in recent Physics Data Challenges. In the near to medium term future we must use a mixed environment with different types of grid mid...
Su(4) properties of the Dirac-Kaehler equation
International Nuclear Information System (INIS)
Linhares, C.A.; Mignaco, J.A.
1991-01-01
We use the Dirac-Kaehler formalism in the space of differential forms (endowed with a Clifford product) to study the SU(4) symmetry related to the description of spin-1/2 particles found previously in the usual matrix treatment. We show that differential forms may be taken as the generators spanning the algebra of the SU(4) group and how the operations of this group can be related to a change of frame of reference in the algebra. We demonstrate that minimal left ideals of the algebra constitute irreducible representations for spin-1/2 particles for Clifford operation from the left, and exhibit how these ideals are related via space inversion, time reversal and their product. We also consider the dual space of minimal right ideals and show how the Dirac-Kaehler differential operator acts from the right, leaving the minimal right ideals invariant. This allows the introduction of an adjoint form and through the definition of a suitable scalar product, of conserved currents. We emphasize the relevance of all these features to the problem of proliferation of fermion species in the continuum limit of the lattice formalism. (author)
The LHCb Experience on the Grid from the DIRAC Accounting Data
Puig, A; Graciani, R; Casajús, A
2011-01-01
DIRAC is the software framework developed by LHCb to manage all its computing operations on the Grid. Since 2003 it has been used for large scale Monte Carlo simulation productions and for user analysis of these data. Since the end of 2009, with the start-up of LHC, DIRAC also takes care of the distribution, reconstruction, selection and analysis of the physics data taken by the detector apparatus. During 2009, DIRAC executed almost 5 million jobs for LHCb. In order to execute this workload slightly over 6 million of pilot jobs were submitted, out of which approximately one third were aborted by the Grid infrastructure. In 2010, thanks to their improved efficiency, DIRAC pilots are able, on average, to match and execute between 2 and 3 LHCb jobs during their lifetime, largely reducing the load on the Grid infrastructure. Given the large amount of submitted jobs and used resources, it becomes essential to store detailed information about their execution to track the behaviour of the system. The DIRAC Accountin...
Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations
International Nuclear Information System (INIS)
Esteban, M.J.; Georgiev, V.; Sere, E.
1995-01-01
The Maxwell-Dirac system describes the interaction of an electron with its own electromagnetic field. We prove the existence of soliton-like solutions of Maxwell-Dirac in (3+1)-Minkowski space-time. The solutions obtained are regular, stationary in time, and localized in space. They are found by a variational method, as critical points of an energy functional. This functional is strongly indefinite and presents a lack of compactness. We also find soliton-like solutions for the Klein-Gordon-Dirac system, arising in the Yukawa model. (author). 32 refs
All-Metallic Vertical Transistors Based on Stacked Dirac Materials
Wang, Yangyang; Ni, Zeyuan; Liu, Qihang; Quhe, Ruge; Zheng, Jiaxin; Ye, Meng; Yu, Dapeng; Shi, Junjie; Yang, Jinbo; Lu, Jing
2014-01-01
It is an ongoing pursuit to use metal as a channel material in a field effect transistor. All metallic transistor can be fabricated from pristine semimetallic Dirac materials (such as graphene, silicene, and germanene), but the on/off current ratio is very low. In a vertical heterostructure composed by two Dirac materials, the Dirac cones of the two materials survive the weak interlayer van der Waals interaction based on density functional theory method, and electron transport from the Dirac ...
Dirac equations for generalised Yang-Mills systems
International Nuclear Information System (INIS)
Lechtenfeld, O.; Nahm, W.; Tchrakian, D.H.
1985-06-01
We present Dirac equations in 4p dimensions for the generalised Yang-Mills (GYM) theories introduced earlier. These Dirac equations are related to the self-duality equations of the GYM and are checked to be elliptic in a 'BPST' background. In this background these Dirac equations are integrated exactly. The possibility of imposing supersymmetry in the GYM-Dirac system is investigated, with negative results. (orig.)
A framework for unified Dirac gauginos
Directory of Open Access Journals (Sweden)
Benakli Karim
2017-01-01
Full Text Available We identify the Minimal Dirac Gaugino Supersymmetric Standard Model (MDGSSM as the minimal field content with Dirac gauginos allowing unification of gauge coupling. We stress that its parameter space describes also other most popular models as the MSSM, NMSSM and MRSSM. We discuss the generation of trilinear couplings in models of gauge mediation that has been overlooked in the past. We study the different source of Higgs mixings and constraints from the ƿ parameter. Finally, we provide new experimental limits on the masses of the scalar octets.
Dirac particle tunneling from black rings
International Nuclear Information System (INIS)
Jiang Qingquan
2008-01-01
Recent research shows that Hawking radiation can be treated as a quantum tunneling process, and Hawking temperatures of Dirac particles across the horizon of a black hole can be correctly recovered via the fermion tunneling method. In this paper, motivated by the fermion tunneling method, we attempt to apply the analysis to derive Hawking radiation of Dirac particles via tunneling from black ring solutions of 5-dimensional Einstein-Maxwell-dilaton gravity theory. Finally, it is interesting to find that, as in the black hole case, fermion tunneling can also result in correct Hawking temperatures for the rotating neutral, dipole, and charged black rings.
Kapitza–Dirac effect with traveling waves
International Nuclear Information System (INIS)
Hayrapetyan, Armen G; Götte, Jörg B; Grigoryan, Karen K; Petrosyan, Rubik G
2015-01-01
We report on the possibility of diffracting electrons from light waves traveling inside a dielectric medium. We show that, in the frame of reference which moves with the group velocity of light, the traveling wave acts as a stationary diffraction grating from which electrons can diffract, similar to the conventional Kapitza–Dirac effect. To characterize the Kapitza–Dirac effect with traveling light waves, we make use of the Hamiltonian Analogy between electron optics and quantum mechanics and apply the Helmholtz–Kirchhoff theory of diffraction. (fast track communication)
Are Dirac electrons faster than light?
International Nuclear Information System (INIS)
De Angelis, G.F.
1986-01-01
This paper addresses the problem of path integral solutions of the Dirac equation. The path integral construction of the Dirac propagator which extends Fynman's checkerboard rule in more than one space dimension is discussed. A distinguished feature of such extension is the fact that the speed of a relativistic electron is actually greater than the speed of light when the space has more than one dimension. A technique employed in obtaining an extension to higher space dimension is described which consists in comparing continuity equations of quantum mechanical origin with forward Kolmogorov equations for suitable chosen classes of random processes
Heun Polynomials and Exact Solutions for the Massless Dirac Particle in the C-Metric
Kar, Priyasri; Singh, Ritesh K.; Dasgupta, Ananda; Panigrahi, Prasanta K.
2018-03-01
The equation of motion of a massless Dirac particle in the C-metric leads to the general Heun equation (GHE) for the radial and the polar variables. The GHE, under certain parametric conditions, is cast in terms of a new set of su(1, 1) generators involving differential operators of degrees ±1/2 and 0. Additional Heun polynomials are obtained using this new algebraic structure and are used to construct some exact solutions for the radial and the polar parts of the Dirac equation.
Spin eigen-states of Dirac equation for quasi-two-dimensional electrons
Energy Technology Data Exchange (ETDEWEB)
Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)
2015-10-15
Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.
New exact solutions of the Dirac equation. 8
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Sukhomlin, N.B.; Shapovalov, V.N.
1978-01-01
The paper continues the investigation into the exact solutions of the Dirac, Klein-Gordon, and Lorentz equations for a charge in an external electromagnetic field. The fields studied do not allow for separation of variables in the Dirac equation, but solutions to the Dirac equation are obtained
Kondo effect in three-dimensional Dirac and Weyl systems
Mitchell, Andrew K.; Fritz, Lars
2015-01-01
Magnetic impurities in three-dimensional Dirac and Weyl systems are shown to exhibit a fascinatingly diverse range of Kondo physics, with distinctive experimental spectroscopic signatures. When the Fermi level is precisely at the Dirac point, Dirac semimetals are in fact unlikely candidates for a
Dirac cones beyond the honeycomb lattice : a symmetry based approach
Miert, G. van; de Morais Smith, Cristiane
2016-01-01
Recently, several new materials exhibiting massless Dirac fermions have been proposed. However, many of these do not have the typical graphene honeycomb lattice, which is often associated with Dirac cones. Here, we present a classification of these different two-dimensional Dirac systems based on
Exact solutions of time-dependent Dirac equations and the quantum-classical correspondence
International Nuclear Information System (INIS)
Zhang Zhiguo
2006-01-01
Exact solutions to the Dirac equations with a time-dependent mass and a static magnetic field or a time-dependent linear potential are given. Matrix elements of the coordinate, momentum and velocity operator are calculated. In the large quantum number limit, these matrix elements give the classical solution
Dirac-Kahler fermion with noncommutative differential forms on a lattice
International Nuclear Information System (INIS)
Kanamori, I.; Kawamoto, N.
2004-01-01
Noncommutativity between a differential form and a function allows us to define differential operator satisfying Leibniz's rule on a lattice. We propose a new associative Clifford product defined on the lattice by introducing the noncommutative differential forms. We show that this Clifford product naturally leads to the Dirac-Kaehler fermion on the lattice
Itinerant quantum multicriticality of two-dimensional Dirac fermions
Roy, Bitan; Goswami, Pallab; Juričić, Vladimir
2018-05-01
We analyze emergent quantum multicriticality for strongly interacting, massless Dirac fermions in two spatial dimensions (d =2 ) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break O(S1) and O(S2) symmetries in the ordered phase. Performing a renormalization-group analysis by using the ɛ =(3 -d ) expansion scheme, we show that all the coupling constants in the critical hyperplane flow toward a new attractive fixed point, supporting an enlarged O(S1+S2) chiral symmetry. Such a fixed point acts as an exotic quantum multicritical point (MCP), governing the continuous semimetal-insulator as well as insulator-insulator (for example, antiferromagnet to valence bond solid) quantum phase transitions. In comparison with the lower symmetric semimetal-insulator quantum critical points, possessing either O(S1) or O(S2) chiral symmetry, the MCP displays enhanced correlation length exponents, and anomalous scaling dimensions for both fermionic and bosonic fields. We discuss the scaling properties of the ratio of bosonic and fermionic masses, and the increased dc resistivity at the MCP. By computing the scaling dimensions of different local fermion bilinears in the particle-hole channel, we establish that most of the four fermion operators or generalized density-density correlation functions display faster power-law decays at the MCP compared to the free fermion and lower symmetric itinerant quantum critical points. Possible generalization of this scenario to higher-dimensional Dirac fermions is also outlined.
Dirac's aether in relativistic quantum mechanics
International Nuclear Information System (INIS)
Petroni, N.C.; Bari Univ.; Vigier, J.P.
1984-01-01
The paper concerns Dirac's aether model, based on a stochastic covariant distribution of subquantum motions. Stochastic derivation of the relativistic quantum equations; deterministic nonlocal interpretation of the Aspect-Rapisarda experiments on the EPR paradox; and photon interference with itself; are all discussed. (U.K.)
Dirac's minimum degree condition restricted to claws
Broersma, Haitze J.; Ryjacek, Z.; Schiermeyer, I.
1997-01-01
Let G be a graph on n 3 vertices. Dirac's minimum degree condition is the condition that all vertices of G have degree at least . This is a well-known sufficient condition for the existence of a Hamilton cycle in G. We give related sufficiency conditions for the existence of a Hamilton cycle or a
International Nuclear Information System (INIS)
Ferreira, P.L.; Alcaras, J.A.C.
1980-01-01
The group theoretical properties of the Dirac groups of rank n are discussed together with the properties and construction of their IR's. The cases n even and n odd show distinct features. Furthermore, for n odd, the cases n=4K+1 and n=4K+3 exhibit some different properties too. (Author) [pt
Higher dimensional supersymmetric quantum mechanics and Dirac ...
Indian Academy of Sciences (India)
We exhibit the supersymmetric quantum mechanical structure of the full 3+1 dimensional Dirac equation considering `mass' as a function of coordinates. Its usefulness in solving potential problems is discussed with speciﬁc examples. We also discuss the `physical' signiﬁcance of the supersymmetric states in this formalism.
Applications of Dirac's Delta Function in Statistics
Khuri, Andre
2004-01-01
The Dirac delta function has been used successfully in mathematical physics for many years. The purpose of this article is to bring attention to several useful applications of this function in mathematical statistics. Some of these applications include a unified representation of the distribution of a function (or functions) of one or several…
On Kaehler's geometric description of dirac fields
International Nuclear Information System (INIS)
Goeckeler, M.; Joos, H.
1983-12-01
A differential geometric generalization of the Dirac equation due to E. Kaehler seems to be an appropriate starting point for the lattice approximation of matter fields. It is the purpose of this lecture to illustrate several aspects of this approach. (orig./HSI)
SU(4) properties of the Dirac equation
International Nuclear Information System (INIS)
Linhares, C.A.; Mignaco, J.A.
1988-01-01
The Dirac equation in four dimensions has an intimate connection with the representations of the group SU(4). This connection is shown in detail and subsequente properties are displayed in the continuum as well as in the lattice description. (author) [pt
Mass and oscillations of Dirac neutrinos
International Nuclear Information System (INIS)
Collot, J.
1989-01-01
In the most economical extension of the standard model, we have presented the theory of massive Dirac neutrinos. We have particularly emphasized that, in this model, a complete analogy between quarks and leptons can be erected and predicts neutrino flavor oscillations. We have reviewed the last experimental results concerning kinetic neutrino mass experiments and neutrino oscillation investigations
First level trigger of the DIRAC experiment
International Nuclear Information System (INIS)
Afanas'ev, L.G.; Karpukhin, V.V.; Kulikov, A.V.; Gallas, M.
2001-01-01
The logic of the first level trigger of the DIRAC experiment at CERN is described. A parallel running of different trigger modes with tagging of events and optional independent prescaling is realized. A CAMAC-based trigger system is completely computer controlled
Evolution kernel for the Dirac field
International Nuclear Information System (INIS)
Baaquie, B.E.
1982-06-01
The evolution kernel for the free Dirac field is calculated using the Wilson lattice fermions. We discuss the difficulties due to which this calculation has not been previously performed in the continuum theory. The continuum limit is taken, and the complete energy eigenfunctions as well as the propagator are then evaluated in a new manner using the kernel. (author)
Probabilistic solution of the Dirac equation
International Nuclear Information System (INIS)
Blanchard, P.; Combe, P.
1985-01-01
Various probabilistic representations of the 2, 3 and 4 dimensional Dirac equation are given in terms of expectation with respect to stochastic jump processes and are used to derive the nonrelativistic limit even in the presence of an external electromagnetic field. (orig.)
Poisson geometry from a Dirac perspective
Meinrenken, Eckhard
2018-03-01
We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop Quantum Groups and Gravity at the University of Waterloo, April 2016.
A Route to Dirac Liquid Theory: A Fermi Liquid Description for Dirac Materials
Gochan, Matthew; Bedell, Kevin
Since the pioneering work developed by L.V. Landau sixty years ago, Fermi Liquid Theory has seen great success in describing interacting Fermi systems. While much interest has been generated over the study of non-Fermi Liquid systems, Fermi Liquid theory serves as a formidable model for many systems and offers a rich amount of of results and insight. The recent classification of Dirac Materials, and the lack of a unifying theoretical framework for them, has motivated our study. Dirac materials are a versatile class of materials in which an abundance of unique physical phenomena can be observed. Such materials are found in all dimensions, with the shared property that their low-energy fermionic excitations behave as massless Dirac fermions and are therefore governed by the Dirac equation. The most popular Dirac material, graphene, is the focus of this work. We present our Fermi Liquid description of Graphene. We find many interesting results, specifically in the transport and dynamics of the system. Additionally, we expand on previous work regarding the Virial Theorem and its impact on the Fermi Liquid parameters in graphene. Finally, we remark on viscoelasticity of Dirac Materials and other unusual results that are consequences of AdS-CFT.
The GridPP DIRAC project - DIRAC for non-LHC communities
Bauer, D; Currie, R; Fayer, S; Huffman, A; Martyniak, J; Rand, D; Richards, A
2015-01-01
The GridPP consortium in the UK is currently testing a multi-VO DIRAC service aimed at non-LHC VOs. These VOs (Virtual Organisations) are typically small and generally do not have a dedicated computing support post. The majority of these represent particle physics experiments (e.g. NA62 and COMET), although the scope of the DIRAC service is not limited to this field. A few VOs have designed bespoke tools around the EMI-WMS & LFC, while others have so far eschewed distributed resources as they perceive the overhead for accessing them to be too high. The aim of the GridPP DIRAC project is to provide an easily adaptable toolkit for such VOs in order to lower the threshold for access to distributed resources such as Grid and cloud computing. As well as hosting a centrally run DIRAC service, we will also publish our changes and additions to the upstream DIRAC codebase under an open-source license. We report on the current status of this project and show increasing adoption of DIRAC within the non-LHC communiti...
The GridPP DIRAC project - DIRAC for non-LHC communities
Bauer, D.; Colling, D.; Currie, R.; Fayer, S.; Huffman, A.; Martyniak, J.; Rand, D.; Richards, A.
2015-12-01
The GridPP consortium in the UK is currently testing a multi-VO DIRAC service aimed at non-LHC VOs. These VOs (Virtual Organisations) are typically small and generally do not have a dedicated computing support post. The majority of these represent particle physics experiments (e.g. NA62 and COMET), although the scope of the DIRAC service is not limited to this field. A few VOs have designed bespoke tools around the EMI-WMS & LFC, while others have so far eschewed distributed resources as they perceive the overhead for accessing them to be too high. The aim of the GridPP DIRAC project is to provide an easily adaptable toolkit for such VOs in order to lower the threshold for access to distributed resources such as Grid and cloud computing. As well as hosting a centrally run DIRAC service, we will also publish our changes and additions to the upstream DIRAC codebase under an open-source license. We report on the current status of this project and show increasing adoption of DIRAC within the non-LHC communities.
Identifying Dirac cones in carbon allotropes with square symmetry
Energy Technology Data Exchange (ETDEWEB)
Wang, Jinying [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); Huang, Huaqing; Duan, Wenhui [Department of Physics, Tsinghua University, Beijing 100084 (China); Liu, Zhirong, E-mail: LiuZhiRong@pku.edu.cn [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); State Key Laboratory for Structural Chemistry of Unstable and Stable Species and Beijing National Laboratory for Molecular Sciences (BNLMS), Peking University, Beijing 100871 (China)
2013-11-14
A theoretical study is conducted to search for Dirac cones in two-dimensional carbon allotropes with square symmetry. By enumerating the carbon atoms in a unit cell up to 12, an allotrope with octatomic rings is recognized to possess Dirac cones under a simple tight-binding approach. The obtained Dirac cones are accompanied by flat bands at the Fermi level, and the resulting massless Dirac-Weyl fermions are chiral particles with a pseudospin of S = 1, rather than the conventional S = 1/2 of graphene. The spin-1 Dirac cones are also predicted to exist in hexagonal graphene antidot lattices.
On the solution of the Dirac equation in de Sitter space
International Nuclear Information System (INIS)
Klishevich, V V; Tyumentsev, V A
2005-01-01
It is shown that the maximal number of first-order symmetry operators for the Dirac equation (including spin symmetries), both in arbitrary signature flat space and in de Sitter space, is equal. The isomorphic representation of 11-dimensional nonlinear symmetry algebra (W-algebra) of first-order operators for the Dirac operator in flat space and de Sitter space is considered. The algebra is an extension of the Lie algebra of the group of pseudo-orthogonal rotations and this extension is unique. We have found all linear Lie subalgebras in the nonlinear algebra that satisfy the conditions of the noncommutative integration theorem. Using one subalgebra we have integrated the Dirac equation in the generalized spherical system of coordinates and have constructed the complete class of exact solutions. The solution is found by a method that differs from the variable separation method and is new in the literature. The massive particle spectrum, models of particle into antiparticle transmutation, the disappearance of particles and the quantization conditions of the motion are discussed. One can use the results of the paper to pose the boundary problem for the Dirac equation in de Sitter space if the interval is used in the boundary condition. As an example, we consider a model of asymptotically flat space that is glued from the de Sitter space and flat space. We interpret the model as a gravitational well or barrier
Quantum mechanics of Yano tensors: Dirac equation in curved spacetime
International Nuclear Information System (INIS)
Cariglia, Marco
2004-01-01
In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank 2, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors
Numerical implementation of the Dirac equation on hypercube multicomputers
International Nuclear Information System (INIS)
Wells, J.C.
1991-01-01
Motivated by an interest in nonperturbative electromagnetic lepton-pair production in relativistic heavy-ion collisions, we discuss the numerical methods used in implementing a lattice solution of the time-dependent Dirac equation in three-dimensional Cartesian coordinates. Discretization is obtained using the lattice basis-spline collocation method, in which quantum-state vectors and coordinate-space operators are expressed in terms of basis-spline functions, and represented on a spatial lattice. All numerical procedures reduce to a series of matrix-vector operations which we perform on the Intel iPSC/860 hypercube multicomputer. We discuss solutions to the problems of limited node memory and node-to-node communication overhead inherent in using distributed-memory, multiple-instruction, multiple-data parallel computers
A new formalism for Dirac-like theories with curved space-time
International Nuclear Information System (INIS)
Halliday, D.W.
1992-01-01
This paper develops a formalism for Dirac-like equations (linear complex differential equations, linear in all derivatives), allowing for general coordinate and open-quotes spin-spaceclose quotes (internal space) transformations. A correspondence principle is also developed by requiring solutions to the Dirac-like equations to be solutions to a Klein-Gordon equation that is likewise generally invariant. Through this treatment, previous generalizations of the Dirac equation are incorporated, and various aspects of these methods are analyzed. Furthermore, the Yang-Mills-like gauge fields allowed, or required, by the formalism are expressed, and found to be associated with much larger symmetries than most would desire, suggesting either there has been much greater symmetry breaking than expected, or else few of the particles accepted as fundamental really are. It is also found that unless the space-time is open-quotes parallelizableclose quotes (so there exist fields that are everywhere parallel transported into themselves, which is not generally the case), or some of the wave function components (and separately some of the Yang-Mills fields) are interdependent, one cannot have the Dirac gamma operators commuting with the momentum operators, while simultaneously having a spin-space metric that is compatible with the Yang-Mills fields
SARAH 3.2: Dirac gauginos, UFO output, and more
Staub, Florian
2013-07-01
SARAH is a Mathematica package optimized for the fast, efficient and precise study of supersymmetric models beyond the MSSM: a new model can be defined in a short form and all vertices are derived. This allows SARAH to create model files for FeynArts/FormCalc, CalcHep/CompHep and WHIZARD/O'Mega. The newest version of SARAH now provides the possibility to create model files in the UFO format which is supported by MadGraph 5, MadAnalysis 5, GoSam, and soon by Herwig++. Furthermore, SARAH also calculates the mass matrices, RGEs and 1-loop corrections to the mass spectrum. This information is used to write source code for SPheno in order to create a precision spectrum generator for the given model. This spectrum-generator-generator functionality as well as the output of WHIZARD and CalcHep model files has seen further improvement in this version. Also models including Dirac gauginos are supported with the new version of SARAH, and additional checks for the consistency of the implementation of new models have been created. Program summaryProgram title:SARAH Catalogue identifier: AEIB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIB_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3 22 411 No. of bytes in distributed program, including test data, etc.: 3 629 206 Distribution format: tar.gz Programming language: Mathematica. Computer: All for which Mathematica is available. Operating system: All for which Mathematica is available. Classification: 11.1, 11.6. Catalogue identifier of previous version: AEIB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 182 (2011) 808 Does the new version supersede the previous version?: Yes, the new version includes all known features of the previous version but also provides the new features mentioned below
Dirac phenomenology and hyperon-nucleus interactions
Energy Technology Data Exchange (ETDEWEB)
Mares, J; Jennings, B K [TRIUMF, Vancouver, British Columbia (Canada); Cooper, E D [Fraser Valley Univ. College, Chilliwack, British Columbia (Canada). Dept. of Physics
1993-05-01
We discuss various aspects of hyperon-nucleus interactions in the relativistic mean field theory. First, characteristics of {Lambda}, {Sigma} and {identical_to} hypernuclei, as well as multi strange baryonic objects, are investigated. The spin-orbit splittings and magnetic moments are shown to be very sensitive to the value of the tensor coupling f{omega}y. Second, optical potentials for {Lambda} and {Sigma} scattering off nuclei are developed based on a global nucleon-nucleon Dirac optical potential and SU(3) symmetry. The tensor coupling has a large effect on the predictions for the analyzing power. Third, the Dirac approach is used in the calculations of the non-mesonic decay of {Lambda} hypernuclei. The large discrepancy between the decay rates and data suggests the need for additional meson exchanges. (authors). 62 refs.,7 figs., 6 tabs.
Classical electromagnetic radiation of the Dirac electron
Lanyi, G.
1973-01-01
A wave-function-dependent four-vector potential is added to the Dirac equation in order to achieve conservation of energy and momentum for a Dirac electron and its emitted electromagnetic field. The resultant equation contains solutions which describe transitions between different energy states of the electron. As a consequence it is possible to follow the space-time evolution of such a process. This evolution is shown in the case of the spontaneous emission of an electromagnetic field by an electron bound in a hydrogen-like atom. The intensity of the radiation and the spectral distribution are calculated for transitions between two eigenstates. The theory gives a self-consistent deterministic description of some simple radiation processes without using quantum electrodynamics or the correspondence principle.
Floquet-Engineered Valleytronics in Dirac Systems.
Kundu, Arijit; Fertig, H A; Seradjeh, Babak
2016-01-08
Valley degrees of freedom offer a potential resource for quantum information processing if they can be effectively controlled. We discuss an optical approach to this problem in which intense light breaks electronic symmetries of a two-dimensional Dirac material. The resulting quasienergy structures may then differ for different valleys, so that the Floquet physics of the system can be exploited to produce highly polarized valley currents. This physics can be utilized to realize a valley valve whose behavior is determined optically. We propose a concrete way to achieve such valleytronics in graphene as well as in a simple model of an inversion-symmetry broken Dirac material. We study the effect numerically and demonstrate its robustness against moderate disorder and small deviations in optical parameters.
Crucial test of the Dirac cosmologies
International Nuclear Information System (INIS)
Steigman, G.
1978-01-01
In a cosmology consistent with the Cosmological Principle (large scale, statistical isotropy and homogeneity of the universe), a Planck spectrum is not preserved as the universe evolves unless the number of photons in a comoving volume is conserved. It is shown that a large class of cosmological models based on Dirac's Large Numbers Hypothesis (LNH) violate this constraint. The observed isotropy and spectral distribution of the microwave background radiation thus provide a crucial test of such cosmologies. After reviewing the LNH, the general evolution of radiation spectra in cosmologies consistent with the cosmological principle is outlined. It is shown that the predicted deviations from a Planck spectrum for Dirac cosmologies (as well as for ''tired-light'' cosmologies) are enormous. The Planckian (or near-Planckian) spectral form for the microwave radiation provides a crucial test, failed by such cosmologies
Excitation spectrum of correlated Dirac fermions
Jalali, Z.; Jafari, S. A.
2015-04-01
Motivated by the puzzling optical conductivity measurements in graphene, we speculate on the possible role of strong electronic correlations on the two-dimensional Dirac fermions. In this work we employ the slave-particle method to study the excitations of the Hubbard model on honeycomb lattice, away from half-filling. Since the ratio U/t ≈ 3.3 in graphene is not infinite, double occupancy is not entirely prohibited and hence a finite density of doublonscan be generated. We therefore extend the Ioff-Larkin composition rule to include a finite density of doublons. We then investigate the role played by each of these auxiliary particles in the optical absorption of strongly correlated Dirac fermions.
Dirac gauginos in low scale supersymmetry breaking
International Nuclear Information System (INIS)
Goodsell, Mark D.; Tziveloglou, Pantelis
2014-01-01
It has been claimed that Dirac gaugino masses are necessary for realistic models of low-scale supersymmetry breaking, and yet very little attention has been paid to the phenomenology of a light gravitino when gauginos have Dirac masses. We begin to address this deficit by investigating the couplings and phenomenology of the gravitino in the effective Lagrangian approach. We pay particular attention to the phenomenology of the scalar octets, where new decay channels open up. This leads us to propose a new simplified effective scenario including only light gluinos, sgluons and gravitinos, allowing the squarks to be heavy – with the possible exception of the third generation. Finally, we comment on the application of our results to Fake Split Supersymmetry
Renormalization group evolution of Dirac neutrino masses
International Nuclear Information System (INIS)
Lindner, Manfred; Ratz, Michael; Schmidt, Michael Andreas
2005-01-01
There are good reasons why neutrinos could be Majorana particles, but there exist also a number of very good reasons why neutrinos could have Dirac masses. The latter option deserves more attention and we derive therefore analytic expressions describing the renormalization group evolution of mixing angles and of the CP phase for Dirac neutrinos. Radiative corrections to leptonic mixings are in this case enhanced compared to the quark mixings because the hierarchy of neutrino masses is milder and because the mixing angles are larger. The renormalization group effects are compared to the precision of current and future neutrino experiments. We find that, in the MSSM framework, radiative corrections of the mixing angles are for large tan β comparable to the precision of future experiments
Dirac equation in Kerr space-time
Energy Technology Data Exchange (ETDEWEB)
Iyer, B R; Kumar, Arvind [Bombay Univ. (India). Dept. of Physics
1976-06-01
The weak-field low-velocity approximation of Dirac equation in Kerr space-time is investigated. The interaction terms admit of an interpretation in terms of a 'dipole-dipole' interaction in addition to coupling of spin with the angular momentum of the rotating source. The gravitational gyro-factor for spin is identified. The charged case (Kerr-Newman) is studied using minimal prescription for electromagnetic coupling in the locally intertial frame and to the leading order the standard electromagnetic gyro-factor is retrieved. A first order perturbation calculation of the shift of the Schwarzchild energy level yields the main interesting result of this work: the anomalous Zeeman splitting of the energy level of a Dirac particle in Kerr metric.
LHCb: Pilot Framework and the DIRAC WMS
Graciani, R; Casajus, A
2009-01-01
DIRAC, the LHCb community Grid solution, has pioneered the use of pilot jobs in the Grid. Pilot jobs provide a homogeneous interface to an heterogeneous set of computing resources. At the same time, pilot jobs allow to delay the scheduling decision to the last moment, thus taking into account the precise running conditions at the resource and last moment requests to the system. The DIRAC Workload Management System provides one single scheduling mechanism for jobs with very different profiles. To achieve an overall optimisation, it organizes pending jobs in task queues, both for individual users and production activities. Task queues are created with jobs having similar requirements. Following the VO policy a priority is assigned to each task queue. Pilot submission and subsequent job matching are based on these priorities following a statistical approach. Details of the implementation and the security aspects of this framework will be discussed.
Permanent Magnet Dipole for DIRAC Design Report
Vorozhtsov, Alexey
2012-01-01
Two dipole magnets including one spare unit are needed for the for the DIRAC experiment. The proposed design is a permanent magnet dipole. The design based on Sm2Co17 blocks assembled together with soft ferromagnetic pole tips. The magnet provides integrated field strength of 24.6 10-3 T×m inside the aperture of 60 mm. This Design Report summarizes the main magnetic and mechanic design parameters of the permanent dipole magnets.
Data acquisition software for DIRAC experiment
Olshevsky, V G
2001-01-01
The structure and basic processes of data acquisition software of the DIRAC experiment for the measurement of pi /sup +/ pi /sup -/ atom lifetime are described. The experiment is running on the PS accelerator of CERN. The developed software allows one to accept, record and distribute up to 3 Mbytes of data to consumers in one accelerator supercycle of 14.4 s duration. The described system is successfully in use in the experiment since its startup in 1998. (13 refs).
Data acquisition software for DIRAC experiment
Olshevsky, V.; Trusov, S.
2001-08-01
The structure and basic processes of data acquisition software of the DIRAC experiment for the measurement of π +π - atom lifetime are described. The experiment is running on the PS accelerator of CERN. The developed software allows one to accept, record and distribute up to 3 Mbytes of data to consumers in one accelerator supercycle of 14.4 s duration. The described system is successfully in use in the experiment since its startup in 1998.
Data acquisition software for DIRAC experiment
International Nuclear Information System (INIS)
Olshevsky, V.; Trusov, S.
2001-01-01
The structure and basic processes of data acquisition software of the DIRAC experiment for the measurement of π + π - atom lifetime are described. The experiment is running on the PS accelerator of CERN. The developed software allows one to accept, record and distribute up to 3 Mbytes of data to consumers in one accelerator supercycle of 14.4 s duration. The described system is successfully in use in the experiment since its startup in 1998
Quantum transport through 3D Dirac materials
Energy Technology Data Exchange (ETDEWEB)
Salehi, M. [Department of Physics, Sharif University of Technology, Tehran 11155-9161 (Iran, Islamic Republic of); Jafari, S.A., E-mail: jafari@physics.sharif.edu [Department of Physics, Sharif University of Technology, Tehran 11155-9161 (Iran, Islamic Republic of); Center of Excellence for Complex Systems and Condensed Matter (CSCM), Sharif University of Technology, Tehran 1458889694 (Iran, Islamic Republic of)
2015-08-15
Bismuth and its alloys provide a paradigm to realize three dimensional materials whose low-energy effective theory is given by Dirac equation in 3+1 dimensions. We study the quantum transport properties of three dimensional Dirac materials within the framework of Landauer–Büttiker formalism. Charge carriers in normal metal satisfying the Schrödinger equation, can be split into four-component with appropriate matching conditions at the boundary with the three dimensional Dirac material (3DDM). We calculate the conductance and the Fano factor of an interface separating 3DDM from a normal metal, as well as the conductance through a slab of 3DDM. Under certain circumstances the 3DDM appears transparent to electrons hitting the 3DDM. We find that electrons hitting the metal-3DDM interface from metallic side can enter 3DDM in a reversed spin state as soon as their angle of incidence deviates from the direction perpendicular to interface. However the presence of a second interface completely cancels this effect.
Quantum transport through 3D Dirac materials
International Nuclear Information System (INIS)
Salehi, M.; Jafari, S.A.
2015-01-01
Bismuth and its alloys provide a paradigm to realize three dimensional materials whose low-energy effective theory is given by Dirac equation in 3+1 dimensions. We study the quantum transport properties of three dimensional Dirac materials within the framework of Landauer–Büttiker formalism. Charge carriers in normal metal satisfying the Schrödinger equation, can be split into four-component with appropriate matching conditions at the boundary with the three dimensional Dirac material (3DDM). We calculate the conductance and the Fano factor of an interface separating 3DDM from a normal metal, as well as the conductance through a slab of 3DDM. Under certain circumstances the 3DDM appears transparent to electrons hitting the 3DDM. We find that electrons hitting the metal-3DDM interface from metallic side can enter 3DDM in a reversed spin state as soon as their angle of incidence deviates from the direction perpendicular to interface. However the presence of a second interface completely cancels this effect
The Integration of CloudStack and OCCI/OpenNebula with DIRAC
International Nuclear Information System (INIS)
Méndez Muñoz, Víctor; Merino Arévalo, Gonzalo; Fernández Albor, Víctor; Saborido Silva, Juan José; Graciani Diaz, Ricardo; Casajús Ramo, Adriàn; Fernández Pena, Tomás
2012-01-01
The increasing availability of Cloud resources is arising as a realistic alternative to the Grid as a paradigm for enabling scientific communities to access large distributed computing resources. The DIRAC framework for distributed computing is an easy way to efficiently access to resources from both systems. This paper explains the integration of DIRAC with two open-source Cloud Managers: OpenNebula (taking advantage of the OCCI standard) and CloudStack. These are computing tools to manage the complexity and heterogeneity of distributed data center infrastructures, allowing to create virtual clusters on demand, including public, private and hybrid clouds. This approach has required to develop an extension to the previous DIRAC Virtual Machine engine, which was developed for Amazon EC2, allowing the connection with these new cloud managers. In the OpenNebula case, the development has been based on the CernVM Virtual Software Appliance with appropriate contextualization, while in the case of CloudStack, the infrastructure has been kept more general, which permits other Virtual Machine sources and operating systems being used. In both cases, CernVM File System has been used to facilitate software distribution to the computing nodes. With the resulting infrastructure, the cloud resources are transparent to the users through a friendly interface, like the DIRAC Web Portal. The main purpose of this integration is to get a system that can manage cloud and grid resources at the same time. This particular feature pushes DIRAC to a new conceptual denomination as interware, integrating different middleware. Users from different communities do not need to care about the installation of the standard software that is available at the nodes, nor the operating system of the host machine which is transparent to the user. This paper presents an analysis of the overhead of the virtual layer, doing some tests to compare the proposed approach with the existing Grid solution. License
Micromagnetic sensors and Dirac fermions in HgTe heterostructures
Energy Technology Data Exchange (ETDEWEB)
Buettner, Bastian
2012-08-06
cross-section of (100.20) nm{sup 2} confirms the expected resolution ability, extracted from the noise of the sensor. The observed high signal-to-noise ratio validates the detection limit of this sensor in terms of geometry. This would be reached for a magnet (same material) with quadratic crosssection for an edge length of 3.3 nm. Moreover, the feasibility of this sensor for operation in a wide temperature range (T=mK..>200 K) and high magnetic fields has been confirmed. The second micromagnetic sensor is the micro-SQUID (micro-Superconducting-QUantum-Interference-Device) based on niobium. The typical sensor area of the devices built in this work was (1.0.1.0) {mu}m{sup 2}, with constrictions of about 20 nm. The characterization of this device demonstrates an amazing field sensitivity (regarding its size) of {delta}B<1 {mu}T. Even though the sensor was 25 times larger than the best micro-Hall sensor, it provided an excellent flux resolution in the order of {delta}{Phi}{approx}5.10{sup -4} {Phi}{sub 0} and a similar magnetic moment resolution of {delta}M{approx}10{sup 2} {mu}{sub B}. Furthermore, the introduction of an ellipsoidal permalloy magnet (axes: 200 nm and 400 nm, thickness 30 nm) substantiates the suitability for the detection of minuscule, localized magnetic fields. The second part of the thesis deals with the peculiar transport properties of HgTe quantum wells. These rely on the linear contribution to the band structure inherent to the heterostructure. Therefore the system can be described by an effective Dirac Hamiltonian, whose Dirac mass is tunable by the variation of the quantum well thickness. By fabrication and characterization of a systematical series of substrates, a system with vanishing Dirac mass (zero energy gap) has been confirmed. This heterostructure therefore resembles graphene (a monolayer of graphite), with the difference of exhibiting only one valley in the energy dispersion of the Brillouin zone. Thus parasitical intervalley scattering
Micromagnetic sensors and Dirac fermions in HgTe heterostructures
International Nuclear Information System (INIS)
Buettner, Bastian
2012-01-01
, extracted from the noise of the sensor. The observed high signal-to-noise ratio validates the detection limit of this sensor in terms of geometry. This would be reached for a magnet (same material) with quadratic crosssection for an edge length of 3.3 nm. Moreover, the feasibility of this sensor for operation in a wide temperature range (T=mK..>200 K) and high magnetic fields has been confirmed. The second micromagnetic sensor is the micro-SQUID (micro-Superconducting-QUantum-Interference-Device) based on niobium. The typical sensor area of the devices built in this work was (1.0.1.0) μm 2 , with constrictions of about 20 nm. The characterization of this device demonstrates an amazing field sensitivity (regarding its size) of δB -4 Φ 0 and a similar magnetic moment resolution of δM∼10 2 μ B . Furthermore, the introduction of an ellipsoidal permalloy magnet (axes: 200 nm and 400 nm, thickness 30 nm) substantiates the suitability for the detection of minuscule, localized magnetic fields. The second part of the thesis deals with the peculiar transport properties of HgTe quantum wells. These rely on the linear contribution to the band structure inherent to the heterostructure. Therefore the system can be described by an effective Dirac Hamiltonian, whose Dirac mass is tunable by the variation of the quantum well thickness. By fabrication and characterization of a systematical series of substrates, a system with vanishing Dirac mass (zero energy gap) has been confirmed. This heterostructure therefore resembles graphene (a monolayer of graphite), with the difference of exhibiting only one valley in the energy dispersion of the Brillouin zone. Thus parasitical intervalley scattering cannot occur. The existence of this system has been proven by the agreement of theoretical predictions, based on widely accepted band structure calculations with the experiment (Landau level dispersion, conductivity). Furthermore, another particularity of the band structure - the transition from
Micromagnetic sensors and Dirac fermions in HgTe heterostructures
Energy Technology Data Exchange (ETDEWEB)
Buettner, Bastian
2012-08-06
nanomagnet with a cross-section of (100.20) nm{sup 2} confirms the expected resolution ability, extracted from the noise of the sensor. The observed high signal-to-noise ratio validates the detection limit of this sensor in terms of geometry. This would be reached for a magnet (same material) with quadratic crosssection for an edge length of 3.3 nm. Moreover, the feasibility of this sensor for operation in a wide temperature range (T=mK..>200 K) and high magnetic fields has been confirmed. The second micromagnetic sensor is the micro-SQUID (micro-Superconducting-QUantum-Interference-Device) based on niobium. The typical sensor area of the devices built in this work was (1.0.1.0) {mu}m{sup 2}, with constrictions of about 20 nm. The characterization of this device demonstrates an amazing field sensitivity (regarding its size) of {delta}B<1 {mu}T. Even though the sensor was 25 times larger than the best micro-Hall sensor, it provided an excellent flux resolution in the order of {delta}{Phi}{approx}5.10{sup -4} {Phi}{sub 0} and a similar magnetic moment resolution of {delta}M{approx}10{sup 2} {mu}{sub B}. Furthermore, the introduction of an ellipsoidal permalloy magnet (axes: 200 nm and 400 nm, thickness 30 nm) substantiates the suitability for the detection of minuscule, localized magnetic fields. The second part of the thesis deals with the peculiar transport properties of HgTe quantum wells. These rely on the linear contribution to the band structure inherent to the heterostructure. Therefore the system can be described by an effective Dirac Hamiltonian, whose Dirac mass is tunable by the variation of the quantum well thickness. By fabrication and characterization of a systematical series of substrates, a system with vanishing Dirac mass (zero energy gap) has been confirmed. This heterostructure therefore resembles graphene (a monolayer of graphite), with the difference of exhibiting only one valley in the energy dispersion of the Brillouin zone. Thus parasitical intervalley
Wave Functions for Time-Dependent Dirac Equation under GUP
Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen
2018-04-01
In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009
Full utilization of semi-Dirac cones in photonics
Yasa, Utku G.; Turduev, Mirbek; Giden, Ibrahim H.; Kurt, Hamza
2018-05-01
In this study, realization and applications of anisotropic zero-refractive-index materials are proposed by exposing the unit cells of photonic crystals that exhibit Dirac-like cone dispersion to rotational symmetry reduction. Accidental degeneracy of two Bloch modes in the Brillouin zone center of two-dimensional C2-symmetric photonic crystals gives rise to the semi-Dirac cone dispersion. The proposed C2-symmetric photonic crystals behave as epsilon-and-mu-near-zero materials (ɛeff≈ 0 , μeff≈ 0 ) along one propagation direction, but behave as epsilon-near-zero material (ɛeff≈ 0 , μeff≠ 0 ) for the perpendicular direction at semi-Dirac frequency. By extracting the effective medium parameters of the proposed C4- and C2-symmetric periodic media that exhibit Dirac-like and semi-Dirac cone dispersions, intrinsic differences between isotropic and anisotropic materials are investigated. Furthermore, advantages of utilizing semi-Dirac cone materials instead of Dirac-like cone materials in photonic applications are demonstrated in both frequency and time domains. By using anisotropic transmission behavior of the semi-Dirac materials, photonic application concepts such as beam deflectors, beam splitters, and light focusing are proposed. Furthermore, to the best of our knowledge, semi-Dirac cone dispersion is also experimentally demonstrated for the first time by including negative, zero, and positive refraction states of the given material.
Quasiparticle dynamics in reshaped helical Dirac cone of topological insulators.
Miao, Lin; Wang, Z F; Ming, Wenmei; Yao, Meng-Yu; Wang, Meixiao; Yang, Fang; Song, Y R; Zhu, Fengfeng; Fedorov, Alexei V; Sun, Z; Gao, C L; Liu, Canhua; Xue, Qi-Kun; Liu, Chao-Xing; Liu, Feng; Qian, Dong; Jia, Jin-Feng
2013-02-19
Topological insulators and graphene present two unique classes of materials, which are characterized by spin-polarized (helical) and nonpolarized Dirac cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in topological insulators. Here, we report the experimental observation of the renormalized quasiparticle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi(2)Te(3) substrate from angle-resolved photoemission spectroscopy. First-principles band calculations indicate that the quasiparticle spectra are likely associated with the hybridization between the extrinsic substrate-induced Dirac states of Bi bilayer and the intrinsic surface Dirac states of Bi(2)Te(3) film at close energy proximity. Without such hybridization, only single-particle Dirac spectra are observed in a single Bi bilayer grown on Bi(2)Se(3), where the extrinsic Dirac states Bi bilayer and the intrinsic Dirac states of Bi(2)Se(3) are well separated in energy. The possible origins of many-body interactions are discussed. Our findings provide a means to manipulate topological surface states.
Prototype of a production system for Cherenkov Telescope Array with DIRAC
International Nuclear Information System (INIS)
Arrabito, L; Bregeon, J; Haupt, A; Graciani Diaz, R; Stagni, F; Tsaregorodtsev, A
2015-01-01
The Cherenkov Telescope Array (CTA) — an array of many tens of Imaging Atmospheric Cherenkov Telescopes deployed on an unprecedented scale — is the next generation instrument in the field of very high energy gamma-ray astronomy. CTA will operate as an open observatory providing data products to the scientific community. An average data stream of about 10 GB/s for about 1000 hours of observation per year, thus producing several PB/year, is expected. Large CPU time is required for data-processing as well for massive Monte Carlo simulations needed for detector calibration purposes. The current CTA computing model is based on a distributed infrastructure for the archive and the data off-line processing. In order to manage the off-line data-processing in a distributed environment, CTA has evaluated the DIRAC (Distributed Infrastructure with Remote Agent Control) system, which is a general framework for the management of tasks over distributed heterogeneous computing environments. In particular, a production system prototype has been developed, based on the two main DIRAC components, i.e. the Workload Management and Data Management Systems. After three years of successful exploitation of this prototype, for simulations and analysis, we proved that DIRAC provides suitable functionalities needed for the CTA data processing. Based on these results, the CTA development plan aims to achieve an operational production system, based on the DIRAC Workload Management System, to be ready for the start of CTA operation phase in 2017-2018. One more important challenge consists of the development of a fully automatized execution of the CTA workflows. For this purpose, we have identified a third DIRAC component, the so-called Transformation System, which offers very interesting functionalities to achieve this automatisation. The Transformation System is a ’data-driven’ system, allowing to automatically trigger data-processing and data management operations according to pre
Local moment formation in Dirac electrons
International Nuclear Information System (INIS)
Mashkoori, M; Mahyaeh, I; Jafari, S A
2015-01-01
Elemental bismuth and its compounds host strong spin-orbit interaction which is at the heart of topologically non-trivial alloys based on bismuth. These class of materials are described in terms of 4x4 matrices at each v point where spin and orbital labels of the underlying electrons are mixed. In this work we investigate the single impurity Anderson model (SIAM) within a mean field approximation to address the nature of local magnetic moment formation in a generic Dirac Hamiltonian. Despite the spin-mixing in the Hamiltonian, within the Hartree approximation it turns out that the impuritys Green function is diagonal in spin label. In the three dimensional Dirac materials defined over a bandwidth D and spin-orbit parameter γ, that hybridizes with impurity through V, a natural dimensionless parameter V 2 D/2πγ 3 emerges. So neither the hybridization strength, V, nor the spin-orbit coupling γ, but a combination thereof governs the phase diagram. By tuning chemical potential and the impurity level, we present phase diagram for various values of Hubbard U. Numerical results suggest that strong spin-orbit coupling enhances the local moment formation both in terms of its strength and the area of the local moment region. In the case that we tune the chemical potential in a similar way as normal metal we find that magnetic region is confined to μ ≥ ε 0 , in sharp contrast to 2D Dirac fermions. If one fixes the chemical potential and tunes the impurity level, phase diagram has two magnetic regions which corresponds to hybridization of impurity level with lower and upper bands. (paper)
General-Covariant Quantum Mechanics of Dirac Particle in Curved Space-Times
International Nuclear Information System (INIS)
Tagirov, Eh.A.
1994-01-01
A general covariant analog of the standard non-relativistic Quantum Mechanics with relativistic corrections in normal geodesic frames in the general Riemannian space-time is constructed for the Dirac particle. Not only the Pauli equation with hermitian Hamiltonian and the pre-Hilbert structure of space of its solutions but also the matrix elements of hermitian operators of momentum, (curvilinear) spatial coordinates and spin of the particle are deduced as general-covariant asymptotic approximation in c -2 , c being the velocity of light, to their naturally determined general-relativistic pre images. It is shown that the Hamiltonian in the Pauli equation originated by the Dirac equation is unitary equivalent to the operator of energy, originated by the metric energy-momentum tensor of the spinor field. Commutation and other properties of the observables connected with the considered change of geometrical background of Quantum Mechanics are briefly discussed. 7 refs
The Dirac distorted wave Born approximation
International Nuclear Information System (INIS)
Cooper, T.; Sherif, H.S.; Johansson, J.; Sawafta, R.I.
1985-02-01
The purpose of this investigation is to illuminate the assumptions which are made when one writes down a Dirac DWBA matrix element. Due to the strong nature of the nucleon-nucleon potentials it is difficult to justify some of the steps involved in the general case; however by limiting ourselves to situations where only one (interacting) nucleon is present we can side-step this difficulty. We conclude the excellent agreement with the experiment justifies, a posteriori, the procedure, however we would like to remind the reader that, at least for proton inelastic scattering to collective states, the same quality of agreement can be obtained purely within a Schrodinger formalism
Dirac gauginos, gauge mediation and unification
International Nuclear Information System (INIS)
Benakli, K.
2010-03-01
We investigate the building of models with Dirac gauginos and perturbative gauge coupling unification. Here, in contrast to the MSSM, additional fields are required for unification, and these can naturally play the role of the messengers of supersymmetry breaking. We present a framework within which such models can be constructed, including the constraints that the messenger sector must satisfy; and the renormalisation group equations for the soft parameters, which differ from those of the MSSM. For illustration, we provide the spectrum at the electroweak scale for explicit models whose gauge couplings unify at the scale predicted by heterotic strings. (orig.)
Dirac gauginos, gauge mediation and unification
Energy Technology Data Exchange (ETDEWEB)
Benakli, K. [UPMC Univ. Paris 06 (France). Laboratoire de Physique Theorique et Hautes Energies, CNRS; Goodsell, M.D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2010-03-15
We investigate the building of models with Dirac gauginos and perturbative gauge coupling unification. Here, in contrast to the MSSM, additional fields are required for unification, and these can naturally play the role of the messengers of supersymmetry breaking. We present a framework within which such models can be constructed, including the constraints that the messenger sector must satisfy; and the renormalisation group equations for the soft parameters, which differ from those of the MSSM. For illustration, we provide the spectrum at the electroweak scale for explicit models whose gauge couplings unify at the scale predicted by heterotic strings. (orig.)
Dirac Gauginos, Gauge Mediation and Unification
Benakli, K
2010-01-01
We investigate the building of models with Dirac gauginos and perturbative gauge coupling unification. Here, in contrast to the MSSM, additional fields are required for unification, and these can naturally play the role of the messengers of supersymmetry breaking. We present a framework within which such models can be constructed, including the constraints that the messenger sector must satisfy; and the renormalisation group equations for the soft parameters, which differ from those of the MSSM. For illustration, we provide the spectrum at the electroweak scale for explicit models whose gauge couplings unify at the scale predicted by heterotic strings.
Incomplete Dirac reduction of constrained Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Chandre, C., E-mail: chandre@cpt.univ-mrs.fr
2015-10-15
First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.
Dispersionless wave packets in Dirac materials
Czech Academy of Sciences Publication Activity Database
Jakubský, Vít; Tušek, M.
2017-01-01
Roč. 378, MAR (2017), s. 171-182 ISSN 0003-4916 R&D Projects: GA ČR(CZ) GJ15-07674Y; GA ČR GA17-01706S Institutional support: RVO:61389005 Keywords : quantum systems * wave packets * dispersion * dirac materials Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 2.465, year: 2016
Dirac's equation and the nature of quantum field theory
International Nuclear Information System (INIS)
Plotnitsky, Arkady
2012-01-01
This paper re-examines the key aspects of Dirac's derivation of his relativistic equation for the electron in order advance our understanding of the nature of quantum field theory. Dirac's derivation, the paper argues, follows the key principles behind Heisenberg's discovery of quantum mechanics, which, the paper also argues, transformed the nature of both theoretical and experimental physics vis-à-vis classical physics and relativity. However, the limit theory (a crucial consideration for both Dirac and Heisenberg) in the case of Dirac's theory was quantum mechanics, specifically, Schrödinger's equation, while in the case of quantum mechanics, in Heisenberg's version, the limit theory was classical mechanics. Dirac had to find a new equation, Dirac's equation, along with a new type of quantum variables, while Heisenberg, to find new theory, was able to use the equations of classical physics, applied to different, quantum-mechanical variables. In this respect, Dirac's task was more similar to that of Schrödinger in his work on his version of quantum mechanics. Dirac's equation reflects a more complex character of quantum electrodynamics or quantum field theory in general and of the corresponding (high-energy) experimental quantum physics vis-à-vis that of quantum mechanics and the (low-energy) experimental quantum physics. The final section examines this greater complexity and its implications for fundamental physics.
Special function solutions of the free particle Dirac equation
International Nuclear Information System (INIS)
Strange, P
2012-01-01
The Dirac equation is one of the fundamental equations in physics. Here we present and discuss two novel solutions of the free particle Dirac equation. These solutions have an exact analytical form in terms of Airy or Mathieu functions and exhibit unexpected properties including an enhanced Doppler effect, accelerating wavefronts and solutions with a degree of localization. (paper)
On oscillations of neutrinos with Dirac and Majorana masses
International Nuclear Information System (INIS)
Bilenky, S.M.; Hosek, J.; Petcov, S.T.; Bylgarska Akademiya na Naukite, Sofia)
1980-01-01
Pontecorvo neutrino beam oscillations are discussed assuming both Dirac and Majorana neutrino mass terms. It is proved that none of possible experiments on neutrino oscillations, including those on effects of CP violation, can distinguish between these two possibilities. Neutrino oscillations with concomitant Dirac and Majorana mass terms are also considered
Equivalence of Dirac quantization and Schwinger's action principle quantization
International Nuclear Information System (INIS)
Das, A.; Scherer, W.
1987-01-01
We show that the method of Dirac quantization is equivalent to Schwinger's action principle quantization. The relation between the Lagrange undetermined multipliers in Schwinger's method and Dirac's constraint bracket matrix is established and it is explicitly shown that the two methods yield identical (anti)commutators. This is demonstrated in the non-trivial example of supersymmetric quantum mechanics in superspace. (orig.)
Upper-Division Student Difficulties with the Dirac Delta Function
Wilcox, Bethany R.; Pollock, Steven J.
2015-01-01
The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them.…
Multi-component bi-Hamiltonian Dirac integrable equations
Energy Technology Data Exchange (ETDEWEB)
Ma Wenxiu [Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700 (United States)], E-mail: mawx@math.usf.edu
2009-01-15
A specific matrix iso-spectral problem of arbitrary order is introduced and an associated hierarchy of multi-component Dirac integrable equations is constructed within the framework of zero curvature equations. The bi-Hamiltonian structure of the obtained Dirac hierarchy is presented be means of the variational trace identity. Two examples in the cases of lower order are computed.
The algebraic manipulation program DIRAC on IBM personal computers
International Nuclear Information System (INIS)
Grozin, A.G.; Perlt, H.
1989-01-01
The version DIRAC (2.2) for IBM compatible personal computers is described. It is designed to manipulate algebraically with polynomials and tensors. After a short introduction concerning implementation and usage on personal computers an example program is given. It contains a detailed user's guide to DIRAC (2.2) and, additionally some useful applications. 4 refs
A matricial approach for the Dirac-Kahler formalism
International Nuclear Information System (INIS)
Goto, M.
1987-01-01
A matricial approach for the Dirac-Kahler formalism is considered. It is shown that the matrical approach i) brings a great computational simplification compared to the common use of differential forms and that ii) by an appropriate choice of notation, it can be extended to the lattice, including a matrix Dirac-Kahler equation. (author) [pt
Dirac in 20th century physics: a centenary assessment
International Nuclear Information System (INIS)
Sanyuk, Valerii I; Sukhanov, Alexander D
2003-01-01
Current views on Dirac's creative heritage and on his role in the formation and development of quantum physics and in shaping the physical picture of the world are discussed. Dirac's fundamental ideas in later life (1948 - 1984) and their current development are given considerable attention. (from the history of physics)
Remarks about singular solutions to the Dirac equation
International Nuclear Information System (INIS)
Uhlir, M.
1975-01-01
In the paper singular solutions of the Dirac equation are investigated. They are derived in the Lorentz-covariant way of functions proportional to static multipole fields of scalar and (or) electromagnetic fields and of regular solutions of the Dirac equations. The regularization procedure excluding divergences of total energy, momentum and angular momentum of the spinor field considered is proposed
Graphene Dirac point tuned by ferroelectric polarization field
Wang, Xudong; Chen, Yan; Wu, Guangjian; Wang, Jianlu; Tian, Bobo; Sun, Shuo; Shen, Hong; Lin, Tie; Hu, Weida; Kang, Tingting; Tang, Minghua; Xiao, Yongguang; Sun, Jinglan; Meng, Xiangjian; Chu, Junhao
2018-04-01
Graphene has received numerous attention for future nanoelectronics and optoelectronics. The Dirac point is a key parameter of graphene that provides information about its carrier properties. There are lots of methods to tune the Dirac point of graphene, such as chemical doping, impurities, defects, and disorder. In this study, we report a different approach to tune the Dirac point of graphene using a ferroelectric polarization field. The Dirac point can be adjusted to near the ferroelectric coercive voltage regardless its original position. We have ensured this phenomenon by temperature-dependent experiments, and analyzed its mechanism with the theory of impurity correlation in graphene. Additionally, with the modulation of ferroelectric polymer, the current on/off ratio and mobility of graphene transistor both have been improved. This work provides an effective method to tune the Dirac point of graphene, which can be readily used to configure functional devices such as p-n junctions and inverters.
Optical analogue of relativistic Dirac solitons in binary waveguide arrays
Energy Technology Data Exchange (ETDEWEB)
Tran, Truong X., E-mail: truong.tran@mpl.mpg.de [Department of Physics, Le Quy Don University, 236 Hoang Quoc Viet str., 10000 Hanoi (Viet Nam); Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen (Germany); Longhi, Stefano [Department of Physics, Politecnico di Milano and Istituto di Fotonica e Nanotecnologie del Consiglio Nazionale delle Ricerche, Piazza L. da Vinci 32, I-20133 Milano (Italy); Biancalana, Fabio [Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen (Germany); School of Engineering and Physical Sciences, Heriot-Watt University, EH14 4AS Edinburgh (United Kingdom)
2014-01-15
We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory. -- Highlights: •An optical analogue of Dirac solitons in nonlinear binary waveguide arrays is suggested. •Analytical solutions to pseudo-relativistic solitons are presented. •A correspondence of optical coupled-mode equations with the nonlinear relativistic Dirac equation is established.
Bosonic Analogue of Dirac Composite Fermi Liquid
Mross, David; Alicea, Jason; Motrunich, Olexei
The status of particle-hole symmetry has long posed a challenge to the theory of the quantum Hall effect. It is expected to be present in the half-filled Landau level, but is absent in the conventional field theory, i.e., the composite Fermi liquid. Recently, Son proposed an alternative, explicitly particle-hole symmetric theory which features composite fermions that exhibit a Dirac dispersion. In my talk, I will introduce an analogous particle-hole-symmetric metallic state of bosons at odd-integer filling. This state hosts composite fermions whose energy dispersion features a quadratic band touching and corresponding 2 Ï Berry flux, protected by particle-hole and discrete rotation symmetries. As in the Dirac composite Fermi liquid introduced by Son, breaking particle-hole symmetry recovers the familiar Chern-Simons theory. I will discuss realizations of this phase both in 2D and on bosonic topological insulator surfaces, as well as its signatures in experiments and simulations.
Veselago focusing of anisotropic massless Dirac fermions
Zhang, Shu-Hui; Yang, Wen; Peeters, F. M.
2018-05-01
Massless Dirac fermions (MDFs) emerge as quasiparticles in various novel materials such as graphene and topological insulators, and they exhibit several intriguing properties, of which Veselago focusing is an outstanding example with a lot of possible applications. However, up to now Veselago focusing merely occurred in p-n junction devices based on the isotropic MDF, which lacks the tunability needed for realistic applications. Here, motivated by the emergence of novel Dirac materials, we investigate the propagation behaviors of anisotropic MDFs in such a p-n junction structure. By projecting the Hamiltonian of the anisotropic MDF to that of the isotropic MDF and deriving an exact analytical expression for the propagator, precise Veselago focusing is demonstrated without the need for mirror symmetry of the electron source and its focusing image. We show a tunable focusing position that can be used in a device to probe masked atom-scale defects. This study provides an innovative concept to realize Veselago focusing relevant for potential applications, and it paves the way for the design of novel electron optics devices by exploiting the anisotropic MDF.
White dwarfs, the galaxy and Dirac's cosmology
International Nuclear Information System (INIS)
Stothers, R.
1976-01-01
Reference is made to the apparent absence, or deficiency, of white dwarfs fainter than about 10 -4 L solar mass. An explanation is here proposed on the basis of Dirac's cosmological hypothesis that the gravitational constant, G, has varied with the time elapsed since the beginning of the expansion of the Universe as t -1 and the number of particles in the Universe has increases as t 2 , if the measurements are made in atomic units. For a white dwarf the Chandrasekhar mass limit is a collection of fundamental constants proportional to Gsup(-3/2) and therefore increases with time as tsup(3/2). In the 'additive' version of Dirac's theory the actual mass, M, of a relatively small object like a star remains essentially unchanged by the creation of new matter in the Universe and hence a white dwarf will become more stable with the course of time; but in the 'multiplicative' version of the theory, M increases as t 2 and may eventually exceed the Chandrasekhar limit, and if this happens, gravitational collapse of the white dwarf into an invisible black hole or neutron star will quickly occur. It is considered interesting to find whether the 'multiplicative' theory may have a bearing on the apparent deficiency of faint white dwarfs, and to consider whether there are any possible consequences for galactic evolution. This is here discussed. (U.K.)
White dwarfs, the galaxy and Dirac's cosmology
Energy Technology Data Exchange (ETDEWEB)
Stothers, R [National Aeronautics and Space Administration, Greenbelt, Md. (USA). Goddard Space Flight Center
1976-08-05
Reference is made to the apparent absence, or deficiency, of white dwarfs fainter than about 10/sup -4/L solar mass. An explanation is here proposed on the basis of Dirac's cosmological hypothesis that the gravitational constant, G, has varied with the time elapsed since the beginning of the expansion of the Universe as t/sup -1/ and the number of particles in the Universe has increases as t/sup 2/, if the measurements are made in atomic units. For a white dwarf the Chandrasekhar mass limit is a collection of fundamental constants proportional to Gsup(-3/2) and therefore increases with time as tsup(3/2). In the 'additive' version of Dirac's theory the actual mass, M, of a relatively small object like a star remains essentially unchanged by the creation of new matter in the Universe and hence a white dwarf will become more stable with the course of time; but in the 'multiplicative' version of the theory, M increases as t/sup 2/ and may eventually exceed the Chandrasekhar limit, and if this happens, gravitational collapse of the white dwarf into an invisible black hole or neutron star will quickly occur. It is considered interesting to find whether the 'multiplicative' theory may have a bearing on the apparent deficiency of faint white dwarfs, and to consider whether there are any possible consequences for galactic evolution. This is here discussed.
Dirac-Kähler approach connected to quantum mechanics in Grassmann space
Mankoc Borstnik, N.
2000-01-01
We compare the way one of us got spinors out of fields, which are a priori antisymmetric tensor fields, to the Dirac-Kähler rewriting. Since using our Grassmann formulation is simple it may be useful in describing the Dirac-Kähler formulation of spinors and in generalizing it to vector internal degrees of freedom and to charges. The ``cheat'' concerning the Lorentz transformations for spinors is the same in both cases and is put clearly forward in the Grassmann formulation. Also the generalizations are clearly pointed out. The discrete symmetries are discussed, in particular the appearance of two kinds of the time-reversal operators as well as the unavoidability of four families.
Three-Dimensional Dirac Oscillator with Minimal Length: Novel Phenomena for Quantized Energy
Directory of Open Access Journals (Sweden)
Malika Betrouche
2013-01-01
Full Text Available We study quantum features of the Dirac oscillator under the condition that the position and the momentum operators obey generalized commutationrelations that lead to the appearance of minimal length with the order of the Planck length, ∆xmin=ℏ3β+β′, where β and β′ are two positive small parameters. Wave functions of the system and the corresponding energy spectrum are derived rigorously. The presence of the minimal length accompanies a quadratic dependence of the energy spectrum on quantum number n, implying the property of hard confinement of the system. It is shown that the infinite degeneracy of energy levels appearing in the usual Dirac oscillator is vanished by the presence of the minimal length so long as β≠0. Not only in the nonrelativistic limit but also in the limit of the standard case (β=β′=0, our results reduce to well known usual ones.
BelleII@home: Integrate volunteer computing resources into DIRAC in a secure way
Wu, Wenjing; Hara, Takanori; Miyake, Hideki; Ueda, Ikuo; Kan, Wenxiao; Urquijo, Phillip
2017-10-01
The exploitation of volunteer computing resources has become a popular practice in the HEP computing community as the huge amount of potential computing power it provides. In the recent HEP experiments, the grid middleware has been used to organize the services and the resources, however it relies heavily on the X.509 authentication, which is contradictory to the untrusted feature of volunteer computing resources, therefore one big challenge to utilize the volunteer computing resources is how to integrate them into the grid middleware in a secure way. The DIRAC interware which is commonly used as the major component of the grid computing infrastructure for several HEP experiments proposes an even bigger challenge to this paradox as its pilot is more closely coupled with operations requiring the X.509 authentication compared to the implementations of pilot in its peer grid interware. The Belle II experiment is a B-factory experiment at KEK, and it uses DIRAC for its distributed computing. In the project of BelleII@home, in order to integrate the volunteer computing resources into the Belle II distributed computing platform in a secure way, we adopted a new approach which detaches the payload running from the Belle II DIRAC pilot which is a customized pilot pulling and processing jobs from the Belle II distributed computing platform, so that the payload can run on volunteer computers without requiring any X.509 authentication. In this approach we developed a gateway service running on a trusted server which handles all the operations requiring the X.509 authentication. So far, we have developed and deployed the prototype of BelleII@home, and tested its full workflow which proves the feasibility of this approach. This approach can also be applied on HPC systems whose work nodes do not have outbound connectivity to interact with the DIRAC system in general.
Topological insulators Dirac equation in condensed matter
Shen, Shun-Qing
2017-01-01
This new edition presents a unified description of these insulators from one to three dimensions based on the modified Dirac equation. It derives a series of solutions of the bound states near the boundary, and describes the current status of these solutions. Readers are introduced to topological invariants and their applications to a variety of systems from one-dimensional polyacetylene, to two-dimensional quantum spin Hall effect and p-wave superconductors, three-dimensional topological insulators and superconductors or superfluids, and topological Weyl semimetals, helping them to better understand this fascinating field. To reflect research advances in topological insulators, several parts of the book have been updated for the second edition, including: Spin-Triplet Superconductors, Superconductivity in Doped Topological Insulators, Detection of Majorana Fermions and so on. In particular, the book features a new chapter on Weyl semimetals, a topic that has attracted considerable attention and has already b...
New experimental proposals for testing Dirac equation
International Nuclear Information System (INIS)
Camacho, Abel; Macias, Alfredo
2004-01-01
The advent of phenomenological quantum gravity has ushered us in the search for experimental tests of the deviations from general relativity predicted by quantum gravity or by string theories, and as a by-product of this quest the possible modifications that some field equations, for instance, the motion equation of spin-1/2-particles, have already been considered. In the present Letter a modified Dirac equation, whose extra term embraces a second-order time derivative, is taken as mainstay, and three different experimental proposals to detect it are put forward. The novelty in these ideas is that two of them do not fall within the extant approaches in this context, to wit, red-shift, atomic interferometry, or Hughes-Drever type-like experiments
Topological Insulators Dirac Equation in Condensed Matters
Shen, Shun-Qing
2012-01-01
Topological insulators are insulating in the bulk, but process metallic states around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, Topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field. This book is intended for researchers and graduate students working in the field of topological in...
DIRAC reliable data management for LHCb
Smith, A C
2008-01-01
DIRAC, LHCb's Grid Workload and Data Management System, utilizes WLCG resources and middleware components to perform distributed computing tasks satisfying LHCb's Computing Model. The Data Management System (DMS) handles data transfer and data access within LHCb. Its scope ranges from the output of the LHCb Online system to Grid-enabled storage for all data types. It supports metadata for these files in replica and bookkeeping catalogues, allowing dataset selection and localization. The DMS controls the movement of files in a redundant fashion whilst providing utilities for accessing all metadata. To do these tasks effectively the DMS requires complete self integrity between its components and external physical storage. The DMS provides highly redundant management of all LHCb data to leverage available storage resources and to manage transient errors in underlying services. It provides data driven and reliable distribution of files as well as reliable job output upload, utilizing VO Boxes at LHCb Tier1 sites ...
Dark matter asymmetry in supersymmetric Dirac leptogenesis
International Nuclear Information System (INIS)
Choi, Ki-Young; Chun, Eung Jin; Shin, Chang Sub
2013-01-01
We discuss asymmetric or symmetric dark matter candidate in the supersymmetric Dirac leptogenesis scenario. By introducing a singlet superfield coupling to right-handed neutrinos, the overabundance problem of dark matter can be evaded and various possibilities for dark matter candidate arise. If the singlino is the lightest supersymmetric particle (LSP), it becomes naturally asymmetric dark matter. On the other hand, the right-handed sneutrino is a symmetric dark matter candidate whose relic density can be determined by the usual thermal freeze-out process. The conventional neutralino or gravitino LSP can be also a dark matter candidate as its non-thermal production from the right-handed sneutrino can be controlled appropriately. In our scenario, the late-decay of heavy supersymmetric particles mainly produces the right-handed sneutrino and neutrino which is harmless to the standard prediction of the Big-Bang Nucleosynthesis
Topology-optimized dual-polarization Dirac cones
Lin, Zin; Christakis, Lysander; Li, Yang; Mazur, Eric; Rodriguez, Alejandro W.; Lončar, Marko
2018-02-01
We apply a large-scale computational technique, known as topology optimization, to the inverse design of photonic Dirac cones. In particular, we report on a variety of photonic crystal geometries, realizable in simple isotropic dielectric materials, which exhibit dual-polarization Dirac cones. We present photonic crystals of different symmetry types, such as fourfold and sixfold rotational symmetries, with Dirac cones at different points within the Brillouin zone. The demonstrated and related optimization techniques open avenues to band-structure engineering and manipulating the propagation of light in periodic media, with possible applications to exotic optical phenomena such as effective zero-index media and topological photonics.
Majorana mass term, Dirac neutrinos and selective neutrino oscillations
International Nuclear Information System (INIS)
Leung, C.N.
1987-01-01
In a theory of neutrino mixing via a Majorana mass term involving only the left-handed neutrinos there exist selection rules for neutrino oscillations if true Dirac and/or exactly zero mass eigenstates are present. In the case of three neutrino flavours no oscillation is allowed if the mass spectrum contains one Dirac and one nondegenerate Majorana massive neutrino. The origin of these selection rules and their implications are discussed and the number of possible CP-violating phases in the lepton mixing matrix when Dirac and Majorana mass eigenstates coexist is given. (orig.)
Strangest man the hidden life of Paul Dirac, quantum genius
Farmelo, Graham
2009-01-01
Paul Dirac was among the great scientific geniuses of the modern age. One of the discoverers of quantum mechanics, the most revolutionary theory of the past century, his contributions had a unique insight, eloquence, clarity, and mathematical power. His prediction of antimatter was one of the greatest triumphs in the history of physics. One of Einstein's most admired colleagues, Dirac was in 1933 the youngest theoretician ever to win the Nobel Prize in physics. Dirac's personality is legendary. He was an extraordinarily reserved loner, relentlessly literal-minded and appeared to have no empath
Energy Technology Data Exchange (ETDEWEB)
Costella, J P
1995-05-22
In this short note, it is argued that [p, q] {ne} i{Dirac_h}, contrary to the oiginal claims of Born and Jordan, and Dirac. Rather, [p, q] is equal to something that is infinitesimally different from i{Dirac_h}. While this difference is usually harmless, it does provide the solution of the Born-Jordan `trace paradox` of [p, q]. More recently, subtleties of a very similar form have been found to be of fundamental importance in quantum field theory. 3 refs.
A strong-topological-metal material with multiple Dirac cones
Ji, Huiwen; Pletikosić, I; Gibson, Q. D.; Sahasrabudhe, Girija; Valla, T.; Cava, R. J.
2015-01-01
We report a new, cleavable, strong-topological-metal, Zr2Te2P, which has the same tetradymite-type crystal structure as the topological insulator Bi2Te2Se. Instead of being a semiconductor, however, Zr2Te2P is metallic with a pseudogap between 0.2 and 0.7 eV above the fermi energy (EF). Inside this pseudogap, two Dirac dispersions are predicted: one is a surface-originated Dirac cone protected by time-reversal symmetry (TRS), while the other is a bulk-originated and slightly gapped Dirac cone...
Determinant of twisted chiral Dirac operator on the lattice
International Nuclear Information System (INIS)
Fosco, C.D.; Randjbar Daemi, S.
1995-04-01
Using the overlap formulation, we calculate the fermionic determinant on the lattice for chiral fermions with twisted boundary conditions in two dimensions. When the lattice spacing tends to zero we recover the results on the usual string-theory continuum calculations. (author). 13 refs
Optimised Dirac operators on the lattice. Construction, properties and applications
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, W. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik]|[Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2006-11-15
We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the epsilon-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian - the chiral condensate and the pion decay constant - from QCD simulations with extremely light quarks. (orig.)
Optimised Dirac operators on the lattice: construction, properties and applications
International Nuclear Information System (INIS)
Bietenholz, Wolfgang
2006-12-01
We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the e-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian - the chiral condensate and the pion decay constant - from QCD simulations with extremely light quarks. (author)
Optimised Dirac operators on the lattice. Construction, properties and applications
International Nuclear Information System (INIS)
Bietenholz, W.; Deutsches Elektronen-Synchrotron
2006-11-01
We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the epsilon-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian - the chiral condensate and the pion decay constant - from QCD simulations with extremely light quarks. (orig.)
Topological susceptibility from the twisted mass Dirac operator spectrum
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krzysztof [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Garcia-Ramos, Elena [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany); Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Collaboration: European Twisted Mass Collaboration
2013-12-15
We present results of our computation of the topological susceptibility with N{sub f}=2 and N{sub f}= +1+1 flavours of maximally twisted mass fermions, using the method of spectral projectors. We perform a detailed study of the quark mass dependence and discretization effects. We make an attempt to confront our data with chiral perturbation theory and extract the chiral condensate from the quark mass dependence of the topological susceptibility. We compare the value with the results of our direct computation from the slope of the mode number. We emphasize the role of autocorrelations and the necessity of long Monte Carlo runs to obtain results with good precision. We also show our results for the spectral projector computation of the ratio of renormalization constants Z{sub P}/Z{sub S}.
Topological susceptibility from the twisted mass Dirac operator spectrum
International Nuclear Information System (INIS)
Cichy, Krzysztof; Jansen, Karl; Cyprus Univ., Nicosia
2013-12-01
We present results of our computation of the topological susceptibility with N f =2 and N f = +1+1 flavours of maximally twisted mass fermions, using the method of spectral projectors. We perform a detailed study of the quark mass dependence and discretization effects. We make an attempt to confront our data with chiral perturbation theory and extract the chiral condensate from the quark mass dependence of the topological susceptibility. We compare the value with the results of our direct computation from the slope of the mode number. We emphasize the role of autocorrelations and the necessity of long Monte Carlo runs to obtain results with good precision. We also show our results for the spectral projector computation of the ratio of renormalization constants Z P /Z S .
Optimised Dirac operators on the lattice: construction, properties and applications
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, Wolfgang [Humbolt-Universitaet zu Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing (NIC)
2006-12-15
We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the e-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian - the chiral condensate and the pion decay constant - from QCD simulations with extremely light quarks. (author)
Spin force and torque in non-relativistic Dirac oscillator on a sphere
Shikakhwa, M. S.
2018-03-01
The spin force operator on a non-relativistic Dirac oscillator (in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin-orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle. When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggests that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the Zitterbewegung. It is suggested that the underlying physics that gives rise to the spin force and the Zitterbewegung is one and the same in NRDO and in systems that manifest spin Hall effect.
Pseudoclassical supergauge model for a (2 + 1) Dirac particle
International Nuclear Information System (INIS)
Gitman, D.M.; Gonsalves, A.E.; Tyhtin, I.V.
1997-01-01
A new pseudo-classical supergauge model of the Dirac particle in 2 + 1 dimensions is proposed. Two ways of its quantization are discussed. Both reproduce the minimal quantum theory of the particle. 24 refs
Magnetotransport in Layered Dirac Fermion System Coupled with Magnetic Moments
Iwasaki, Yoshiki; Morinari, Takao
2018-03-01
We theoretically investigate the magnetotransport of Dirac fermions coupled with localized moments to understand the physical properties of the Dirac material EuMnBi2. Using an interlayer hopping form, which simplifies the complicated interaction between the layers of Dirac fermions and the layers of magnetic moments in EuMnBi2, the theory reproduces most of the features observed in this system. The hysteresis observed in EuMnBi2 can be caused by the valley splitting that is induced by the spin-orbit coupling and the external magnetic field with the molecular field created by localized moments. Our theory suggests that the magnetotransport in EuMnBi2 is due to the interplay among Dirac fermions, localized moments, and spin-orbit coupling.
Using OSG Computing Resources with (iLC)Dirac
AUTHOR|(SzGeCERN)683529; Petric, Marko
2017-01-01
CPU cycles for small experiments and projects can be scarce, thus making use of all available resources, whether dedicated or opportunistic, is mandatory. While enabling uniform access to the LCG computing elements (ARC, CREAM), the DIRAC grid interware was not able to use OSG computing elements (GlobusCE, HTCondor-CE) without dedicated support at the grid site through so called 'SiteDirectors', which directly submit to the local batch system. This in turn requires additional dedicated effort for small experiments on the grid site. Adding interfaces to the OSG CEs through the respective grid middleware is therefore allowing accessing them within the DIRAC software without additional sitespecific infrastructure. This enables greater use of opportunistic resources for experiments and projects without dedicated clusters or an established computing infrastructure with the DIRAC software. To allow sending jobs to HTCondor-CE and legacy Globus computing elements inside DIRAC the required wrapper classes were develo...
Invariance properties of the Dirac equation with external electro ...
Indian Academy of Sciences (India)
. Introduction. The objective of this short paper is to investigate the invariance properties of the Dirac equation with external electro-magnetic field. There exists a large number of literatures on the problem beginning almost from the formulation ...
LHCb: Analysing DIRAC's Behavior using Model Checking with Process Algebra
Remenska, Daniela
2012-01-01
DIRAC is the Grid solution designed to support LHCb production activities as well as user data analysis. Based on a service-oriented architecture, DIRAC consists of many cooperating distributed services and agents delivering the workload to the Grid resources. Services accept requests from agents and running jobs, while agents run as light-weight components, fulfilling specific goals. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check for changes in the service states, and react to these accordingly. A characteristic of DIRAC's architecture is the relatively low complexity in the logic of each agent; the main source of complexity lies in their cooperation. These agents run concurrently, and communicate using the services' databases as a shared memory for synchronizing the state transitions. Although much effort is invested in making DIRAC reliable, entities occasionally get into inconsistent states, leadi...
Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations
Lorz, Alexander
2011-01-17
Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the dynamics of the limiting concentration points and of the weights of the Dirac masses? What is the long time asymptotics of these Dirac masses? Can several Dirac masses coexist? We will explain how these questions relate to the so-called "constrained Hamilton-Jacobi equation" and how a form of canonical equation can be established. This equation has been established assuming smoothness. Here we build a framework where smooth solutions exist and thus the full theory can be developed rigorously. We also show that our form of canonical equation comes with a kind of Lyapunov functional. Numerical simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models Darwinian evolution. © Taylor & Francis Group, LLC.
Dirac directional emission in anisotropic zero refractive index photonic crystals.
He, Xin-Tao; Zhong, Yao-Nan; Zhou, You; Zhong, Zhi-Chao; Dong, Jian-Wen
2015-08-14
A certain class of photonic crystals with conical dispersion is known to behave as isotropic zero-refractive-index medium. However, the discrete building blocks in such photonic crystals are limited to construct multidirectional devices, even for high-symmetric photonic crystals. Here, we show multidirectional emission from low-symmetric photonic crystals with semi-Dirac dispersion at the zone center. We demonstrate that such low-symmetric photonic crystal can be considered as an effective anisotropic zero-refractive-index medium, as long as there is only one propagation mode near Dirac frequency. Four kinds of Dirac multidirectional emitters are achieved with the channel numbers of five, seven, eleven, and thirteen, respectively. Spatial power combination for such kind of Dirac directional emitter is also verified even when multiple sources are randomly placed in the anisotropic zero-refractive-index photonic crystal.
Dark matter scenarios in a constrained model with Dirac gauginos
Goodsell, Mark D.; Müller, Tobias; Porod, Werner; Staub, Florian
2015-01-01
We perform the first analysis of Dark Matter scenarios in a constrained model with Dirac Gauginos. The model under investigation is the Constrained Minimal Dirac Gaugino Supersymmetric Standard model (CMDGSSM) where the Majorana mass terms of gauginos vanish. However, $R$-symmetry is broken in the Higgs sector by an explicit and/or effective $B_\\mu$-term. This causes a mass splitting between Dirac states in the fermion sector and the neutralinos, which provide the dark matter candidate, become pseudo-Dirac states. We discuss two scenarios: the universal case with all scalar masses unified at the GUT scale, and the case with non-universal Higgs soft-terms. We identify different regions in the parameter space which fullfil all constraints from the dark matter abundance, the limits from SUSY and direct dark matter searches and the Higgs mass. Most of these points can be tested with the next generation of direct dark matter detection experiments.
Elastic gauge fields and Hall viscosity of Dirac magnons
Ferreiros, Yago; Vozmediano, María A. H.
2018-02-01
We analyze the coupling of elastic lattice deformations to the magnon degrees of freedom of magnon Dirac materials. For a honeycomb ferromagnet we find that, as happens in the case of graphene, elastic gauge fields appear coupled to the magnon pseudospinors. For deformations that induce constant pseudomagnetic fields, the spectrum around the Dirac nodes splits into pseudo-Landau levels. We show that when a Dzyaloshinskii-Moriya interaction is considered, a topological gap opens in the system and a Chern-Simons effective action for the elastic degrees of freedom is generated. Such a term encodes a phonon Hall viscosity response, entirely generated by quantum fluctuations of magnons living in the vicinity of the Dirac points. The magnon Hall viscosity vanishes at zero temperature, and grows as temperature is raised and the states around the Dirac points are increasingly populated.
Science in culture the life of Paul Dirac
Abbott, A
2000-01-01
The life of Paul Dirac has been used as the theme of a show held underground at the Delphi experiment at CERN. The 'Oracle of Delphi' was created as an outreach project and has been extremely successful (1 p).
Large optical conductivity of Dirac semimetal Fermi arc surface states
Shi, Li-kun; Song, Justin C. W.
2017-08-01
Fermi arc surface states, a hallmark of topological Dirac semimetals, can host carriers that exhibit unusual dynamics distinct from that of their parent bulk. Here we find that Fermi arc carriers in intrinsic Dirac semimetals possess a strong and anisotropic light-matter interaction. This is characterized by a large Fermi arc optical conductivity when light is polarized transverse to the Fermi arc; when light is polarized along the Fermi arc, Fermi arc optical conductivity is significantly muted. The large surface spectral weight is locked to the wide separation between Dirac nodes and persists as a large Drude weight of Fermi arc carriers when the system is doped. As a result, large and anisotropic Fermi arc conductivity provides a novel means of optically interrogating the topological surfaces states of Dirac semimetals.
International Nuclear Information System (INIS)
Ziino, G.
1989-01-01
We assume a strictly invariant definition of the Dirac parity operator under fermion ↔ antifermion exchange. We see that the opposite-intrinsic-parity condition then requires two opposite-mass Dirac equations for the fermion and the antifermion. This leads us to introduce an asymptotically left-handed (fermion) and right-handed (antifermion) chiral field, as just an alternative basis in the internal space spanned by the new pair of charge-conjugate Dirac fields. Hence a dual intrinsic model of a spin - 1/2 massive fermion is drawn: it predicts the coexistence of two anticommuting general varieties of conserved charges, namely a scalar variety, responsible for parity-invariant phenomenology, plus a pseudoscalar one, responsible for chiral phenomenology. In this light, CP-symmetry is seen to be nothing but P-symmetry; and a spontaneous CP-violation mechanism is also derived, that should work in any single process occurring via both scalar-and pseudoscalar-charge interactions. We show, at last, that our scheme automatically yields Weyl's one for a merely left-handed neutrino and a merely right-handed antineutrino, further assigning them the special meaning of pure pseudoscalar-charge objects. Some general consequences as regards magnetic monopoles are briefly discussed too
Quantum field theory of photon—Dirac fermion interacting system in graphene monolayer
International Nuclear Information System (INIS)
Nguyen, Bich Ha; Nguyen, Van Hieu
2016-01-01
The purpose of the present work is to elaborate quantum field theory of interacting systems comprising Dirac fermion fields in a graphene monolayer and the electromagnetic field. Since the Dirac fermions are confined in a two-dimensional plane, the interaction Hamiltonian of this system contains the projection of the electromagnetic field operator onto the plane of a graphene monolayer. Following the quantization procedure in traditional quantum electrodynamics we chose to work in the gauge determined by the weak Lorentz condition imposed on the state vectors of all physical states of the system. The explicit expression of the two-point Green function of the projection onto a graphene monolayer of a free electromagnetic field is derived. This two-point Green function and the expression of the interaction Hamiltonian together with the two-point Green functions of free Dirac fermion fields established in our previous work form the basics of the perturbation theory of the above-mentioned interacting field system. As an example, the perturbation theory is applied to the study of two-point Green functions of this interacting system of quantum fields. (paper)
Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization
Energy Technology Data Exchange (ETDEWEB)
Cortez, Jerónimo, E-mail: jacq@ciencias.unam.mx [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, México D.F. 04510 (Mexico); Elizaga Navascués, Beatriz, E-mail: beatriz.elizaga@iem.cfmac.csic.es [Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid (Spain); Martín-Benito, Mercedes, E-mail: m.martin@hef.ru.nl [Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Heyendaalseweg 135, NL-6525 AJ Nijmegen (Netherlands); Mena Marugán, Guillermo A., E-mail: mena@iem.cfmac.csic.es [Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid (Spain); Velhinho, José M., E-mail: jvelhi@ubi.pt [Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001, Covilhã (Portugal)
2017-01-15
We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.
Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization
International Nuclear Information System (INIS)
Cortez, Jerónimo; Elizaga Navascués, Beatriz; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.; Velhinho, José M.
2017-01-01
We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.
The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
International Nuclear Information System (INIS)
Contreras-Astorga, Alonso; Schulze-Halberg, Axel
2014-01-01
We introduce the confluent version of the quantum-mechanical supersymmetry formalism for the Dirac equation with a pseudoscalar potential. Application of the formalism to spectral problems is discussed, regularity conditions for the transformed potentials are derived, and normalizability of the transformed solutions is established. Our findings extend and complement former results [L. M. Nieto, A. A. Pecheritsin, and B. F. Samsonov, “Intertwining technique for the one-dimensional stationary Dirac equation,” Ann. Phys. 305, 151–189 (2003)
Topological Crystalline Insulators and Dirac Octets in Anti-perovskites
Hsieh, Timothy H.; Liu, Junwei; Fu, Liang
2014-01-01
We predict a new class of topological crystalline insulators (TCI) in the anti-perovskite material family with the chemical formula A$_3$BX. Here the nontrivial topology arises from band inversion between two $J=3/2$ quartets, which is described by a generalized Dirac equation for a "Dirac octet". Our work suggests that anti-perovskites are a promising new venue for exploring the cooperative interplay between band topology, crystal symmetry and electron correlation.
Relativistic Photoionization Computations with the Time Dependent Dirac Equation
2016-10-12
Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6795--16-9698 Relativistic Photoionization Computations with the Time Dependent Dirac... Photoionization Computations with the Time Dependent Dirac Equation Daniel F. Gordon and Bahman Hafizi Naval Research Laboratory 4555 Overlook Avenue, SW...Unclassified Unlimited Unclassified Unlimited 22 Daniel Gordon (202) 767-5036 Tunneling Photoionization Ionization of inner shell electrons by laser
Einstein-Cartan-Dirac theory in (1+2)-dimensions
Energy Technology Data Exchange (ETDEWEB)
Dereli, Tekin [Koc University, Department of Physics, Istanbul (Turkey); Oezdemir, Nese [Istanbul Technical University, Department of Physics Engineering, Istanbul (Turkey); Sert, Oezcan [Pamukkale University, Department of Physics, Denizli (Turkey)
2013-01-15
Einstein-Cartan theory is formulated in (1+2) dimensions using the algebra of exterior differential forms. A Dirac spinor is coupled to gravity and the field equations are obtained by a variational principle. The space-time torsion is found to be given algebraically in terms of a quadratic spinor condensate field. Circularly symmetric, exact solutions that collapse to AdS{sub 3} geometry in the absence of the Dirac condensate are found. (orig.)
Lie algebras for the Dirac-Clifford ring
International Nuclear Information System (INIS)
Mignaco, J.A.; Linhares, C.A.
1992-01-01
It is shown in a general way that the Dirac-Clifford ring formed by the Dirac matrices and all their products, for all even and odd spacetime dimensions D, span the cumulation algebras SU(2 D/2 ) for even D and SU(2 (D- 1 )/2 ) + SU(2 (D-1)/2 ) for odd D. Some physical consequences of these results are discussed. (author)
Neural network real time event selection for the DIRAC experiment
Kokkas, P; Tauscher, Ludwig; Vlachos, S
2001-01-01
The neural network first level trigger for the DIRAC experiment at CERN is presented. Both the neural network algorithm used and its actual hardware implementation are described. The system uses the fast plastic scintillator information of the DIRAC spectrometer. In 210 ns it selects events with two particles having low relative momentum. Such events are selected with an efficiency of more than 0.94. The corresponding rate reduction for background events is a factor of 2.5. (10 refs).
The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
Energy Technology Data Exchange (ETDEWEB)
Contreras-Astorga, Alonso, E-mail: aloncont@iun.edu; Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, E-mail: xbataxel@gmail.com [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2014-10-15
We introduce the confluent version of the quantum-mechanical supersymmetry formalism for the Dirac equation with a pseudoscalar potential. Application of the formalism to spectral problems is discussed, regularity conditions for the transformed potentials are derived, and normalizability of the transformed solutions is established. Our findings extend and complement former results [L. M. Nieto, A. A. Pecheritsin, and B. F. Samsonov, “Intertwining technique for the one-dimensional stationary Dirac equation,” Ann. Phys. 305, 151–189 (2003)].
The Dirac equation in the Lobachevsky space-time
International Nuclear Information System (INIS)
Paramonov, D.V.; Paramonova, N.N.; Shavokhina, N.S.
2000-01-01
The product of the Lobachevsky space and the time axis is termed the Lobachevsky space-time. The Lobachevsky space is considered as a hyperboloid's sheet in the four-dimensional pseudo-Euclidean space. The Dirac-Fock-Ivanenko equation is reduced to the Dirac equation in two special forms by passing from Lame basis in the Lobachevsky space to the Cartesian basis in the enveloping pseudo-Euclidean space
Simulation of Zitterbewegung by modelling the Dirac equation in Metamaterials
Ahrens, Sven; Jiang, Jun; Sun, Yong; Zhu, Shi-Yao
2015-01-01
We develop a dynamic description of an effective Dirac theory in metamaterials, in which the wavefunction is modeled by the corresponding electric and magnetic field in the metamaterial. This electro-magnetic field can be probed in the experimental setup, which means that the wavefunction of the effective theory is directly accessible by measurement. Our model is based on a plane wave expansion, which ravels the identification of Dirac spinors with single-frequency excitations of the electro-...
Nonlinear Excitations in Strongly-Coupled Fermi-Dirac Plasmas
Akbari-Moghanjoughi, M.
2012-01-01
In this paper we use the conventional quantum hydrodynamics (QHD) model in combination with the Sagdeev pseudopotential method to explore the effects of Thomas-Fermi nonuniform electron distribution, Coulomb interactions, electron exchange and ion correlation on the large-amplitude nonlinear soliton dynamics in Fermi-Dirac plasmas. It is found that in the presence of strong interactions significant differences in nonlinear wave dynamics of Fermi-Dirac plasmas in the two distinct regimes of no...
Revivals of zitterbewegung of a bound localized Dirac particle
International Nuclear Information System (INIS)
Romera, Elvira
2011-01-01
In this paper a bound localized Dirac particle is shown to exhibit a revival of the zitterbewegung (ZB) oscillation amplitude. These revivals go beyond the known quasiclassical regenerations in which the ZB oscillation amplitude is decreasing from period to period. This phenomenon is studied in a Dirac oscillator and it is shown that it is possible to set up wave packets in which there is a regeneration of the initial ZB amplitude.
Bound-state Dirac eigenvalues for scalar potentials
International Nuclear Information System (INIS)
Ram, B.; Arafah, M.
1981-01-01
The Dirac equation is solved with a linear and a quadratic scalar potential using an approach in which the Dirac equation is first transformed to a one-dimensional Schroedinger equation with an effective potential. The WKB method is used to obtain the energy eigenvalues. The eigenvalues for the quadratic scalar potential are real just as they are for the linear potential. The results with the linear potential agree well with those obtained by Critchfield. (author)
[P.A.M. Dirac and antimatter applied to medicine].
Kulenović, Fahrudin; Vobornik, Slavenka; Dalagija, Faruk
2003-01-01
Regarding to the hundredth anniversary of P. Dirac birth, it was made review on life and work of this genius in the history of physics and science generally. His ingenious scientific work, that significantly marked contemporary time, was presented in the simplest way with aim to approach more number of readers. Special accent was put on application of Dirac's ideas about antiparticles in medical practice.
General-transformation matrix for Dirac spinors and the calculation of spinorial amplitudes
International Nuclear Information System (INIS)
Nam, K.; Moravcsik, M.J.
1983-01-01
A general transformation matrix T(p's';p,s) is constructed which transforms a Dirac spinor psi(p,s) into another Dirac spinor psi(p',s') with arbitrarily given momenta and polarization states by expoloting the so-called Stech operator as one of generators for those transformations. This transformation matrix is then used in a calculation to yield the spinorial matrix element M = anti psi(p',s')GAMMApsi(p,s) for any spin polarization state. The final expressions of these matrix elements show the explicit structure of spin dependence for the process described by these spinorial amplitudes. The kinematical limiting cases such as very low energy or high energy of the various matrix elements can also be easily displayed. Our method is superior to the existing one in the following points. Since we have a well-defined transformation operator between two Dirac spinor states, we can evaluate the necessary phase factor of the matrix elements in an unambiguous way without introducing the coordinate system. This enables us to write down the Feynman amplitudes of complicated processes in any spin basis very easily in terms of previously calculated matrix elements of anti psiGAMMApsi which are building blocks of those Feynman amplitudes. The usefulness of the results is illustrated on Compton scattering and on the elastic scattering of two identical massive leptons where the phase factor is important. It is also shown that the Stech operator as a polarization operator is simply related to the operator K = #betta#(polarized μ . polarized L + 1)/2 which is often used in bound state problems
Particle creation and Dirac's large number hypothesis; and Reply
International Nuclear Information System (INIS)
Canuto, V.; Adams, P.J.; Hsieh, S.H.; Tsiang, E.; Steigman, G.
1976-01-01
The claim made by Steigman (Nature; 261:479 (1976)), that the creation of matter as postulated by Dirac (Proc. R. Soc.; A338:439 (1974)) is unnecessary, is here shown to be incorrect. It is stated that Steigman's claim that Dirac's large Number Hypothesis (LNH) does not require particle creation is wrong because he has assumed that which he was seeking to prove, that is that rho does not contain matter creation. Steigman's claim that Dirac's LNH leads to nonsensical results in the very early Universe is superficially correct, but this only supports Dirac's contention that the LNH may not be valid in the very early Universe. In a reply Steigman points out that in Dirac's original cosmology R approximately tsup(1/3) and using this model the results and conclusions of the present author's paper do apply but using a variation chosen by Canuto et al (T approximately t) Dirac's LNH cannot apply. Additionally it is observed that a cosmological theory which only predicts the present epoch is of questionable value. (U.K.)
The Lorentz-Dirac equation in light of quantum theory
International Nuclear Information System (INIS)
Nikishov, A.I.
1996-01-01
To high accuracy, an electron in ultrarelativistic motion 'sees' an external field in its rest frame as a crossed field (E=H, E·H=0). In this case, quantum expressions allow the introduction of a local intensity of the radiation, which determines the radiative term of the force of radiative reaction. For γ=(1-v2)-1/2>> 1 this term is much larger than the mass term, i.e., the term with xd3do. Under these conditions, the reduced Lorentz-Dirac equation, which is obtained from the full Lorentz-Dirac equation by eliminating the terms xd3do and xe on the right side using the equation of motion without taking into account the force of radiative reaction, is equivalent to good accuracy to the original Lorentz-Dirac equation. Exact solutions to the reduced Lorentz-Dirac equation are obtained for a constant field and the field of a plane wave. For γ∼1 a local expression for the radiative term cannot be obtained quantitatively from the quantum expressions. In this case the mass (Lorentz-Dirac) terms in the original and reduced Lorentz-Dirac equations are not small compared to the radiative term. The predictions of these equations, which depend appreciably on the mass terms, are therefore less reliable
Split Dirac Supersymmetry: An Ultraviolet Completion of Higgsino Dark Matter
Energy Technology Data Exchange (ETDEWEB)
Fox, Patrick J. [Fermilab; Kribs, Graham D. [Oregon U.; Martin, Adam [Notre Dame U.
2014-10-07
Motivated by the observation that the Higgs quartic coupling runs to zero at an intermediate scale, we propose a new framework for models of split supersymmetry, in which gauginos acquire intermediate scale Dirac masses of $\\sim 10^{8-11}$ GeV. Scalar masses arise from one-loop finite contributions as well as direct gravity-mediated contributions. Like split supersymmetry, one Higgs doublet is fine-tuned to be light. The scale at which the Dirac gauginos are introduced to make the Higgs quartic zero is the same as is necessary for gauge coupling unification. Thus, gauge coupling unification persists (nontrivially, due to adjoint multiplets), though with a somewhat higher unification scale $\\gtrsim 10^{17}$ GeV. The $\\mu$-term is naturally at the weak scale, and provides an opportunity for experimental verification. We present two manifestations of Split Dirac Supersymmetry. In the "Pure Dirac" model, the lightest Higgsino must decay through R-parity violating couplings, leading to an array of interesting signals in colliders. In the "Hypercharge Impure" model, the bino acquires a Majorana mass that is one-loop suppressed compared with the Dirac gluino and wino. This leads to weak scale Higgsino dark matter whose overall mass scale, as well as the mass splitting between the neutral components, is naturally generated from the same UV dynamics. We outline the challenges to discovering pseudo-Dirac Higgsino dark matter in collider and dark matter detection experiments.
Dirac equation in low dimensions: The factorization method
Energy Technology Data Exchange (ETDEWEB)
Sánchez-Monroy, J.A., E-mail: antosan@if.usp.br [Instituto de Física, Universidade de São Paulo, 05508-090, São Paulo, SP (Brazil); Quimbay, C.J., E-mail: cjquimbayh@unal.edu.co [Departamento de Física, Universidad Nacional de Colombia, Bogotá, D. C. (Colombia); CIF, Bogotá (Colombia)
2014-11-15
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equations in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to two Klein–Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials. - Highlights: • The low-dimensional Dirac equation in the presence of static potentials is solved. • The factorization method is generalized for energy-dependent Hamiltonians. • The shape invariance is generalized for energy-dependent Hamiltonians. • The stability of the Dirac sea is related to the existence of supersymmetric partner Hamiltonians.
Separation of Dirac's Hamiltonian by Van Vleck transformation
Jørgensen, Flemming
2017-01-01
The now classic Foldy-Wouthuysen transformation (FWT) was introduced as successive unitary transformations. This fundamental idea has become the standard in later developments such as the Douglas-Kroll transformation (DKT) - but it is not the only possibility. FWT can be seen as a simple special case of the general Van Vleck transformation (VVT) which besides the successive version has another, known as the canonical because of a series of nice mathematical properties discovered gradually over time. The aim of the present paper is to compare the two approaches - which give identical results in the lower orders, but not in the higher. After having recapitalised both, we apply them to Dirac's Hamiltonian for the electron in a constant electromagnetic field, written with so few assumptions about the operators that the mathematical techniques stand out separated from the terminology of relativistic quantum mechanics. FWT for a free particle is dealt with by a recent geometric approach to VVT. The original FWT is continued through the next non-zero orders. DKT is considered with special weight on equivalent formulations of the generalised and the optimised forms introduced by Wolf, Reiher and Hess.
Understanding quaternions and the Dirac belt trick
International Nuclear Information System (INIS)
Staley, Mark
2010-01-01
The Dirac belt trick is often employed in physics classrooms to show that a 2π rotation is not topologically equivalent to the absence of rotation whereas a 4π rotation is, mirroring a key property of quaternions and their isomorphic cousins, spinors. The belt trick can leave the student wondering if a real understanding of quaternions and spinors has been achieved, or if the trick is just an amusing analogy. The goal of this paper is to demystify the belt trick and to show that it suggests an underlying four-dimensional parameter space for rotations that is simply connected. An investigation into the geometry of this four-dimensional space leads directly to the system of quaternions, and to an interpretation of three-dimensional vectors as the generators of rotations in this larger four-dimensional world. The paper also shows why quaternions are the natural extension of complex numbers to four dimensions. The level of the paper is suitable for undergraduate students of physics.
DIRAC: reliable data management for LHCb
International Nuclear Information System (INIS)
Smith, A C; Tsaregorodtsev, A
2008-01-01
DIRAC, LHCb's Grid Workload and Data Management System, utilizes WLCG resources and middleware components to perform distributed computing tasks satisfying LHCb's Computing Model. The Data Management System (DMS) handles data transfer and data access within LHCb. Its scope ranges from the output of the LHCb Online system to Grid-enabled storage for all data types. It supports metadata for these files in replica and bookkeeping catalogues, allowing dataset selection and localization. The DMS controls the movement of files in a redundant fashion whilst providing utilities for accessing all metadata. To do these tasks effectively the DMS requires complete self integrity between its components and external physical storage. The DMS provides highly redundant management of all LHCb data to leverage available storage resources and to manage transient errors in underlying services. It provides data driven and reliable distribution of files as well as reliable job output upload, utilizing VO Boxes at LHCb Tier1 sites to prevent data loss. This paper presents several examples of mechanisms implemented in the DMS to increase reliability, availability and integrity, highlighting successful design choices and limitations discovered
International Nuclear Information System (INIS)
Muñoz, J L Gómez; Delgado, F
2016-01-01
This paper introduces QUANTUM, a free library of commands of Wolfram Mathematica that can be used to perform calculations directly in Dirac braket and operator notation. Its development started several years ago, in order to study quantum random walks. Later, many other features were included, like operator and commutator algebra, simulation and graphing of quantum computing circuits, generation and solution of Heisenberg equations of motion, among others. To the best of our knowledge, QUANTUM remains a unique tool in its use of Dirac notation, because it is used both in the input and output of the calculations. This work depicts its usage and features in Quantum Computing and Quantum Hamilton Dynamics. (paper)
Dirac and non-Dirac conditions in the two-potential theory of magnetic charge
Scott, John; Evans, Timothy J.; Singleton, Douglas; Dzhunushaliev, Vladimir; Folomeev, Vladimir
2018-05-01
We investigate the Cabbibo-Ferrari, two-potential approach to magnetic charge coupled to two different complex scalar fields, Φ _1 and Φ _2, each having different electric and magnetic charges. The scalar field, Φ _1, is assumed to have a spontaneous symmetry breaking self-interaction potential which gives a mass to the "magnetic" gauge potential and "magnetic" photon, while the other "electric" gauge potential and "electric" photon remain massless. The magnetic photon is hidden until one reaches energies of the order of the magnetic photon rest mass. The second scalar field, Φ _2, is required in order to make the theory non-trivial. With only one field one can always use a duality rotation to rotate away either the electric or magnetic charge, and thus decouple either the associated electric or magnetic photon. In analyzing this system of two scalar fields in the Cabbibo-Ferrari approach we perform several duality and gauge transformations, which require introducing non-Dirac conditions on the initial electric and magnetic charges. We also find that due to the symmetry breaking the usual Dirac condition is altered to include the mass of the magnetic photon. We discuss the implications of these various conditions on the charges.
Double Dirac Point Semimetal in Two-Dimensional Material: Ta2Se3
Ma, Yandong; Jing, Yu; Heine, Thomas
2017-01-01
Here, we report by first-principles calculations one new stable 2D Dirac material, Ta2Se3 monolayer. For this system, stable layered bulk phase exists, and exfoliation should be possible. Ta2Se3 monolayer is demonstrated to support two Dirac points close to the Fermi level, achieving the exotic 2D double Dirac semimetal. And like 2D single Dirac and 2D node-line semimetals, spin-orbit coupling could introduce an insulating state in this new class of 2D Dirac semimetals. Moreover, the Dirac fe...
Dirac matrices for Chern-Simons gravity
Energy Technology Data Exchange (ETDEWEB)
Izaurieta, Fernando; Ramirez, Ricardo; Rodriguez, Eduardo [Departamento de Matematica y Fisica Aplicadas, Universidad Catolica de la Santisima Concepcion, Alonso de Ribera 2850, 4090541 Concepcion (Chile)
2012-10-06
A genuine gauge theory for the Poincare, de Sitter or anti-de Sitter algebras can be constructed in (2n- 1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices {Gamma}{sub ab} in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices {Gamma}{sub ab} can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical cofficient {alpha}{sub s}. We then give a general algorithm that computes the {alpha}-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors B{sup ab} with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, 'minimal' algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n = 25, which easily covers all foreseeable applications of the trace formula.
Application of a Lorentz transformation in six dimensions to an extension of dirac equation
International Nuclear Information System (INIS)
Sabry, A.A.
2000-01-01
On applying a six dimensional Lorentz transformation (by adding three time components to the usual 3 space components) a covariant extended Dirac equation in this six dimensional space is suggested. From the free field solution of the extended equation we obtained four solutions for E , the first component of energy which depends on very big masses M and M 0 . The observed masses of the leptons and their corresponding neutrinos satisfying the same free field equation, can then be obtained on using second quantisation procedures on the field operators
Relativistic space-charge-limited current for massive Dirac fermions
Ang, Y. S.; Zubair, M.; Ang, L. K.
2017-04-01
A theory of relativistic space-charge-limited current (SCLC) is formulated to determine the SCLC scaling, J ∝Vα/Lβ , for a finite band-gap Dirac material of length L biased under a voltage V . In one-dimensional (1D) bulk geometry, our model allows (α ,β ) to vary from (2,3) for the nonrelativistic model in traditional solids to (3/2,2) for the ultrarelativistic model of massless Dirac fermions. For 2D thin-film geometry we obtain α =β , which varies between 2 and 3/2, respectively, at the nonrelativistic and ultrarelativistic limits. We further provide rigorous proof based on a Green's-function approach that for a uniform SCLC model described by carrier-density-dependent mobility, the scaling relations of the 1D bulk model can be directly mapped into the case of 2D thin film for any contact geometries. Our simplified approach provides a convenient tool to obtain the 2D thin-film SCLC scaling relations without the need of explicitly solving the complicated 2D problems. Finally, this work clarifies the inconsistency in using the traditional SCLC models to explain the experimental measurement of a 2D Dirac semiconductor. We conclude that the voltage scaling 3 /2 <α <2 is a distinct signature of massive Dirac fermions in a Dirac semiconductor and is in agreement with experimental SCLC measurements in MoS2.
Dirac equation and optical wave propagation in one dimension
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, Gabriel [Catedras CONACYT, Universidad Autonoma de San Luis Potosi (Mexico); Coordinacion para la Innovacion y la Aplicacion de la Ciencia y la Tecnologia, Universidad Autonoma de San Luis Potosi (Mexico)
2018-02-15
We show that the propagation of transverse electric (TE) polarized waves in one-dimensional inhomogeneous settings can be written in the form of the Dirac equation in one space dimension with a Lorentz scalar potential, and consequently perform photonic simulations of the Dirac equation in optical structures. In particular, we propose how the zero energy state of the Jackiw-Rebbi model can be generated in an optical set-up by controlling the refractive index landscape, where TE-polarized waves mimic the Dirac particles and the soliton field can be tuned by adjusting the refractive index. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Shot noise in systems with semi-Dirac points
International Nuclear Information System (INIS)
Zhai, Feng; Wang, Juan
2014-01-01
We calculate the ballistic conductance and shot noise of electrons through a two-dimensional stripe system (width W ≫ length L) with semi-Dirac band-touching points. We find that the ratio between zero-temperature noise power and mean current (the Fano factor) is highly anisotropic. When the transport is along the linear-dispersion direction and the Fermi energy is fixed at the semi-Dirac point, the Fano factor has a universal value F = 0.179 while a minimum conductivity exists and scales with L 1∕2 . Along the parabolic dispersion direction, the Fano factor at the semi-Dirac point has a contact-independent limit exceeding 0.9, which varies weakly with L due to the common-path interference of evanescent waves. Our findings suggest a way to discern the type of band-touching points
Spin-1 Dirac-Weyl fermions protected by bipartite symmetry
Energy Technology Data Exchange (ETDEWEB)
Lin, Zeren [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); School of Physics, Peking University, Beijing 100871 (China); Liu, Zhirong, E-mail: LiuZhiRong@pku.edu.cn [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); Center for Nanochemistry, Beijing National Laboratory for Molecular Sciences (BNLMS), Peking University, Beijing 100871 (China)
2015-12-07
We propose that bipartite symmetry allows spin-1 Dirac-Weyl points, a generalization of the spin-1/2 Dirac points in graphene, to appear as topologically protected at the Fermi level. In this spirit, we provide methodology to construct spin-1 Dirac-Weyl points of this kind in a given 2D space group and get the classification of the known spin-1 systems in the literature. We also apply the workflow to predict two new systems, P3m1-9 and P31m-15, to possess spin-1 at K/K′ in the Brillouin zone of hexagonal lattice. Their stability under various strains is investigated and compared with that of T{sub 3}, an extensively studied model of ultracold atoms trapped in optical lattice with spin-1 also at K/K′.
New approaches for searching for the Dirac magnetic monopole
International Nuclear Information System (INIS)
Kukhtin, V.V.; Krivokhizhin, V.G.; Stetsenko, S.G.; Cheplakov, A.P.
2012-01-01
Three new approaches, not applied earlier, are proposed to search for the Dirac monopole - an object whose existence was proposed by P.Dirac more than 80 years ago to explain the electrical charge quantization. The first approach assumes that the monopole must be accelerated by a magnetic field, and such acceleration is constant in the magnetic field which is homogeneous and constant. The conclusion about the object movement nature can be drawn by measuring the time marks for equidistant registering planes. The second approach is supposed to reconstruct the movement trajectory in the homogeneous and permanent electrical field, which is the circle or its part for the magnetic monopole. The third approach is based on the constancy of energy losses by Dirac monopole due to medium ionization in the multilayer passive dielectric tracking detectors placed in the homogeneous and permanent electrical field
Time-dependent massless Dirac fermions in graphene
Energy Technology Data Exchange (ETDEWEB)
Khantoul, Boubakeur, E-mail: bobphys@gmail.com [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom); Department of Physics, University of Jijel, BP 98, Ouled Aissa, 18000 Jijel (Algeria); Fring, Andreas, E-mail: a.fring@city.ac.uk [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom)
2015-10-30
Using the Lewis–Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some explicit time-dependence in addition to one resulting from being minimally coupled to a time-dependent vector potential. The eigenvalue equations for the two spinor components of the Lewis–Riesenfeld invariant are found to decouple into a pair of supersymmetric invariants in a similar fashion as the known decoupling for the time-independent Dirac Hamiltonians. - Highlights: • An explicit analytical solution for a massless 2+1 dimensional time-dependent Dirac equation is found. • All steps of the Lewis–Riesenfeld method have been carried out.
Maxwell-Like Equations for Free Dirac Electrons
Bruce, S. A.
2018-03-01
In this article, we show that the wave equation for a free Dirac electron can be represented in a form that is analogous to Maxwell's electrodynamics. The electron bispinor wavefunction is explicitly expressed in terms of its real and imaginary components. This leads us to incorporate into it appropriate scalar and pseudo-scalar fields in advance, so that a full symmetry may be accomplished. The Dirac equation then takes on a form similar to that of a set of inhomogeneous Maxwell's equations involving a particular self-source. We relate plane wave solutions of these equations to waves corresponding to free Dirac electrons, identifying the longitudinal component of the electron motion, together with the corresponding Zitterbewegung ("trembling motion").
Dirac vacuum: Acceleration and external-field effects
International Nuclear Information System (INIS)
Jauregui, R.; Torres, M.; Hacyan, S.
1991-01-01
The quantization of the massive spin-1/2 field in Rindler coordinates is considered, including the effects of a background magnetic field. We calculate the expectation values of conserved quantities such as the stress-energy tensor, current density, and spin distribution, as detected by an accelerated observer. The ratio of the energy and particle densities is given by a Fermi-Dirac distribution, but the spectrum of these quantities takes in general a complicated form that cannot be simply interpreted as a thermal spectrum. For the free-particle case the spectrum of the energy-stress tensor has a Fermi-Dirac form only in the massless limit. In the presence of the magnetic field the Dirac vacuum is magnetized and exhibits plasmalike properties
String effects on Fermi-Dirac correlation measurements
International Nuclear Information System (INIS)
Duran Delgado, R.M.; Gustafson, G.; Loennblad, L.
2007-01-01
We investigate some recent measurements of Fermi-Dirac correlations by the LEP collaborations indicating surprisingly small source radii for the production of baryons in e + e - annihilation at the Z 0 peak. In hadronization models there is besides the Fermi-Dirac correlation effect also a strong dynamical (anti-) correlation. We demonstrate that the extraction of the pure FD effect is highly dependent on a realistic Monte Carlo event generator, both for separation of those dynamical correlations that are not related to Fermi-Dirac statistics, and for corrections of the data and background subtractions. Although the model can be tuned to well reproduce single particle distributions, there are large model uncertainties when it comes to correlations between identical baryons. We therefore, unfortunately, have to conclude that it is at present not possible to draw any firm conclusion about the source radii relevant for baryon production at LEP. (orig.)
Luciano Maiani and Jean Iliopoulos awarded the Dirac Medal
2007-01-01
Luciano Maiani, when he was Director-General of CERN. Jean Iliopoulos in 1999. (©CNRS Photothèque - Julien Quideau)On 8 August, the 2007 Dirac Medal, one of the most prestigious prizes in the fields of theoretical physics and mathematics, was awarded to Luciano Maiani, professor at Rome’s La Sapienza University and former Director-General of CERN, and to Jean Iliopoulos, emeritus Director of Research at the CNRS Laboratory of Theoretical Physics. The medal was awarded to both physicists for their joint "work on the physics of the charm quark, a major contribution to the birth of the Standard Model, the modern theory of Elementary Particles." Founded by the Abdus Salam International Centre for Theoretical Physics (ICTP) in 1985, the Dirac Medal is awarded annually on 8 August, the birthday of the famous physicist Paul Dirac, winner of the 1933 Nobel Prize for Physics. It is awarded to ...
Dirac charge dynamics in graphene by infrared spectroscopy
International Nuclear Information System (INIS)
Martin, Michael C; Li, Z.Q.; Henriksen, E.A.; Jiang, Z.; Hao, Z.; Martin, Michael C; Kim, P.; Stormer, H.L.; Basov, Dimitri N.
2008-01-01
A remarkable manifestation of the quantum character of electrons in matter is offered by graphene, a single atomic layer of graphite. Unlike conventional solids where electrons are described with the Schroedinger equation, electronic excitations in graphene are governed by the Dirac hamiltonian. Some of the intriguing electronic properties of graphene, such as massless Dirac quasiparticles with linear energy-momentum dispersion, have been confirmed by recent observations. Here, we report an infrared spectromicroscopy study of charge dynamics in graphene integrated in gated devices. Our measurements verify the expected characteristics of graphene and, owing to the previously unattainable accuracy of infrared experiments, also uncover significant departures of the quasiparticle dynamics from predictions made for Dirac fermions in idealized, free-standing graphene. Several observations reported here indicate the relevance of many-body interactions to the electromagnetic response of graphene
Accidental degeneracy of double Dirac cones in a phononic crystal
Chen, Ze-Guo; Ni, Xu; Wu, Ying; He, Cheng; Sun, Xiao-Chen; Zheng, Li-Yang; Lu, Ming-Hui; Chen, Yan-Feng
2014-01-01
Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of the Brillouin zone in a two-dimensional honeycomb lattice phononic crystal, which is a result of accidental degeneracy of two double-degenerate states. In the vicinity of the quadruple-degenerate state, the dispersion relation is linear. Such quadruple degeneracy is analyzed by rigorous representation theory of groups. Using method, a reduced Hamiltonian is obtained to describe the linear Dirac dispersion relations of this quadruple-degenerate state, which is well consistent with the simulation results. Near such accidental degeneracy, we observe some unique properties in wave propagating, such as defect-insensitive propagating character and the Talbot effect.
Accidental degeneracy of double Dirac cones in a phononic crystal
Chen, Ze-Guo
2014-04-09
Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of the Brillouin zone in a two-dimensional honeycomb lattice phononic crystal, which is a result of accidental degeneracy of two double-degenerate states. In the vicinity of the quadruple-degenerate state, the dispersion relation is linear. Such quadruple degeneracy is analyzed by rigorous representation theory of groups. Using method, a reduced Hamiltonian is obtained to describe the linear Dirac dispersion relations of this quadruple-degenerate state, which is well consistent with the simulation results. Near such accidental degeneracy, we observe some unique properties in wave propagating, such as defect-insensitive propagating character and the Talbot effect.
Electronic structure of a graphene superlattice with massive Dirac fermions
International Nuclear Information System (INIS)
Lima, Jonas R. F.
2015-01-01
We study the electronic and transport properties of a graphene-based superlattice theoretically by using an effective Dirac equation. The superlattice consists of a periodic potential applied on a single-layer graphene deposited on a substrate that opens an energy gap of 2Δ in its electronic structure. We find that extra Dirac points appear in the electronic band structure under certain conditions, so it is possible to close the gap between the conduction and valence minibands. We show that the energy gap E g can be tuned in the range 0 ≤ E g ≤ 2Δ by changing the periodic potential. We analyze the low energy electronic structure around the contact points and find that the effective Fermi velocity in very anisotropic and depends on the energy gap. We show that the extra Dirac points obtained here behave differently compared to previously studied systems
International Nuclear Information System (INIS)
Dick, Viktor
2016-04-01
In this work, the spectrum of the overlap Dirac operator has been computed and analyzed on configurations that had been created using highly improved staggered quarks. Although the overlap operator is expensive to compute, it has the advantage that it fully implements chiral symmetry in the same way as the continuum QCD Dirac operator even at finite lattice spacings. This opened the possibility to investigate chiral aspects of QCD and, in particular, the question if the axial anomaly is suppressed at the chiral transition temperature T c . The obtained results indicate that the axial anomaly is still present at T c and even at 1.5 T c as evidenced by a splitting in the integrated pion and delta susceptibilities. The spectrum shows a peak in the near-zero region consisting of zero modes and pairs of near-zero modes. The breaking of the axial symmetry was identified as being caused by these infrared modes. It was discussed how this infrared contribution might change in the thermodynamic, continuum, and chiral limits. The obtained data supports the expectation that the peak becomes narrower with decreasing quark masses, resulting in a Dirac-delta peak in the chiral limit. The area under the peak was found to decrease with decreasing lattice spacing, so in order to resolve how much of it survives the continuum limit further investigations are needed, in particular ones where already for the generation of gauge configurations chiral fermions are used. The infrared modes were investigated and found to be highly localized, supporting the picture of QCD at high temperatures as a dilute instanton gas. The instantons were found to have an average size of 0.239(4) fm and a density of 0.154(5) fm -4 at 1.5 T c . Near-zero modes were found to be induced by instanton-anti-instanton molecules, which are weakly bound. At temperatures closer to T c , this picture becomes more complicated but these features sometimes still can be recognized. In conclusion, in QCD at temperatures
PREFACE: International Workshop on Dirac Electrons in Solids 2015
Ogata, M.; Suzumura, Y.; Fuseya, Y.; Matsuura, H.
2015-04-01
It is our pleasure to publish the Proceedings of the International Workshop on Dirac Electrons in Solids held in University of Tokyo, Japan, for January 14-15, 2015. The workshop was organized by the entitled project which lasted from April 2012 to March 2015 with 10 theorists. It has been supported by a Grand-in-Aid for Scientific Research (A) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan. The subjects discussed in the workshop include bismuth, organic conductors, graphene, topological insulators, new materials including Ca3PbO, and new directions in theory (superconductivity, orbital susceptibility, etc). The number of participants was about 70 and the papers presented in the workshop include four invited talks, 16 oral presentations, and 23 poster presentations. Dirac electron systems appear in various systems, such as graphene, quasi-two-dimensional organic conductors, bismuth, surface states in topological insulators, new materials like Ca3PbO. In these systems, characteristic transport properties caused by the linear dispersion of Dirac electrons and topological properties, have been extensively discussed. In addition to these, there are many interesting research fields such as Spin-Hall effect, orbital diamagnetism due to interband effects, Landau levels characteristic to Dirac dispersion, anomalous interlayer transport phenomena and magnetoresistance, the effects of spin-orbit interaction, and electron correlation. The workshop focused on recent developments of theory and experiment of Dirac electron systems in the above materials. We note that all papers published in this volume of Journal of Physics: Conference Series were peer reviewed. Reviews were performed by expert referees with professional knowledge and high scientific standards in this field. Editors made efforts so that the papers may satisfy the criterion of a proceedings journal published by IOP Publishing. We hope that all the participants of the workshop
Chemistry at the dirac point of graphene
Sarkar, Santanu
device mobility. To this end, we find that the organometallic hexahapto metal complexation chemistry of graphene, in which the graphene pi-band constructively hybridizes with the vacant d-orbitals of transition metals, allows the fabrication of field effect devices which retain a high degree of the mobility with enhanced on-off ratio. In summary, we find that the singular electronic structure of graphene at the Dirac point governs the chemical reactivity of graphene and this chemistry will play a vital role in propelling graphene to assume its role as the next generation electronic material beyond silicon.
Out-of-Bounds Hydrodynamics in Anisotropic Dirac Fluids
Link, Julia M.; Narozhny, Boris N.; Kiselev, Egor I.; Schmalian, Jörg
2018-05-01
We study hydrodynamic transport in two-dimensional, interacting electronic systems with merging Dirac points at charge neutrality. The dispersion along one crystallographic direction is Dirac-like, while it is Newtonian-like in the orthogonal direction. As a result, the electrical conductivity is metallic in one and insulating in the other direction. The shear viscosity tensor contains six independent components, which can be probed by measuring an anisotropic thermal flow. One of the viscosity components vanishes at zero temperature leading to a generalization of the previously conjectured lower bound for the shear viscosity to entropy density ratio.
Geometric interpretation for the Dirac field in curved space
International Nuclear Information System (INIS)
Ranganathan, D.
1987-01-01
The imposition of the condition of length invariance on a Weyl manifold that does not lead uniquely to general relativity is shown. Rather, in this limit, the Weyl vector field can be interpreted as a Dirac current. The action is also the same as the Einstein Dirac one, if and only if, the spinor field is anticommuting. The allowed interactions are greatly restricted. They are only minimal gauge couplings and Yukawa interactions with a scalar field transforming according to the rules of Utiyama [Prog. Theor. Phys. 53, 565 (1975)
Levinson theorem for Dirac particles in n dimensions
International Nuclear Information System (INIS)
Jiang Yu
2005-01-01
We study the Levinson theorem for a Dirac particle in an n-dimensional central field by use of the Green function approach, based on an analysis of the n-dimensional radial Dirac equation obtained through a simple algebraic derivation. We show that the zero-momentum phase shifts are related to the number of bound states with |E|< m plus the number of half-bound states of zero momenta--i.e., |E|=m--which are denoted by finite, but not square-integrable, wave functions
Dirac potentials in a coupled channel approach to inelastic scattering
International Nuclear Information System (INIS)
Mishra, V.K.; Clark, B.C.; Cooper, E.D.; Mercer, R.L.
1990-01-01
It has been shown that there exist transformations that can be used to change the Lorentz transformation character of potentials, which appear in the Dirac equation for elastic scattering. We consider the situation for inelastic scattering described by coupled channel Dirac equations. We examine a two-level problem where both the ground and excited states are assumed to have zero spin. Even in this simple case we have not found an appropriate transformation. However, if the excited state has zero excitation energy it is possible to find a transformation
Radiative heat transfer in 2D Dirac materials
International Nuclear Information System (INIS)
Rodriguez-López, Pablo; Tse, Wang-Kong; Dalvit, Diego A R
2015-01-01
We compute the radiative heat transfer between two sheets of 2D Dirac materials, including topological Chern insulators and graphene, within the framework of the local approximation for the optical response of these materials. In this approximation, which neglects spatial dispersion, we derive both numerically and analytically the short-distance asymptotic of the near-field heat transfer in these systems, and show that it scales as the inverse of the distance between the two sheets. Finally, we discuss the limitations to the validity of this scaling law imposed by spatial dispersion in 2D Dirac materials. (paper)
Rigid particle revisited: Extrinsic curvature yields the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Deriglazov, Alexei, E-mail: alexei.deriglazov@ufjf.edu.br [Depto. de Matemática, ICE, Universidade Federal de Juiz de Fora, MG (Brazil); Laboratory of Mathematical Physics, Tomsk Polytechnic University, 634050 Tomsk, Lenin Ave. 30 (Russian Federation); Nersessian, Armen, E-mail: arnerses@ysu.am [Yerevan State University, 1 Alex Manoogian St., Yerevan 0025 (Armenia); Laboratory of Mathematical Physics, Tomsk Polytechnic University, 634050 Tomsk, Lenin Ave. 30 (Russian Federation)
2014-03-01
We reexamine the model of relativistic particle with higher-derivative linear term on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here. We found that, contrary to common opinion, quantization of the model in terms of so(3.2)-algebra yields massive Dirac equation. -- Highlights: •New way of canonical quantization of relativistic rigid particle is proposed. •Quantization made in terms of so(3.2) angular momentum algebra. •Quantization yields massive Dirac equation.
Job monitoring on DIRAC for Belle II distributed computing
Kato, Yuji; Hayasaka, Kiyoshi; Hara, Takanori; Miyake, Hideki; Ueda, Ikuo
2015-12-01
We developed a monitoring system for Belle II distributed computing, which consists of active and passive methods. In this paper we describe the passive monitoring system, where information stored in the DIRAC database is processed and visualized. We divide the DIRAC workload management flow into steps and store characteristic variables which indicate issues. These variables are chosen carefully based on our experiences, then visualized. As a result, we are able to effectively detect issues. Finally, we discuss the future development for automating log analysis, notification of issues, and disabling problematic sites.
Hole doped Dirac states in silicene by biaxial tensile strain
Kaloni, Thaneshwor P.; Cheng, Yingchun; Schwingenschlö gl, Udo
2013-01-01
The effects of biaxial tensile strain on the structure, electronic states, and mechanical properties of silicene are studied by ab-initio calculations. Our results show that up to 5% strain the Dirac cone remains essentially at the Fermi level, while higher strain induces hole doped Dirac states because of weakened Si–Si bonds. We demonstrate that the silicene lattice is stable up to 17% strain. It is noted that the buckling first decreases with the strain (up to 10%) and then increases again, which is accompanied by a band gap variation. We also calculate the Grüneisen parameter and demonstrate a strain dependence similar to that of graphene.
Hole doped Dirac states in silicene by biaxial tensile strain
Kaloni, Thaneshwor P.
2013-03-11
The effects of biaxial tensile strain on the structure, electronic states, and mechanical properties of silicene are studied by ab-initio calculations. Our results show that up to 5% strain the Dirac cone remains essentially at the Fermi level, while higher strain induces hole doped Dirac states because of weakened Si–Si bonds. We demonstrate that the silicene lattice is stable up to 17% strain. It is noted that the buckling first decreases with the strain (up to 10%) and then increases again, which is accompanied by a band gap variation. We also calculate the Grüneisen parameter and demonstrate a strain dependence similar to that of graphene.
Dirac neutrinos and hybrid inflation from string theory
International Nuclear Information System (INIS)
Antusch, Stefan; Eyton-Williams, Oliver J.; King, Steve F.
2005-01-01
We consider a possible scenario for the generation of Dirac neutrino masses motivated by type-I string theory. The smallness of the neutrino Yukawa couplings is explained by an anisotropic compactification with one compactification radius larger than the others. In addition to this we utilise small Yukawa couplings to develop strong links between the origin of neutrino masses and the physics driving inflation. We construct a minimal model which simultaneously accommodates small Dirac neutrino masses leading to bi-large lepton mixing as well as an inflationary solution to the strong CP and to the μ problem
Twisting dirac fermions: circular dichroism in bilayer graphene
Suárez Morell, E.; Chico, Leonor; Brey, Luis
2017-09-01
Twisted bilayer graphene is a chiral system which has been recently shown to present circular dichroism. In this work we show that the origin of this optical activity is the rotation of the Dirac fermions’ helicities in the top and bottom layer. Starting from the Kubo formula, we obtain a compact expression for the Hall conductivity that takes into account the dephasing of the electromagnetic field between the top and bottom layers and gathers all the symmetries of the system. Our results are based in both a continuum and a tight-binding model, and they can be generalized to any two-dimensional Dirac material with a chiral stacking between layers.
Daudé, Thierry
2017-01-01
In this paper, the authors study the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. In the first part, they establish the existence and asymptotic completeness of time-dependent wave operators associated to our Dirac fields. This leads to the definition of the time-dependent scattering operator that encodes the far-field behavior (with respect to a stationary observer) in the asymptotic regions of the black hole: the event and cosmological horizons. The authors also use the miraculous property (quoting Chandrasekhar)-that the Dirac equation can be separated into radial and angular ordinary differential equations-to make the link between the time-dependent scattering operator and its stationary counterpart. This leads to a nice expression of the scattering matrix at fixed energy in terms of stationary solutions of the system of separated equations. In a second part, the authors use this expression of ...
Tilted Dirac Cone Effect on Interlayer Magnetoresistance in α-(BEDT-TTF)2I3
Tajima, Naoya; Morinari, Takao
2018-04-01
We report the effect of Dirac cone tilting on interlayer magnetoresistance in α-(BEDT-TTF)2I3, which is a Dirac semimetal under pressure. Fitting of the experimental data by the theoretical formula suggests that the system is close to a type-II Dirac semimetal.
Non-relativistic Limit of a Dirac Polaron in Relativistic Quantum Electrodynamics
Arai, A
2006-01-01
A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral $\\int_{{\\bf R}^3}^\\oplus\\overline{H({\\bf p})}d{\\bf p}$ of a family of self-adjoint operators $\\overline{H({\\bf p})}$ acting in the Hilbert space $\\oplus^4{\\cal F}_{\\rm rad}$, where ${\\cal F}_{\\rm rad}$ is the Hilbert space of the quantum radiation field. The fibre operator $\\overline{H({\\bf p})}$ is called the Hamiltonian of the Dirac polaron with total momentum ${\\bf p} \\in {\\bf R}^3$. The main result of this paper is concerned with the non-relativistic (scaling) limit of $\\overline{H({\\bf p})}$. It is proven that the non-relativistic limit of $\\overline{H({\\bf p})}$ yields a self-adjoint extension of a Hamiltonian of a polaron with spin $1/2$ in non-relativistic quantum electrodynamics.
Dirac's Conception of the Magnetic Monopole, and its Modern Avatars
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 10; Issue 12. Dirac's Conception of the Magnetic Monopole, and its Modern Avatars. Sunil Mukhi. Volume 10 Issue 12 December 2005 pp 193-202. Fulltext. Click here to view fulltext PDF. Permanent link:
Spinors, tensors and the covariant form of Dirac's equation
International Nuclear Information System (INIS)
Chen, W.Q.; Cook, A.H.
1986-01-01
The relations between tensors and spinors are used to establish the form of the covariant derivative of a spinor, making use of the fact that certain bilinear combinations of spinors are vectors. The covariant forms of Dirac's equation are thus obtained and examples in specific coordinate systems are displayed. (author)
U matrix construction for Quantum Chromodynamics through Dirac brackets
International Nuclear Information System (INIS)
Santos, M.A. dos.
1987-09-01
A procedure for obtaining the U matrix using Dirac brackets, recently developed by Kiefer and Rothe, is applied for Quantum Chromodynamics. The correspondent interaction Lagrangian is the same obtained by Schwinger, Christ and Lee, using independent methods. (L.C.J.A.)
Dirac particle in a constant magnetic field: path integral treatment
Energy Technology Data Exchange (ETDEWEB)
Merdaci, A.; Boudiaf, N.; Chetouani, L. [Univ. Mentouri, Constantine (Algeria). Dept. de Physique
2008-05-15
The Green functions related to a Dirac particle in a constant magnetic field are calculated via two methods, global and local, by using the supersymmetric formalism of Fradkin and Gitman. The energy spectrum as well as the corresponding wave functions are extracted following these two approaches. (orig.)
Dirac particle in a constant magnetic field: path integral treatment
International Nuclear Information System (INIS)
Merdaci, A.; Boudiaf, N.; Chetouani, L.
2008-01-01
The Green functions related to a Dirac particle in a constant magnetic field are calculated via two methods, global and local, by using the supersymmetric formalism of Fradkin and Gitman. The energy spectrum as well as the corresponding wave functions are extracted following these two approaches. (orig.)
A rational interpretation of the Dirac equation for the electron
International Nuclear Information System (INIS)
Koga, T.
1975-01-01
Rationalization of the interpretation of the Dirac equation for the electron lies beyond the conventional scope of quantum mechanics. This difficulty motivates a revision of the system of quantum mechanics through which the indeterministic trait is eliminated from the system. (author)
Holographic interaction effects on transport in Dirac semimetals
Jacobs, V.P.J.; Vandoren, S.; Stoof, H.T.C.
2014-01-01
Strongly interacting Dirac semimetals are investigated using a holographic model especially geared to compute the single-particle correlation function for this case, including both interaction effects and non-zero temperature. We calculate the (homogeneous) optical conductivity at zero chemical
Common origin of neutrino mass, dark matter and Dirac leptogenesis
Energy Technology Data Exchange (ETDEWEB)
Borah, Debasish [Department of Physics, Indian Institute of Technology Guwahati, Assam 781039 (India); Dasgupta, Arnab, E-mail: dborah@iitg.ernet.in, E-mail: arnab.d@iopb.res.in [Institute of Physics, HBNI, Sachivalaya Marg, Bhubaneshwar 751005 (India)
2016-12-01
We study the possibility of generating tiny Dirac neutrino masses at one loop level through the scotogenic mechanism such that one of the particles going inside the loop can be a stable cold dark matter (DM) candidate. Majorana mass terms of singlet fermions as well as tree level Dirac neutrino masses are prevented by incorporating the presence of additional discrete symmetries in a minimal fashion, which also guarantee the stability of the dark matter candidate. Due to the absence of total lepton number violation, the observed baryon asymmetry of the Universe is generated through the mechanism of Dirac leptogenesis where an equal and opposite amount of leptonic asymmetry is generated in the left and right handed sectors which are prevented from equilibration due to tiny Dirac Yukawa couplings. Dark matter relic abundance is generated through its usual freeze-out at a temperature much below the scale of leptogenesis. We constrain the relevant parameter space from neutrino mass, baryon asymmetry, Planck bound on dark matter relic abundance, and latest LUX bound on spin independent DM-nucleon scattering cross section. We also discuss the charged lepton flavour violation (μ → e γ) and electric dipole moment of electron in this model in the light of the latest experimental data and constrain the parameter space of the model.
Survey on Dirac equation in general relativity theory
International Nuclear Information System (INIS)
Paillere, P.
1984-10-01
Starting from an infinitesimal transformation expressed with a Killing vector and using systematically the formalism of the local tetrades, we show that, in the area of the general relativity, the Dirac equation may be formulated only versus the four local vectors which determine the gravitational potentials, their gradients and the 4-vector potential of the electromagnetic field [fr
Dirac electronics states in graphene systems: optical spectroscopy studies
Czech Academy of Sciences Publication Activity Database
Orlita, Milan; Potemski, M.
2010-01-01
Roč. 25, č. 6 (2010), 063001/1-063001/22 ISSN 0268-1242 R&D Projects: GA AV ČR KAN400100652 Institutional research plan: CEZ:AV0Z10100521 Keywords : graphene * Dirac fermions Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.323, year: 2010
A new derivation of Dirac's magnetic monopole strength
International Nuclear Information System (INIS)
Panat, P V
2003-01-01
A new derivation of the strength of Dirac's magnetic monopole is presented which does not require an explicit form of the magnetic induction in terms of g, the magnetic pole strength. The derivation essentially uses a modification of Faraday's law of induction and quantization of angular momentum
LHCb : The DIRAC Web Portal 2.0
Mathe, Zoltan; Lazovsky, N; Stagni, Federico
2015-01-01
For many years the DIRAC interware (Distributed Infrastructure with Remote Agent Control) has had a web interface, allowing the users to monitor DIRAC activities and also interact with the system. Since then many new web technologies have emerged, therefore a redesign and a new implementation of the DIRAC Web portal were necessary, taking into account the lessons learnt using the old portal. These new technologies allowed to build a more compact and more responsive web interface that is robust and that enables users to have more control over the whole system while keeping a simple interface. The framework provides a large set of "applications", each of which can be used for interacting with various parts of the system. Communities can also create their own set of personalised web applications, and can easily extend already existing web applications with a minimal effort. Each user can configure and personalise the view for each application and save it using the DIRAC User Profile service as RESTful state prov...
On the representation of generalized Dirac (Clifford) algebras
International Nuclear Information System (INIS)
Srivastava, T.
1981-10-01
Some results of Brauer and Weyl and of Jordan and Wigner on irreducible representations of generalized Dirac (Clifford) algebras have been proved, adopting a new and simple approach which (i) makes the whole subject straightforward for physicists and (ii) simplifies the demonstration of the fundamental theorem of Pauli. (author)
Chiral Tricritical Point: A New Universality Class in Dirac Systems
Yin, Shuai; Jian, Shao-Kai; Yao, Hong
2018-05-01
Tricriticality, as a sister of criticality, is a fundamental and absorbing issue in condensed-matter physics. It has been verified that the bosonic Wilson-Fisher universality class can be changed by gapless fermionic modes at criticality. However, the counterpart phenomena at tricriticality have rarely been explored. In this Letter, we study a model in which a tricritical Ising model is coupled to massless Dirac fermions. We find that the massless Dirac fermions result in the emergence of a new tricritical point, which we refer to as the chiral tricritical point (CTP), at the phase boundary between the Dirac semimetal and the charge-density wave insulator. From functional renormalization group analysis of the effective action, we obtain the critical behaviors of the CTP, which are qualitatively distinct from both the tricritical Ising universality and the chiral Ising universality. We further extend the calculations of the chiral tricritical behaviors of Ising spins to the case of Heisenberg spins. The experimental relevance of the CTP in two-dimensional Dirac semimetals is also discussed.
Hydrogenated arsenenes as planar magnet and Dirac material
Energy Technology Data Exchange (ETDEWEB)
Zhang, Shengli; Cai, Bo; Zeng, Haibo, E-mail: Huziyu@csrc.ac.cn, E-mail: zeng.haibo@njust.edu.cn [Institute of Optoelectronics and Nanomaterials, Herbert Gleiter Institute of Nanoscience, College of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094 (China); Hu, Yonghong [Institute of Optoelectronics and Nanomaterials, Herbert Gleiter Institute of Nanoscience, College of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094 (China); School of Nuclear Technology and Chemistry and Biology, Hubei University of Science and Technology, Xianning 437100 (China); Hu, Ziyu, E-mail: Huziyu@csrc.ac.cn, E-mail: zeng.haibo@njust.edu.cn [Beijing Computational Science Research Center, Beijing 100084 (China)
2015-07-13
Arsenene and antimonene are predicted to have 2.49 and 2.28 eV band gaps, which have aroused intense interest in the two-dimensional (2D) semiconductors for nanoelectronic and optoelectronic devices. Here, the hydrogenated arsenenes are reported to be planar magnet and 2D Dirac materials based on comprehensive first-principles calculations. The semi-hydrogenated (SH) arsenene is found to be a quasi-planar magnet, while the fully hydrogenated (FH) arsenene is a planar Dirac material. The buckling height of pristine arsenene is greatly decreased by the hydrogenation, resulting in a planar and relatively low-mass-density sheet. The electronic structures of arsenene are also evidently altered after hydrogenating from wide-band-gap semiconductor to metallic material for SH arsenene, and then to Dirac material for FH arsenene. The SH arsenene has an obvious magnetism, mainly contributed by the p orbital of the unsaturated As atom. Such magnetic and Dirac materials modified by hydrogenation of arsenene may have potential applications in future optoelectronic and spintronic devices.
Hydrogenated arsenenes as planar magnet and Dirac material
International Nuclear Information System (INIS)
Zhang, Shengli; Cai, Bo; Zeng, Haibo; Hu, Yonghong; Hu, Ziyu
2015-01-01
Arsenene and antimonene are predicted to have 2.49 and 2.28 eV band gaps, which have aroused intense interest in the two-dimensional (2D) semiconductors for nanoelectronic and optoelectronic devices. Here, the hydrogenated arsenenes are reported to be planar magnet and 2D Dirac materials based on comprehensive first-principles calculations. The semi-hydrogenated (SH) arsenene is found to be a quasi-planar magnet, while the fully hydrogenated (FH) arsenene is a planar Dirac material. The buckling height of pristine arsenene is greatly decreased by the hydrogenation, resulting in a planar and relatively low-mass-density sheet. The electronic structures of arsenene are also evidently altered after hydrogenating from wide-band-gap semiconductor to metallic material for SH arsenene, and then to Dirac material for FH arsenene. The SH arsenene has an obvious magnetism, mainly contributed by the p orbital of the unsaturated As atom. Such magnetic and Dirac materials modified by hydrogenation of arsenene may have potential applications in future optoelectronic and spintronic devices
Hydrogenated arsenenes as planar magnet and Dirac material
Zhang, Shengli; Hu, Yonghong; Hu, Ziyu; Cai, Bo; Zeng, Haibo
2015-07-01
Arsenene and antimonene are predicted to have 2.49 and 2.28 eV band gaps, which have aroused intense interest in the two-dimensional (2D) semiconductors for nanoelectronic and optoelectronic devices. Here, the hydrogenated arsenenes are reported to be planar magnet and 2D Dirac materials based on comprehensive first-principles calculations. The semi-hydrogenated (SH) arsenene is found to be a quasi-planar magnet, while the fully hydrogenated (FH) arsenene is a planar Dirac material. The buckling height of pristine arsenene is greatly decreased by the hydrogenation, resulting in a planar and relatively low-mass-density sheet. The electronic structures of arsenene are also evidently altered after hydrogenating from wide-band-gap semiconductor to metallic material for SH arsenene, and then to Dirac material for FH arsenene. The SH arsenene has an obvious magnetism, mainly contributed by the p orbital of the unsaturated As atom. Such magnetic and Dirac materials modified by hydrogenation of arsenene may have potential applications in future optoelectronic and spintronic devices.
Fermi-Dirac statistics and the number theory
Kubasiak, A.; Korbicz, J.; Zakrzewski, J.; Lewenstein, M.
2005-01-01
We relate the Fermi-Dirac statistics of an ideal Fermi gas in a harmonic trap to partitions of given integers into distinct parts, studied in number theory. Using methods of quantum statistical physics we derive analytic expressions for cumulants of the probability distribution of the number of different partitions.
New exact solutions of the Dirac equation. 11
International Nuclear Information System (INIS)
Bagrov, V.G.; Noskov, M.D.
1984-01-01
Investigations into determining new exact solutions of relativistic wave equations started in another paper were continued. Exact solutions of the Dirac, Klein-Gordon equations and classical relativistic equations of motion in four new types of external electromagnetic fields were found
Majorana zero modes in Dirac semimetal Josephson junctions
Li, Chuan; de Boer, Jorrit; de Ronde, Bob; Huang, Yingkai; Golden, Mark; Brinkman, Alexander
We have realized proximity-induced superconductivity in a Dirac semimetal and revealed the topological nature of the superconductivity by the observation of Majorana zero modes. As a Dirac semimetal, Bi0.97Sb0.03 is used, where a three-dimensional Dirac cone exists in the bulk due to an accidental touching between conduction and valence bands. Electronic transport measurements on Hall-bars fabricated out of Bi0.97Sb0.03 flakes consistently show negative magnetoresistance for magnetic fields parallel to the current, which is associated with the chiral anomaly. In perpendicular magnetic fields, we see Shubnikov-de Haas oscillations that indicate very low carrier densities. The low Fermi energy and protection against backscattering in our Dirac semimetal Josephson junctions provide favorable conditions for a large contribution of Majorana zero modes to the supercurrent. In radiofrequency irradiation experiments, we indeed observe these Majorana zero modes in Nb-Bi0.97Sb0.03-Nb Josephson junctions as a 4 π periodic contribution to the current-phase relation.
Dirac Magnon Nodal Loops in Quasi-2D Quantum Magnets.
Owerre, S A
2017-07-31
In this report, we propose a new concept of one-dimensional (1D) closed lines of Dirac magnon nodes in two-dimensional (2D) momentum space of quasi-2D quantum magnetic systems. They are termed "2D Dirac magnon nodal-line loops". We utilize the bilayer honeycomb ferromagnets with intralayer coupling J and interlayer coupling J L , which is realizable in the honeycomb chromium compounds CrX 3 (X ≡ Br, Cl, and I). However, our results can also exist in other layered quasi-2D quantum magnetic systems. Here, we show that the magnon bands of the bilayer honeycomb ferromagnets overlap for J L ≠ 0 and form 1D closed lines of Dirac magnon nodes in 2D momentum space. The 2D Dirac magnon nodal-line loops are topologically protected by inversion and time-reversal symmetry. Furthermore, we show that they are robust against weak Dzyaloshinskii-Moriya interaction Δ DM magnon edge modes.
Radiationless Zitterbewegung of Dirac particles and mass formula
International Nuclear Information System (INIS)
Noboru Hokkyo.
1987-06-01
The Zitterbewegung of the Dirac particle is given a visual representation by solving the two-component difference form of the Dirac equation. It is seen that the space-time trajectory of a Dirac particle can be pictured as a correlated whole of a network of zigzags of left- and right-handed chiral neutrino-like line elements. These zigzags can feel the curl of the external electromagnetic vector potential and give rise to the spin magnetic interaction, confirming Schroedinger's earlier intuitive picture of the spin as the orbital angular momentum of the Zitterbewegung. The network of zigzags associated with an electron splits and reunites in passing through the slits in the electron beam interference experiment. It is proposed to interpret Nambu's empirical mass formula m n =(n/2)137m e =(n/2)((h/2π)/cL), n=integer, as a radiationless condition for the Zitterbewegung of the hadronic Dirac particle of the linear spatial extension of the order of the classical electron radius L=e 2 /m e c 2 . (author). 20 refs, 4 figs
Qualitative analysis of trapped Dirac fermions in graphene
Czech Academy of Sciences Publication Activity Database
Jakubský, Vít; Krejčiřík, David
2014-01-01
Roč. 349, OCT (2014), s. 268-287 ISSN 0003-4916 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : graphene * Dirac fermion * confinement * Varitional principle Subject RIV: BE - Theoretical Physics Impact factor: 2.103, year: 2014
International Nuclear Information System (INIS)
Akemann, Gernot; Bittner, Elmar
2006-01-01
We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-color lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues come in complex conjugate pairs, making the action of this theory real and positive for our choice of two staggered flavors. This enables us to use standard Monte Carlo simulations in testing the influence of the chemical potential and quark mass on complex eigenvalues close to the origin. We find excellent agreement between the analytic predictions and our data for two different volumes over a range of chemical potentials below the chiral phase transition. In particular, we detect the effect of unquenching when going to very small quark masses
Smyth, R. T.; Ballance, C. P.; Ramsbottom, C. A.; Johnson, C. A.; Ennis, D. A.; Loch, S. D.
2018-05-01
Neutral tungsten is the primary candidate as a wall material in the divertor region of the International Thermonuclear Experimental Reactor (ITER). The efficient operation of ITER depends heavily on precise atomic physics calculations for the determination of reliable erosion diagnostics, helping to characterize the influx of tungsten impurities into the core plasma. The following paper presents detailed calculations of the atomic structure of neutral tungsten using the multiconfigurational Dirac-Fock method, drawing comparisons with experimental measurements where available, and includes a critical assessment of existing atomic structure data. We investigate the electron-impact excitation of neutral tungsten using the Dirac R -matrix method, and by employing collisional-radiative models, we benchmark our results with recent Compact Toroidal Hybrid measurements. The resulting comparisons highlight alternative diagnostic lines to the widely used 400.88-nm line.
Hawking radiation of Dirac particles in the hot NUT-Kerr-Newman spacetime
International Nuclear Information System (INIS)
Ahmed, M.
1991-01-01
The Hawking radiation of charged Dirac particles on the horizons of the hot NUT-Kerr-Newman spacetime is studied in this paper. To this end, we obtain the radial decoupled Dirac equation for the electron in the hot NUT-Kerr-Newman spacetime. Next we solve the Dirac equation near the horizons. Finally, by analytic continuation, the Hawking thermal spectrum formula of Dirac particles is obtained. The problem of the Hawking evaporation of Dirac particles in the hot NUT-Kerr-Newman background is thus solved. (orig.)
Analysis of DIRAC's behavior using model checking with process algebra
International Nuclear Information System (INIS)
Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof; Diaz, Ricardo Graciani
2012-01-01
DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.
Analysis of DIRAC's behavior using model checking with process algebra
Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Graciani Diaz, Ricardo; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof
2012-12-01
DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.
Integration of the gUSE/WS-PGRADE and InSilicoLab portals with DIRAC
International Nuclear Information System (INIS)
Navarro, A Puig; Casals, D Viana; Díaz, R Graciani; Ramo, A Casajús; Á Balaskó; P Kacksuk; D Harezlak; J Kocot
2012-01-01
The gUSE (Grid User Support Environment) framework allows to create, store and distribute application workflows. This workflow architecture includes a wide variety of payload execution operations, such as loops, conditional execution of jobs and combination of output. These complex multi-job workflows can easily be created and modified by application developers through the WS-PGRADE portal. The portal also allows end users to download and use existing workflows, as well as executing them. The DIRAC framework for distributed computing, a complete Grid solution for a community of users needing access to distributed computing resources, has been integrated into the gUSE/WS-PGRADE system. This integration allows the execution of gUSE workflows in a distributed computing environment, thus greatly expanding the capability of the portal to several Grids and Cloud Computing facilities. The main features and possibilities of the gUSE/WS-PGRADE-DIRAC system, as well as the benefits for users, will be outlined and discussed.
Algebraic inversion of the Dirac equation for the vector potential in the non-Abelian case
International Nuclear Information System (INIS)
Inglis, S M; Jarvis, P D
2012-01-01
We study the Dirac equation for spinor wavefunctions minimally coupled to an external field, from the perspective of an algebraic system of linear equations for the vector potential. By analogy with the method in electromagnetism, which has been well-studied, and leads to classical solutions of the Maxwell–Dirac equations, we set up the formalism for non-Abelian gauge symmetry, with the SU(2) group and the case of four-spinor doublets. An extended isospin-charge conjugation operator is defined, enabling the hermiticity constraint on the gauge potential to be imposed in a covariant fashion, and rendering the algebraic system tractable. The outcome is an invertible linear equation for the non-Abelian vector potential in terms of bispinor current densities. We show that, via application of suitable extended Fierz identities, the solution of this system for the non-Abelian vector potential is a rational expression involving only Pauli scalar and Pauli triplet, Lorentz scalar, vector and axial vector current densities, albeit in the non-closed form of a Neumann series. (paper)
High-temperature expansion of the one-loop effective action induced by scalar and Dirac particles
Energy Technology Data Exchange (ETDEWEB)
Kalinichenko, Igor; Kazinski, Peter [Tomsk State University, Physics Faculty, Tomsk (Russian Federation)
2017-12-15
The complete nonperturbative expressions for the high-temperature expansion of the one-loop effective action induced by the charged scalar and the charged Dirac particles both at zero and finite temperatures are derived with account of possible nontrivial boundary conditions. The background electromagnetic field is assumed to be stationary and such that the corresponding Klein-Gordon operator or the Dirac Hamiltonian is self-adjoint. The contributions of particles and antiparticles are obtained separately. The explicit expressions for the C-symmetric and the non-C-symmetric vacuum energies of the Dirac fermions are derived. The leading corrections to the high-temperature expansion due to the nontrivial boundary conditions are explicitly found. The corrections to the logarithmic divergence of the effective action that come from the boundary conditions are derived. The high-temperature expansion of the naive one-loop effective action induced by charged fermions turns out to be divergent in the limit of a zero fermion mass. (orig.)
Haddad, L. H.; Carr, Lincoln D.
2015-11-01
We analyze the vortex solution space of the (2+1)-dimensional nonlinear Dirac equation for bosons in a honeycomb optical lattice at length scales much larger than the lattice spacing. Dirac point relativistic covariance combined with s-wave scattering for bosons leads to a large number of vortex solutions characterized by different functional forms for the internal spin and overall phase of the order parameter. We present a detailed derivation of these solutions which include skyrmions, half-quantum vortices, Mermin-Ho and Anderson-Toulouse vortices for vortex winding {\\ell }=1. For {\\ell }≥slant 2 we obtain topological as well as non-topological solutions defined by the asymptotic radial dependence. For arbitrary values of ℓ the non-topological solutions include bright ring-vortices which explicitly demonstrate the confining effects of the Dirac operator. We arrive at solutions through an asymptotic Bessel series, algebraic closed-forms, and using standard numerical shooting methods. By including a harmonic potential to simulate a finite trap we compute the discrete spectra associated with radially quantized modes. We demonstrate the continuous spectral mapping between the vortex and free particle limits for all of our solutions.
Realization of non-symmorphic Dirac cones in PbFCl materials
Schoop, Leslie
While most 3D Dirac semimetals require two bands with different orbital character to be protected, there is also the possibility to find 3D Dirac semimetals that are guaranteed to exist in certain space groups. Those are resulting from the non-symmoprhic symmetry of the space group, which forces the bands to degenerate at high symmetry points in the Brillouin zone. Non-symmorphic space groups can force three- four, six and eight fold degeneracies which led to the proposal to find 3D Dirac Semimetals as well as new quasiparticles in such space groups. Problematic for realizing this types of Dirac materials is that they require and odd band filling in order to have the Fermi level located at or also near by the band crossing points. Therefore, although the first prediction for using non-symmoprhic symmetry to create a Dirac material was made in 2012, it took almost four years for an experimental verification of this type of Dirac crossing. In this talk I will introduce the material ZrSiS that has, besides other Dirac features, a Dirac cone protected by non-symmorphic symmetry at about 0.5 eV below the Fermi level and was the first material where this type of Dirac cone was imaged with ARPES. I will then proceed to discuss ways to shift this crossing to the Fermi edge and finally show an experimental verification of a fourfold Dirac crossing, protected by non-symmorphic symmetry, at the Fermi energy.
New correct solutions of the Dirac equation. 5
International Nuclear Information System (INIS)
Bagrov, V.G.; Byzov, N.N.; Gitman, D.M.; Klimenko, Yu.I.; Meshkov, A.G.; Shapovalov, V.N.; Shakhmatov, V.M.
1975-01-01
Some exact solutions for the Dirac equation, Klein-Gordon equation and classical relativistic equations of motion of an electron in external electromagnetic fields of a special type are considered. When fields E vector and H vector are related by the expression H vector=[n vector E vector]+n vector H 3 , where n vector is a constant unit vector, it turns out that among fields permitting the separation of variables in the Klein-Gordon equation more than half satisfy this relationship. For such fields the solution of the Dirac equation may be simplified considerably. Four specific kinds of fields are examined. The character of electron motion in such fields is peculiar but in the mathematical aspect, part of the problem is reduced to those considered previously
Chirality correlation within Dirac eigenvectors from domain wall fermions
International Nuclear Information System (INIS)
Blum, T.; Christ, N.; Cristian, C.; Liao, X.; Liu, G.; Mawhinney, R.; Wu, L.; Zhestkov, Y.; Dawson, C.
2002-01-01
In the dilute instanton gas model of the QCD vacuum, one expects a strong spatial correlation between chirality and the maxima of the Dirac eigenvectors with small eigenvalues. Following Horvath et al. we examine this question using lattice gauge theory within the quenched approximation. We extend the work of those authors by using weaker coupling, β=6.0, larger lattices, 16 4 , and an improved fermion formulation, domain wall fermions. In contrast with this earlier work, we find a striking correlation between the magnitudes of the chirality density, |ψ † (x)γ 5 ψ(x)|, and the normal density, ψ † (x)ψ(x), for the low-lying Dirac eigenvectors
Spin-polarized gapped Dirac spectrum of unsupported silicene
Energy Technology Data Exchange (ETDEWEB)
Podsiadły-Paszkowska, A., E-mail: agata.podsiadly@gmail.com; Krawiec, M., E-mail: mariusz.krawiec@umcs.pl
2016-06-15
Highlights: • Effects of spin–orbit interaction and atomic reconstruction of silicene on its electronic properties have been studied. • Spin-polarized gapped Dirac spectrum has been revealed. • Two different AFM phases have been obtained. - Abstract: We study effects of the spin–orbit interaction and the atomic reconstruction of silicene on its electronic spectrum. As an example we consider unsupported silicene pulled off from Pb(111) substrate. Using first principles density functional theory we show that the inversion symmetry broken arrangement of atoms and the spin–orbit interaction generate a spin-polarized electronic spectrum with an energy gap in the Dirac cone. These findings are particularly interesting in view of the quantum anomalous and quantum valley Hall effects and should be observable in weakly interacting silicene-substrate systems.
Dynamical class of a two-dimensional plasmonic Dirac system.
Silva, Érica de Mello
2015-10-01
A current goal in plasmonic science and technology is to figure out how to manage the relaxational dynamics of surface plasmons in graphene since its damping constitutes a hinder for the realization of graphene-based plasmonic devices. In this sense we believe it might be of interest to enlarge the knowledge on the dynamical class of two-dimensional plasmonic Dirac systems. According to the recurrence relations method, different systems are said to be dynamically equivalent if they have identical relaxation functions at all times, and such commonality may lead to deep connections between seemingly unrelated physical systems. We employ the recurrence relations approach to obtain relaxation and memory functions of density fluctuations and show that a two-dimensional plasmonic Dirac system at long wavelength and zero temperature belongs to the same dynamical class of standard two-dimensional electron gas and classical harmonic oscillator chain with an impurity mass.
Stability of Dirac Liquids with Strong Coulomb Interaction.
Tupitsyn, Igor S; Prokof'ev, Nikolay V
2017-01-13
We develop and apply the diagrammatic Monte Carlo technique to address the problem of the stability of the Dirac liquid state (in a graphene-type system) against the strong long-range part of the Coulomb interaction. So far, all attempts to deal with this problem in the field-theoretical framework were limited either to perturbative or random phase approximation and functional renormalization group treatments, with diametrically opposite conclusions. Our calculations aim at the approximation-free solution with controlled accuracy by computing vertex corrections from higher-order skeleton diagrams and establishing the renormalization group flow of the effective Coulomb coupling constant. We unambiguously show that with increasing the system size L (up to ln(L)∼40), the coupling constant always flows towards zero; i.e., the two-dimensional Dirac liquid is an asymptotically free T=0 state with divergent Fermi velocity.
The strangest man. The hidden life of Paul Dirac
International Nuclear Information System (INIS)
Farmelo, Graham
2016-01-01
The Strangest Man is the Costa Biography Award-winning account of Paul Dirac, the famous physicist sometimes called the British Einstein. He was one of the leading pioneers of the greatest revolution in twentieth-century science: quantum mechanics. The youngest theoretician ever to win the Nobel Prize for Physics, he was also pathologically reticent, strangely literal-minded and legendarily unable to communicate or empathize. Through his greatest period of productivity, his postcards home contained only remarks about the weather. Based on a previously undiscovered archive of family papers, Graham Farmelo celebrates Dirac's massive scientific achievement while drawing a compassionate portrait of his life and work. Farmelo shows a man who, while hopelessly socially inept, could manage to love and sustain close friendship. The Strangest Man is an extraordinary and moving human story, as well as a study of one of the most exciting times in scientific history.
Analysis of DIRAC's behavior using model checking with process algebra
Remenska, Daniela; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Diaz, Ricardo Graciani; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof
2012-01-01
DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple, the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike con...
Dirac bound states of anharmonic oscillator in external fields
International Nuclear Information System (INIS)
Hamzavi, Majid; Ikhdair, Sameer M.; Falaye, Babatunde J.
2014-01-01
We explore the effect of the external magnetic and Aharonov–Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov–Uvarov (NU) method. -- Highlights: • Effect of the external fields on the energy levels of Dirac particle with the anharmonic oscillator is investigated. • The solutions are discussed in view of spin and pseudospin symmetries limits. • The energy levels and wave function are presented by the Nikiforov–Uvarov method
Performance of combined production and analysis WMS in DIRAC
Paterson, S
2010-01-01
DIRAC, the LHCb community Grid solution, uses generic pilot jobs to obtain a virtual pool of resources for the VO community. In this way agents can request the highest priority user or production jobs from a central task queue and VO policies can be applied with full knowledge of current and previous activities. In this paper the performance of the DIRAC WMS will be presented with emphasis on how the system copes with many varied job requirements. In order to ensure traceability of jobs as well as security, the actual users identity has to be established before running the actual payload workflow. Generic pilot jobs take advantage of the deployment of the gLExec utility in order to achieve this. Experience with gLExec will be described.
Phase diagram of the Dirac spectrum at nonzero chemical potential
International Nuclear Information System (INIS)
Osborn, J. C.; Splittorff, K.; Verbaarschot, J. J. M.
2008-01-01
The Dirac spectrum of QCD with dynamical fermions at nonzero chemical potential is characterized by three regions: a region with a constant eigenvalue density, a region where the eigenvalue density shows oscillations that grow exponentially with the volume and the remainder of the complex plane where the eigenvalue density is zero. In this paper we derive the phase diagram of the Dirac spectrum from a chiral Lagrangian. We show that the constant eigenvalue density corresponds to a pion condensed phase while the strongly oscillating region is given by a kaon condensed phase. The normal phase with nonzero chiral condensate but vanishing Bose condensates coincides with the region of the complex plane where there are no eigenvalues.
How (not) to teach Lorentz covariance of the Dirac equation
International Nuclear Information System (INIS)
Nikolić, Hrvoje
2014-01-01
In the textbook proofs of the Lorentz covariance of the Dirac equation, one treats the wave function as a spinor and gamma matrices as scalars, leading to a quite complicated formalism with several pedagogic drawbacks. As an alternative, I propose to teach the Dirac equation and its Lorentz covariance by using a much simpler, but physically equivalent formalism, in which these drawbacks do not appear. In this alternative formalism, the wave function transforms as a scalar and gamma matrices as components of a vector, such that the standard physically relevant bilinear combinations do not change their transformation properties. The alternative formalism allows also a natural construction of some additional non-standard bilinear combinations with well-defined transformation properties. (paper)
Surface regulated arsenenes as Dirac materials: From density functional calculations
International Nuclear Information System (INIS)
Yuan, Junhui; Xie, Qingxing; Yu, Niannian; Wang, Jiafu
2017-01-01
Highlights: • The presence of Dirac cones in chemically decorated buckled arsenene AsX (X = CN, NC, NCO, NCS, and NCSe) has been revealed. • First-principles calculations show that all these chemically decorated arsenenes are kinetically stable in defending thermal fluctuations in room temperature. - Abstract: Using first principle calculations based on density functional theory (DFT), we have systematically investigated the structure stability and electronic properties of chemically decorated arsenenes, AsX (X = CN, NC, NCO, NCS and NCSe). Phonon dispersion and formation energy analysis reveal that all the five chemically decorated buckled arsenenes are energetically favorable and could be synthesized. Our study shows that wide-bandgap arsenene would turn into Dirac materials when functionalized by -X (X = CN, NC, NCO, NCS and NCSe) groups, rendering new promises in next generation high-performance electronic devices.
Photon-Assisted Spectroscopy of Dirac Electrons in Graphene
Directory of Open Access Journals (Sweden)
Abdelrazek A. S.
2012-01-01
Full Text Available The quantum Goos-Hanchen effect in graphene is investigated. The Goos-Hanchen phase shift is derived by solving the Dirac eigenvalue differential equation. This phase shift varies with the angle of incidence of the quasiparticle Dirac fermions on the bar- rier. Calculations show that the dependence of the phase shift on the angle of incidence is sensitive to the variation of the energy gap of graphene, the applied magnetic field and the frequency of the electromagnetic waves. The present results show that the con- ducting states in the sidebands is very effective in the phase shift for frequencies of the applied electromagnetic field. This investigation is very important for the application of graphene in nanoelectronics and nanophotonics.
Three-dimensional periodic dielectric structures having photonic Dirac points
Bravo-Abad, Jorge; Joannopoulos, John D.; Soljacic, Marin
2015-06-02
The dielectric, three-dimensional photonic materials disclosed herein feature Dirac-like dispersion in quasi-two-dimensional systems. Embodiments include a face-centered cubic (fcc) structure formed by alternating layers of dielectric rods and dielectric slabs patterned with holes on respective triangular lattices. This fcc structure also includes a defect layer, which may comprise either dielectric rods or a dielectric slab with patterned with holes. This defect layer introduces Dirac cone dispersion into the fcc structure's photonic band structure. Examples of these fcc structures enable enhancement of the spontaneous emission coupling efficiency (the .beta.-factor) over large areas, contrary to the conventional wisdom that the .beta.-factor degrades as the system's size increases. These results enable large-area, low-threshold lasers; single-photon sources; quantum information processing devices; and energy harvesting systems.
Dark energy from pNGB mediated Dirac neutrino condensate
Directory of Open Access Journals (Sweden)
Ujjal Kumar Dey
2018-03-01
Full Text Available We consider an extension of the Standard Model that provide an unified description of eV scale neutrino mass and dark energy. An explicit model is presented by augmenting the Standard Model with an SU(2L doublet scalar, a singlet scalar and right handed neutrinos where all of them are assumed to be charged under a global U(1X symmetry. A light pseudo-Nambu–Goldstone Boson, associated with the spontaneously broken U(1X symmetry, acts as a mediator of an attractive force leading to a Dirac neutrino condensate, with large correlation length, and a non-zero gap in the right range providing a cosmologically feasible dark energy scenario. The neutrino mass is generated through the usual Dirac seesaw mechanism. Parameter space, reproducing viable dark energy scenario while having neutrino mass in the right ballpark, is presented.
Particlelike solutions of the Einstein-Dirac equations
Finster, Felix; Smoller, Joel; Yau, Shing-Tung
1999-05-01
The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of solitonlike solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well behaved even for strong coupling.
A spatially homogeneous and isotropic Einstein-Dirac cosmology
Finster, Felix; Hainzl, Christian
2011-04-01
We consider a spatially homogeneous and isotropic cosmological model where Dirac spinors are coupled to classical gravity. For the Dirac spinors we choose a Hartree-Fock ansatz where all one-particle wave functions are coherent and have the same momentum. If the scale function is large, the universe behaves like the classical Friedmann dust solution. If however the scale function is small, quantum effects lead to oscillations of the energy-momentum tensor. It is shown numerically and proven analytically that these quantum oscillations can prevent the formation of a big bang or big crunch singularity. The energy conditions are analyzed. We prove the existence of time-periodic solutions which go through an infinite number of expansion and contraction cycles.
Disordered Dirac fermions: the marriage of three different approaches
Energy Technology Data Exchange (ETDEWEB)
Bhaseen, Miraculous J. E-mail: bhaseen@thphys.ox.ac.uk; Caux, J.-S. E-mail: caux@thphys.ox.ac.uk; Kogan, Ian I. E-mail: kogan@thphys.ox.ac.uk; Tsvelik, Alexei M. E-mail: tsvelik@thphys.ox.ac.uk
2001-12-17
We compare the critical multipoint correlation functions for two-dimensional (massless) Dirac fermions in the presence of a random su(N) (non-Abelian) gauge potential, obtained by three different methods. We critically reexamine previous results obtained using the replica approach and in the limit of infinite disorder strength and compare them to new results (presented here) obtained using the supersymmetric approach to the N=2 case. We demonstrate that this menage a trois of different approaches leads to identical results. Remarkable relations between apparently different conformal field theories (CFTs) are thereby obtained. We further establish a connection between the random Dirac fermion problem and the c=-2 theory of dense polymers. The presence of the c=-2 theory may be seen in all three different treatments of the disorder.
Disordered Dirac fermions: the marriage of three different approaches
International Nuclear Information System (INIS)
Bhaseen, Miraculous J.; Caux, J.-S.; Kogan, Ian I.; Tsvelik, Alexei M.
2001-01-01
We compare the critical multipoint correlation functions for two-dimensional (massless) Dirac fermions in the presence of a random su(N) (non-Abelian) gauge potential, obtained by three different methods. We critically reexamine previous results obtained using the replica approach and in the limit of infinite disorder strength and compare them to new results (presented here) obtained using the supersymmetric approach to the N=2 case. We demonstrate that this menage a trois of different approaches leads to identical results. Remarkable relations between apparently different conformal field theories (CFTs) are thereby obtained. We further establish a connection between the random Dirac fermion problem and the c=-2 theory of dense polymers. The presence of the c=-2 theory may be seen in all three different treatments of the disorder
Three-dimensional periodic dielectric structures having photonic Dirac points
Energy Technology Data Exchange (ETDEWEB)
Bravo-Abad, Jorge; Joannopoulos, John D.; Soljacic, Marin
2015-06-02
The dielectric, three-dimensional photonic materials disclosed herein feature Dirac-like dispersion in quasi-two-dimensional systems. Embodiments include a face-centered cubic (fcc) structure formed by alternating layers of dielectric rods and dielectric slabs patterned with holes on respective triangular lattices. This fcc structure also includes a defect layer, which may comprise either dielectric rods or a dielectric slab with patterned with holes. This defect layer introduces Dirac cone dispersion into the fcc structure's photonic band structure. Examples of these fcc structures enable enhancement of the spontaneous emission coupling efficiency (the .beta.-factor) over large areas, contrary to the conventional wisdom that the .beta.-factor degrades as the system's size increases. These results enable large-area, low-threshold lasers; single-photon sources; quantum information processing devices; and energy harvesting systems.
Peccei-Quinn symmetry for Dirac seesaw and leptogenesis
Energy Technology Data Exchange (ETDEWEB)
Gu, Pei-Hong [Department of Physics and Astronomy, Shanghai Jiao Tong University,800 Dongchuan Road, Shanghai 200240 (China)
2016-07-04
We extend the DFSZ invisible axion model to simultaneously explain small Dirac neutrino masses and cosmic matter-antimatter asymmetry. After the Peccei-Quinn and electroweak symmetry breaking, the effective Yukawa couplings of the Dirac neutrinos to the standard model Higgs scalar can be highly suppressed by the ratio of the vacuum expectation value of an iso-triplet Higgs scalar over the masses of some heavy gauge-singlet fermions, iso-doublet Higgs scalars or iso-triplet fermions. The iso-triplet fields can carry a zero or nonzero hypercharge. Through the decays of the heavy gauge-singlet fermions, iso-doublet scalars or iso-triplet fermions, we can obtain a lepton asymmetry in the left-handed leptons and an opposite lepton asymmetry in the right-handed neutrinos. Since the right-handed neutrinos do not participate in the sphaleron processes, the left-handed lepton asymmetry can be partially converted to a baryon asymmetry.
Dirac equation in noncommutative space for hydrogen atom
Energy Technology Data Exchange (ETDEWEB)
Adorno, T.C., E-mail: tadorno@nonada.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Baldiotti, M.C., E-mail: baldiott@fma.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Chaichian, M., E-mail: Masud.Chaichian@helsinki.f [Department of Physics, University of Helsinki and Helsinki Institute of Physics, PO Box 64, FIN-00014 Helsinki (Finland); Gitman, D.M., E-mail: gitman@dfn.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Tureanu, A., E-mail: Anca.Tureanu@helsinki.f [Department of Physics, University of Helsinki and Helsinki Institute of Physics, PO Box 64, FIN-00014 Helsinki (Finland)
2009-11-30
We consider the energy levels of a hydrogen-like atom in the framework of theta-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S{sub 1/2}, 2P{sub 1/2} and 2P{sub 3/2} is lifted completely, such that new transition channels are allowed.
Dirac equation in noncommutative space for hydrogen atom
International Nuclear Information System (INIS)
Adorno, T.C.; Baldiotti, M.C.; Chaichian, M.; Gitman, D.M.; Tureanu, A.
2009-01-01
We consider the energy levels of a hydrogen-like atom in the framework of θ-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S 1/2 , 2P 1/2 and 2P 3/2 is lifted completely, such that new transition channels are allowed.
Two-loop Dirac neutrino mass and WIMP dark matter
Bonilla, Cesar; Ma, Ernest; Peinado, Eduardo; Valle, Jose W.F.
2018-01-01
We propose a "scotogenic" mechanism relating small neutrino mass and cosmological dark matter. Neutrinos are Dirac fermions with masses arising only in two--loop order through the sector responsible for dark matter. Two triality symmetries ensure both dark matter stability and strict lepton number conservation at higher orders. A global spontaneously broken U(1) symmetry leads to a physical $Diracon$ that induces invisible Higgs decays which add up to the Higgs to dark matter mode. This enhan...
The time-of-flight detector of the DIRAC experiment
International Nuclear Information System (INIS)
Adeva, B.; Gallas, M.V.; Gomez, F.; Lopez-Agueera, A.; Nunez-Pardo, T.; Plo, M.; Rodriguez, A.M.; Rodriguez, X.M.; Saborido, J.J.; Santamarina, C.; Tobar, M.J.; Vazquez, P.
2002-01-01
The construction and performance of a large area time-of-flight detector for the DIRAC experiment at CERN is reported. With an average time resolution of 123 ps per counter at rates up to 1 MHz, it allows excellent separation of pπ - from π + π - pairs up to 4.6 GeV/c momentum, as well as of Coulomb-correlated pion pairs from accidentals. The optimization of scintillator material, photomultiplier performance and readout electronics is described
General method for reducing the two-body Dirac equation
International Nuclear Information System (INIS)
Galeao, A.P.; Ferreira, P.L.
1992-01-01
A semi relativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schroedinger-type equations is also discussed. (author)
The Dirac-Kaehler equation and fermions on the lattice
International Nuclear Information System (INIS)
Becher, P.
1982-05-01
The geometrical description of spinor fields by E. Kaehler is used to formulate a consistent lattice approximation of fermions. The relation to free simple Dirac fields as well as to Susskind's description of lattice fermions is clarified. The first steps towards a quantized interacting theory are given. The correspondence between the calculus of differential forms and concepts of algebraic topology is shown to be a useful method for a completely analogous treatment of the problems in the continuum and on the lattice. (orig.)
Algebraic and Dirac-Hestenes spinors and spinor fields
International Nuclear Information System (INIS)
Rodrigues, Waldyr A. Jr.
2004-01-01
Almost all presentations of Dirac theory in first or second quantization in physics (and mathematics) textbooks make use of covariant Dirac spinor fields. An exception is the presentation of that theory (first quantization) offered originally by Hestenes and now used by many authors. There, a new concept of spinor field (as a sum of nonhomogeneous even multivectors fields) is used. However, a careful analysis (detailed below) shows that the original Hestenes definition cannot be correct since it conflicts with the meaning of the Fierz identities. In this paper we start a program dedicated to the examination of the mathematical and physical basis for a comprehensive definition of the objects used by Hestenes. In order to do that we give a preliminary definition of algebraic spinor fields (ASF) and Dirac-Hestenes spinor fields (DHSF) on Minkowski space-time as some equivalence classes of pairs (Ξ u ,ψ Ξ u ), where Ξ u is a spinorial frame field and ψ Ξ u is an appropriate sum of multivectors fields (to be specified below). The necessity of our definitions are shown by a careful analysis of possible formulations of Dirac theory and the meaning of the set of Fierz identities associated with the bilinear covariants (on Minkowski space-time) made with ASF or DHSF. We believe that the present paper clarifies some misunderstandings (past and recent) appearing on the literature of the subject. It will be followed by a sequel paper where definitive definitions of ASF and DHSF are given as appropriate sections of a vector bundle called the left spin-Clifford bundle. The bundle formulation is essential in order to be possible to produce a coherent theory for the covariant derivatives of these fields on arbitrary Riemann-Cartan space-times. The present paper contains also Appendixes A-E which exhibits a truly useful collection of results concerning the theory of Clifford algebras (including many tricks of the trade) necessary for the intelligibility of the text
Fermi-Dirac statistics plus liquid description of quark partons
International Nuclear Information System (INIS)
Buccella, F.; Migliore, G.; Tibullo, V.
1995-01-01
A previous approach with Fermi-Dirac distributions for fermion partons is here improved to comply with the expected low x behaviour of structure functions. We are so able to get a fair description of the unpolarized and polarized structure functions of the nucleons as well as of neutrino data. We cannot reach definite conclusions, but confirm our suspicion of a relationship between the defects in Gottfried and spin sum rules. (orig.)
Noncommutativity into Dirac Equation with mass dependent on the position
International Nuclear Information System (INIS)
Bastos, Samuel Batista; Almeida, Carlos Alberto Santos; Nunes, Luciana Angelica da Silva
2013-01-01
Full text: In recent years, there is growing interest in the study of theories in non-commutative spaces. Non-commutative fields theories are related with compactifications of M theory, string theory and the quantum Hall effect. Moreover, the role of the non-commutativity of theories of a particle finds large applications when analyzed in scenarios of quantum mechanics and relativistic quantum mechanics. In these contexts investigations on the Schrodinger and Dirac equations with mass depending on the position (MDP) has attracted much attention in the literature. Systems endowed with MDP models are useful for the study of many physical problems. In particular, they are used to study the energy density in problems of many bodies, determining the electronic properties of semiconductor heterostructures and also to describe the properties of heterojunctions and quantum dots. In particular, the investigation of relativistic effects it is important for systems containing heavy atoms or doping by heavy ions. For these types of materials, the study of the properties of the Dirac equation, in the case where the mass becomes variable is of great interest. In this paper, we seek for the non-relativistic limit of the Dirac Hamiltonian in the context of a theory of effective mass, through a Foldy-Wouthuysen transformation. We analyse the Dirac equation with mass dependent on the position, in a smooth step shape mass distribution, in non-commutative space (NC). This potential type kink was recently discussed by several authors in the commutative context and now we present our results in the non-commutative context. (author)
Electric-dipole-induced universality for Dirac fermions in graphene.
De Martino, Alessandro; Klöpfer, Denis; Matrasulov, Davron; Egger, Reinhold
2014-05-09
We study electric dipole effects for massive Dirac fermions in graphene and related materials. The dipole potential accommodates towers of infinitely many bound states exhibiting a universal Efimov-like scaling hierarchy. The dipole moment determines the number of towers, but there is always at least one tower. The corresponding eigenstates show a characteristic angular asymmetry, observable in tunnel spectroscopy. However, charge transport properties inferred from scattering states are highly isotropic.
Algebraic solution for the vector potential in the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Booth, H.S. [School of Mathematics and Physics, University of Tasmania, Hobart Tas (Australia); Centre for Mathematics and its Applications, Australian National University (Australia)]. E-mail: hbooth@wintermute.anu.edu.au; Legg, G.; Jarvis, P.D. [School of Mathematics and Physics, University of Tasmania, Hobart Tas (Australia)
2001-07-20
The Dirac equation for an electron in an external electromagnetic field can be regarded as a singular set of linear equations for the vector potential. Radford's method of algebraically solving for the vector potential is reviewed, with attention to the additional constraints arising from non-maximality of the rank. The extension of the method to general spacetimes is illustrated by examples in diverse dimensions with both c- and a-number wavefunctions. (author)
Topological transport in Dirac nodal-line semimetals
Rui, W. B.; Zhao, Y. X.; Schnyder, Andreas P.
2018-04-01
Topological nodal-line semimetals are characterized by one-dimensional Dirac nodal rings that are protected by the combined symmetry of inversion P and time-reversal T . The stability of these Dirac rings is guaranteed by a quantized ±π Berry phase and their low-energy physics is described by a one-parameter family of (2+1)-dimensional quantum field theories exhibiting the parity anomaly. Here we study the Berry-phase supported topological transport of P T -invariant nodal-line semimetals. We find that small inversion breaking allows for an electric-field-induced anomalous transverse current, whose universal component originates from the parity anomaly. Due to this Hall-like current, carriers at opposite sides of the Dirac nodal ring flow to opposite surfaces when an electric field is applied. To detect the topological currents, we propose a dumbbell device, which uses surface states to filter charges based on their momenta. Suggestions for experiments and device applications are discussed.
MPI support in the DIRAC Pilot Job Workload Management System
International Nuclear Information System (INIS)
Tsaregorodtsev, A; Hamar, V
2012-01-01
Parallel job execution in the grid environment using MPI technology presents a number of challenges for the sites providing this support. Multiple flavors of the MPI libraries, shared working directories required by certain applications, special settings for the batch systems make the MPI support difficult for the site managers. On the other hand the workload management systems with Pilot Jobs became ubiquitous although the support for the MPI applications in the Pilot frameworks was not available. This support was recently added in the DIRAC Project in the context of the GISELA Latin American Grid Initiative. Special services for dynamic allocation of virtual computer pools on the grid sites were developed in order to deploy MPI rings corresponding to the requirements of the jobs in the central task queue of the DIRAC Workload Management System. Pilot Jobs using user space file system techniques install the required MPI software automatically. The same technique is used to emulate shared working directories for the parallel MPI processes. This makes it possible to execute MPI jobs even on the sites not supporting them officially. Reusing so constructed MPI rings for execution of a series of parallel jobs increases dramatically their efficiency and turnaround. In this contribution we describe the design and implementation of the DIRAC MPI Service as well as its support for various types of MPI libraries. Advantages of coupling the MPI support with the Pilot frameworks are outlined and examples of usage with real applications are presented.
Manipulation of Dirac cones in metal-intercalated epitaxial graphene
Wang, Cai-Zhuang; Kim, Minsung; Tringides, Michael; Ho, Kai-Ming
Graphene is one of the most attractive materials from both fundamental and practical points of view due to its characteristic Dirac cones. The electronic property of graphene can be modified through the interaction with substrate or another graphene layer as illustrated in few-layer epitaxial graphene. Recently, metal intercalation became an effective method to manipulate the electronic structure of graphene by modifying the coupling between the constituent layers. In this work, we show that the Dirac cones of epitaxial graphene can be manipulated by intercalating rare-earth metals. We demonstrate that rare-earth metal intercalated epitaxial graphene has tunable band structures and the energy levels of Dirac cones as well as the linear or quadratic band dispersion can be controlled depending on the location of the intercalation layer and density. Our results could be important for applications and characterizations of the intercalated epitaxial graphene. Supported by the U.S. DOE-BES under Contract No. DE-AC02-07CH11358.
Upper-division student difficulties with the Dirac delta function
Directory of Open Access Journals (Sweden)
Bethany R. Wilcox
2015-03-01
Full Text Available The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them. To characterize student difficulties with the delta function at the upper-division level, we examined students’ responses to traditional exam questions and a standardized conceptual assessment, and conducted think-aloud interviews. Our analysis was guided by an analytical framework that focuses on how students activate, construct, execute, and reflect on the Dirac delta function in the context of problem solving in physics. Here, we focus on student difficulties using the delta function to express charge distributions in the context of junior-level electrostatics. Common challenges included invoking the delta function spontaneously, translating a description of a charge distribution into a mathematical expression using delta functions, integrating 3D or non-Cartesian delta function expressions, and recognizing that the delta function can have units. We also briefly discuss implications of these difficulties for instruction.
Evidence for $\\pi K$ -atoms with DIRAC-II
Allkofer, Yves
2008-01-01
DIRAC-II is a fixed-target experiment at the CERN Proton Synchroton (PS) which has been designed to search for piK atoms, a bound state of a piÂ±KÂ± pair, and measure their lifetime. These atoms are observed through an excess of low energetic piK pairs over the background, detected in the two spectrometer arms. This excess comes from the ionization of piK atoms in the target and can be related to their mean life. The piK S-wave scattering length combination |a1/2 - a3/2| (for isospin 1/2 and 3/2) can be related to the latter. The aim of the upgraded DIRAC-II experiment is a measurement of the scattering length combination |a1/2 - a3/2| with a precision of 5%. piK atoms have not been observed so far. The original DIRAC experiment was designed to measure the scattering lengths of pipi atoms. So far, close to 15 000 atoms have been detected, leading to a precision on |a0 - a2| which is better than 10%. In chiral perturbation theories (ChPT) the pipi scattering lengths have been calculated with 2% precision a...
Pilots 2.0: DIRAC pilots for all the skies
Stagni, F; McNab, A; Luzzi, C
2015-01-01
In the last few years, new types of computing infrastructures, such as IAAS (Infrastructure as a Service) and IAAC (Infrastructure as a Client), gained popularity. New resources may come as part of pledged resources, while others are opportunistic. Most of these new infrastructures are based on virtualization techniques. Meanwhile, some concepts, such as distributed queues, lost appeal, while still supporting a vast amount of resources. Virtual Organizations are therefore facing heterogeneity of the available resources and the use of an Interware software like DIRAC to hide the diversity of underlying resources has become essential. The DIRAC WMS is based on the concept of pilot jobs that was introduced back in 2004. A pilot is what creates the possibility to run jobs on a worker node. Within DIRAC, we developed a new generation of pilot jobs, that we dubbed Pilots 2.0. Pilots 2.0 are not tied to a specific infrastructure; rather they are generic, fully configurable and extendible pilots. A Pilot 2.0 can be s...
Theory of Coulomb drag for massless Dirac fermions
International Nuclear Information System (INIS)
Carrega, M; Principi, A; Polini, M; Tudorovskiy, T; Katsnelson, M I
2012-01-01
Coulomb drag between two unhybridized graphene sheets separated by a dielectric spacer has recently attracted considerable theoretical interest. We first review, for the sake of completeness, the main analytical results which have been obtained by other authors. We then illustrate pedagogically the minimal theory of Coulomb drag between two spatially separated two-dimensional systems of massless Dirac fermions which are both away from the charge-neutrality point. This relies on second-order perturbation theory in the screened interlayer interaction and on Boltzmann-transport theory. In this theoretical framework and in the low-temperature limit, we demonstrate that, to leading (i.e. quadratic) order in temperature, the drag transresistivity is completely insensitive to the precise intralayer momentum-relaxation mechanism (i.e. to the functional dependence of the transport scattering time on energy). We also provide analytical results for the low-temperature drag transresistivity for both cases of ‘thick’ and ‘thin’ spacers and for arbitrary values of the dielectric constants of the media surrounding the two Dirac-fermion layers. Finally, we present numerical results for the low-temperature drag transresistivity for the case when one of the media surrounding the Dirac-fermion layers has a frequency-dependent dielectric constant. We conclude by suggesting an experiment that can potentially allow for the observation of departures from the canonical quadratic-in-temperature behavior of the transresistivity. (paper)
Energy Technology Data Exchange (ETDEWEB)
Farmelo, Graham
2016-07-01
The Strangest Man is the Costa Biography Award-winning account of Paul Dirac, the famous physicist sometimes called the British Einstein. He was one of the leading pioneers of the greatest revolution in twentieth-century science: quantum mechanics. The youngest theoretician ever to win the Nobel Prize for Physics, he was also pathologically reticent, strangely literal-minded and legendarily unable to communicate or empathize. Through his greatest period of productivity, his postcards home contained only remarks about the weather. Based on a previously undiscovered archive of family papers, Graham Farmelo celebrates Dirac's massive scientific achievement while drawing a compassionate portrait of his life and work. Farmelo shows a man who, while hopelessly socially inept, could manage to love and sustain close friendship. The Strangest Man is an extraordinary and moving human story, as well as a study of one of the most exciting times in scientific history.
Avoid the tsunami of the Dirac sea in the imaginary time step method
International Nuclear Information System (INIS)
Zhang, Ying; Liang, Haozhao; Meng, Jie
2010-01-01
The discrete single-particle spectra in both the Fermi and Dirac sea have been calculated by the imaginary time step (ITS) method for the Schroedinger-like equation after avoiding the "tsunami" of the Dirac sea, i.e. the diving behavior of the single-particle level into the Dirac sea in the direct application of the ITS method for the Dirac equation. It is found that by the transform from the Dirac equation to the Schroedinger-like equation, the single-particle spectra, which extend from the positive to the negative infinity, can be separately obtained by the ITS evolution in either the Fermi sea or the Dirac sea. Identical results with those in the conventional shooting method have been obtained via the ITS evolution for the equivalent Schroedinger-like equation, which demonstrates the feasibility, practicality and reliability of the present algorithm and dispels the doubts on the ITS method in the relativistic system. (author)
Double Dirac point semimetal in 2D material: Ta2Se3
Ma, Yandong; Jing, Yu; Heine, Thomas
2017-06-01
Here, we report by first-principles calculations one new stable 2D Dirac material, Ta2Se3 monolayer. For this system, stable layered bulk phase exists, and exfoliation should be possible. Ta2Se3 monolayer is demonstrated to support two Dirac points close to the Fermi level, achieving the exotic 2D double Dirac semimetal. And like 2D single Dirac and 2D node-line semimetals, spin-orbit coupling could introduce an insulating state in this new class of 2D Dirac semimetals. Moreover, the Dirac feature in this system is layer-dependent and a metal-to-insulator transition is identified in Ta2Se3 when reducing the layer-thickness from bilayer to monolayer. These findings are of fundamental interests and of great importance for nanoscale device applications.
Self-Assembled Si(111) Surface States: 2D Dirac Material for THz Plasmonics
Wang, Z. F.; Liu, Feng
2015-07-01
Graphene, the first discovered 2D Dirac material, has had a profound impact on science and technology. In the last decade, we have witnessed huge advances in graphene related fundamental and applied research. Here, based on first-principles calculations, we propose a new 2D Dirac band on the Si(111) surface with 1 /3 monolayer halogen coverage. The s p3 dangling bonds form a honeycomb superstructure on the Si(111) surface that results in an anisotropic Dirac band with a group velocity (˜106 m /s ) comparable to that in graphene. Most remarkably, the Si-based surface Dirac band can be used to excite a tunable THz plasmon through electron-hole doping. Our results demonstrate a new way to design Dirac states on a traditional semiconductor surface, so as to make them directly compatible with Si technology. We envision this new type of Dirac material to be generalized to other semiconductor surfaces with broad applications.
On the confinement of a Dirac particle to a two-dimensional ring
International Nuclear Information System (INIS)
Bakke, K.; Furtado, C.
2012-01-01
In this contribution, we propose a new model for studying the confinement of a spin-half particle to a two-dimensional quantum ring for systems described by the Dirac equation by introducing a new coupling into the Dirac equation. We show that the introduction of this new coupling into the Dirac equation yields a generalization of the two-dimensional quantum ring model proposed by Tan and Inkson [W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11 (1996) 1635] for relativistic spin-half quantum particles. -- Highlights: ► Two-dimensional ring model for condensed matter systems described by the Dirac equation. ► Exact solutions of the Dirac equation. ► Persistent currents for Dirac-like systems confined to a two-dimensional quantum ring.
Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS
Schoop, Leslie M.; Ali, Mazhar N.; Straßer, Carola; Topp, Andreas; Varykhalov, Andrei; Marchenko, Dmitry; Duppel, Viola; Parkin, Stuart S. P.; Lotsch, Bettina V.; Ast, Christian R.
2016-01-01
Materials harboring exotic quasiparticles, such as Dirac and Weyl fermions\\cite{xu2015discovery,borisenko2015time,weng2015weyl,xu2015observation}, have garnered much attention from the physics and material science communities. These fermions are massless and, in some materials, have shown exceptional physical properties such as ultrahigh mobility and extremely large magnetoresistances \\cite{liang2015ultrahigh,ali2014large,du2015unsaturated,shekhar2015large}. Recently, new materials have been ...
Dirac mechanics and Landau two-fluid model in /sup 4/HeII
Energy Technology Data Exchange (ETDEWEB)
Rodriguez-Gomez, J [Instituto Universitario Pedagogico de Caracas (Venezuela). Dept. de Matematica y Fisica
1980-07-01
This paper is devoted to the development of the Dirac formalism for singular systems when applied to the Landau two-fluid model in superfluid helium. Notably, the Hamiltonian density is weakly zero (in the sense of Dirac). We obtain the physical and gauge variables and show that all the constraints are of first class and hence that the Dirac bracket coincides with the Poisson bracket. The quantization of this system is left for a future paper.
A compact expression for bilinear combination of Dirac spinors via world tensors
International Nuclear Information System (INIS)
Rogalev, R.N.
1994-01-01
A compact expression for a product of two Dirac spinors is obtained as a linear combination of 16 Dirac γ-matrices. The result is presented in a convenient from, which can give rise to using it for analytical calculations of multiparticle amplitudes. It has been shown that a bilinear combination of Dirac spinors can be expressed by momentum and spin vectors of the corresponding particles up to a phase factor. 8 refs
Considerations concering the generalization of the Dirac equations to unstable fermions
International Nuclear Information System (INIS)
Kniehl, Bernd A.; Sirlin, Alberto
2014-08-01
We discuss the generalization of the Dirac equations and spinors in momentum space to free unstable spin-1/2 fermions taking into account the fundamental requirement of Lorentz covariance. We derive the generalized adjoint Dirac equations and spinors, and explain the very simple relation that exists, in our formulation, between the unstable and stable cases. As an application of the generalized spinors, we evaluate the probability density. We also discuss the behavior of the generalized Dirac equations under time reversal.
Spin symmetry in the Dirac sea derived from the bare nucleon-nucleon interaction
Shen, Shihang; Liang, Haozhao; Meng, Jie; Ring, Peter; Zhang, Shuangquan
2018-06-01
The spin symmetry in the Dirac sea has been investigated with relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. Taking the nucleus 16O as an example and comparing the theoretical results with the data, the definition of the single-particle potential in the Dirac sea is studied in detail. It is found that if the single-particle states in the Dirac sea are treated as occupied states, the ground state properties are in better agreement with experimental data. Moreover, in this case, the spin symmetry in the Dirac sea is better conserved and it is more consistent with the findings using phenomenological relativistic density functionals.
Granular superconductor in a honeycomb lattice as a realization of bosonic Dirac material
Banerjee, S.; Fransson, J.; Black-Schaffer, A. M.; Ågren, H.; Balatsky, A. V.
2016-04-01
We examine the low-energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in a honeycomb lattice structure. Using the example of graphene, we present evidence for the engineered Dirac nodes in the bosonic excitations: the spectra of the collective bosonic modes cross at the K and K' points in the Brillouin zone and form Dirac nodes. We show how two different types of collective phase oscillations are obtained and that they are analogous to the Leggett and the Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. We show that the Dirac node is preserved in the presence of an intergrain interaction, despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sublattice symmetry by choosing different on-site potentials for the two sublattices leads to a gap opening near the Dirac node, in analogy with fermionic Dirac materials. The Dirac node dispersion of bosonic excitations is thus expanding the discussion of the conventional Dirac cone excitations to the case of bosons. We call this case as a representative of bosonic Dirac materials (BDM), similar to the case of Fermionic Dirac materials extensively discussed in the literature.
Do neutron stars disprove multiplicative creation in Dirac's large number hypothesis
International Nuclear Information System (INIS)
Qadir, A.; Mufti, A.A.
1980-07-01
Dirac's cosmology, based on his large number hypothesis, took the gravitational coupling to be decreasing with time and matter to be created as the square of time. Since the effects predicted by Dirac's theory are very small, it is difficult to find a ''clean'' test for it. Here we show that the observed radiation from pulsars is inconsistent with Dirac's multiplicative creation model, in which the matter created is proportional to the density of matter already present. Of course, this discussion makes no comment on the ''additive creation'' model, or on the revised version of Dirac's theory. (author)
Analytical solutions for Dirac and Klein-Gordon equations using Backlund transformations
Energy Technology Data Exchange (ETDEWEB)
Zabadal, Jorge R.; Borges, Volnei, E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio, E-mail: marciophd@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Centro de Estudos Interdisciplinares
2015-07-01
This work presents a new analytical method for solving Klein-Gordon type equations via Backlund transformations. The method consists in mapping the Klein-Gordon model into a first order system of partial differential equations, which contains a generalized velocity field instead of the Dirac matrices. This system is a tensor model for quantum field theory whose space solution is wider than the Dirac model in the original form. Thus, after finding analytical expressions for the wave functions, the Maxwell field can be readily obtained from the Dirac equations, furnishing a self-consistent field solution for the Maxwell-Dirac system. Analytical and numerical results are reported. (author)
Vacuum state of the Dirac field in de Sitter space and entanglement entropy
Energy Technology Data Exchange (ETDEWEB)
Kanno, Sugumi [Department of Theoretical Physics and History of Science,University of the Basque Country,48080 Bilbao (Spain); IKERBASQUE, Basque Foundation for Science,Maria Diaz de Haro 3, 48013, Bilbao (Spain); Sasaki, Misao [Center for Gravitational Physics,Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan); Tanaka, Takahiro [Department of Physics, Kyoto University,Kyoto 606-8502 (Japan); Center for Gravitational Physics,Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan)
2017-03-13
We compute the entanglement entropy of a free massive Dirac field between two causally disconnected open charts in de Sitter space. We first derive the Bunch-Davies vacuum mode functions of the Dirac field. We find there exists no supercurvature mode for the Dirac field. We then give the Bogoliubov transformation between the Bunch-Davies vacuum and the open chart vacua that makes the reduced density matrix diagonal. We find that the Dirac field becomes more entangled than a scalar field as m{sup 2}/H{sup 2} becomes small, and the difference is maximal in the massless limit.
Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.
The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr-Newman geometry, for smooth initial data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays in L∞ {loc} at least at the rate t-5/6. For generic initial data, this rate of decay is sharp. We derive a formula for the probability p that the Dirac particle escapes to infinity. For various conditions on the initial data, we show that p = 0, 1 or 0 < p < 1. The proofs are based on a refined analysis of the Dirac propagator constructed in [4].
Electroweakly-interacting Dirac dark matter
International Nuclear Information System (INIS)
Nagata, Natsumi
2014-11-01
We consider a class of fermionic dark matter candidates that are charged under both the SU(2) L and U(1) Y gauge interactions. Such a dark matter is stringently restricted by the dark matter direct detection experiments, since the Z-boson exchange processes induce too large dark matter-nucleus elastic scattering cross sections. Effects of ultraviolet (UV) physics, however, split it into two Majorana fermions to evade the constraint. These effects may be probed by means of the dark matter-nucleus scattering via the Higgs-boson exchange process, as well as the electric dipole moments induced by the dark matter and its SU(2) L partner fields. In this Letter, we evaluate them with effective operators that describe the UV-physics effects. It turns out that the constraints coming from the experiments for the quantities have already restricted the dark matters with hypercharge Y≥3/2. Future experiments have sensitivities to probe this class of dark matter candidates, and may disfavor the Y≥1 cases if no signal is observed. In this case, only the Y=0 and 1/2 cases may be the remaining possibilities for the SU(2) L charged fermionic dark matter candidates.
Fan, Hong-Yi; Lu, Hai-Liang
Via the route of developing Dirac's symbolic method and following Dirac's assertion: "⋯ for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory", we find the generalized Fresnel operator (GFO) corresponding to the generalized Fresnel transform (GFT) in classical optics. We derive GFO's normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in quantum optics. With the aid of entangled state representation the entangled Fresnel transform is proposed; new eigenfunctions of the complex fractional Fourier transform and fractional Hankel transform are obtained; the two-variable Hermite eigenmodes of light propagation are used in studying the Talbot effect in quadratic-index media; the complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Moreover, quantum optical version of classical z-transforms is obtained on the basis of the eigenvector of creation operator. Throughout our discussions, the coherent state, squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used.
Two-body Dirac equations for nucleon-nucleon scattering
International Nuclear Information System (INIS)
Liu Bin; Crater, Horace
2003-01-01
We investigate the nucleon-nucleon interaction by using the meson exchange model and the two-body Dirac equations of constraint dynamics. This approach to the two-body problem has been successfully tested for QED and QCD relativistic bound states. An important question we wish to address is whether or not the two-body nucleon-nucleon scattering problem can be reasonably described in this approach as well. This test involves a number of related problems. First we must reduce our two-body Dirac equations exactly to a Schroedinger-like equation in such a way that allows us to use techniques to solve them already developed for Schroedinger-like systems in nonrelativistic quantum mechanics. Related to this, we present a new derivation of Calogero's variable phase shift differential equation for coupled Schroedinger-like equations. Then we determine if the use of nine meson exchanges in our equations gives a reasonable fit to the experimental scattering phase shifts for n-p scattering. The data involve seven angular momentum states including the singlet states 1 S 0 , 1 P 1 , 1 D 2 and the triplet states 3 P 0 , 3 P 1 , 3 S 1 , 3 D 1 . Two models that we have tested give us a fairly good fit. The parameters obtained by fitting the n-p experimental scattering phase shift give a fairly good prediction for most of the p-p experimental scattering phase shifts examined (for the singlet states 1 S 0 , 1 D 2 and triplet states 3 P 0 , 3 P 1 ). Thus the two-body Dirac equations of constraint dynamics present us with a fit that encourages the exploration of a more realistic model. We outline generalizations of the meson exchange model for invariant potentials that may possibly improve the fit
Kaehler-Dirac ghosts for self-dual fields
International Nuclear Information System (INIS)
Labastida, J.M.F.; Pernici, M.
1988-01-01
We present the generalization to spacetime dimension D=4n+2 of the Lorentz covariant quadratic lagrangian for pairs of (anti)self-dual fields previously obtained by the authors in D=2. In the process of BRST quantizing this lagrangian a first-order quadratic lagrangian for ghost (anti)self-dual fields is found which, after gauge fixing, can be written in terms of bispinors and it turns out to be a Kaehler-Dirac lagrangian. The coupling to gravity is straightforward and the gravitational anomaly due to (anti)self-dual fields is obtained directly from an action principle. (orig.)
The supersymmetric Dirac equation the application to hydrogenic atoms
Hirshfeld, Allen
2012-01-01
The solution of the Dirac equation for an electron in a Coulomb field is systematically treated here by utilizing new insights provided by supersymmetry. It is shown that each of the concepts has its analogue in the non-relativistic case. Indeed, the non-relativistic case is developed first, in order to introduce the new concepts in a familiar context. The symmetry of the non-relativistic model is already present in the classical limit, so the classical Kepler problem is first discussed in order to bring out the role played by the Laplace vector, one of the central concepts of the whole book.
DIRAC: A high resolution spectrometer for pionium detection
Energy Technology Data Exchange (ETDEWEB)
Adeva, B. E-mail: adevab@usc.es; Afanasyev, L.; Benayoun, M.; Benelli, A.; Berka, Z.; Brekhovskikh, V.; Caragheorgheopol, G.; Cechak, T.; Chiba, M.; Cima, E.; Constantinescu, S.; Detraz, C.; Dreossi, D.; Drijard, D.; Dudarev, A.; Evangelou, I.; Ferro-Luzzi, M.; Gallas, M.V.; Gerndt, J.; Giacomich, R.; Gianotti, P.; Giardoni, M.; Goldin, D.; Gomez, F.; Gorin, A.; Gortchakov, O.; Guaraldo, C.; Hansroul, M.; Iliescu, M.; Zhabitsky, M.; Karpukhin, V.; Kluson, J.; Kobayashi, M.; Kokkas, P.; Komarov, V.; Kruglov, V.; Kruglova, L.; Kulikov, A.; Kuptsov, A.; Kurochkin, V.; Kuroda, K.-I.; Lamberto, A.; Lanaro, A.; Lapshin, V.; Lednicky, R.; Leruste, P.; Levisandri, P.; Lopez Aguera, A.; Lucherini, V.; Maki, T.; Manthos, N.; Manuilov, I.; Montanet, L.; Narjoux, J.-L.; Nemenov, L.; Nikitin, M.; Nunez Pardo, T.; Okada, K.; Olchevskii, V.; Orecchini, D.; Pazos, A.; Pentia, M.; Penzo, A.; Perreau, J.-M.; Petrascu, C.; Plo, M.; Ponta, T.; Pop, D.; Rappazzo, G.F.; Riazantsev, A.; Rodriguez, J.M.; Rodriguez Fernandez, A.; Romero, A.; Rykalin, V.; Santamarina, C.; Saborido, J.; Schacher, J.; Schuetz, Ch.P.; Sidorov, A.; Smolik, J.; Steinacher, M.; Takeutchi, F.; Tarasov, A.; Tauscher, L.; Tobar, M.J.; Triantis, F.; Trusov, S.; Utkin, V.; Vazquez Doce, O.; Vazquez, P.; Vlachos, S.; Yazkov, V.; Yoshimura, Y.; Zrelov, P
2003-12-11
The DIRAC spectrometer has been commissioned at CERN with the aim of detecting {pi}{sup +}{pi}{sup -} atoms produced by a 24 GeV/c high intensity proton beam in thin foil targets. A challenging apparatus is required to cope with the high interaction rates involved, the triggering of pion pairs with very detector efficiency.ation of the imaging sof the latter with resolution around 0.6 MeV/c. The general characteristics of the apparatus are explained and each part is described in some detail. The main features of the trigger system, data-acquisition, monitoring and set-up performances are also given.
DIRAC: A high resolution spectrometer for pionium detection
International Nuclear Information System (INIS)
Adeva, B.; Afanasyev, L.; Benayoun, M.; Benelli, A.; Berka, Z.; Brekhovskikh, V.; Caragheorgheopol, G.; Cechak, T.; Chiba, M.; Cima, E.; Constantinescu, S.; Detraz, C.; Dreossi, D.; Drijard, D.; Dudarev, A.; Evangelou, I.; Ferro-Luzzi, M.; Gallas, M.V.; Gerndt, J.; Giacomich, R.; Gianotti, P.; Giardoni, M.; Goldin, D.; Gomez, F.; Gorin, A.; Gortchakov, O.; Guaraldo, C.; Hansroul, M.; Iliescu, M.; Zhabitsky, M.; Karpukhin, V.; Kluson, J.; Kobayashi, M.; Kokkas, P.; Komarov, V.; Kruglov, V.; Kruglova, L.; Kulikov, A.; Kuptsov, A.; Kurochkin, V.; Kuroda, K.-I.; Lamberto, A.; Lanaro, A.; Lapshin, V.; Lednicky, R.; Leruste, P.; Levisandri, P.; Lopez Aguera, A.; Lucherini, V.; Maki, T.; Manthos, N.; Manuilov, I.; Montanet, L.; Narjoux, J.-L.; Nemenov, L.; Nikitin, M.; Nunez Pardo, T.; Okada, K.; Olchevskii, V.; Orecchini, D.; Pazos, A.; Pentia, M.; Penzo, A.; Perreau, J.-M.; Petrascu, C.; Plo, M.; Ponta, T.; Pop, D.; Rappazzo, G.F.; Riazantsev, A.; Rodriguez, J.M.; Rodriguez Fernandez, A.; Romero, A.; Rykalin, V.; Santamarina, C.; Saborido, J.; Schacher, J.; Schuetz, Ch.P.; Sidorov, A.; Smolik, J.; Steinacher, M.; Takeutchi, F.; Tarasov, A.; Tauscher, L.; Tobar, M.J.; Triantis, F.; Trusov, S.; Utkin, V.; Vazquez Doce, O.; Vazquez, P.; Vlachos, S.; Yazkov, V.; Yoshimura, Y.; Zrelov, P.
2003-01-01
The DIRAC spectrometer has been commissioned at CERN with the aim of detecting π + π - atoms produced by a 24 GeV/c high intensity proton beam in thin foil targets. A challenging apparatus is required to cope with the high interaction rates involved, the triggering of pion pairs with very detector efficiency.ation of the imaging sof the latter with resolution around 0.6 MeV/c. The general characteristics of the apparatus are explained and each part is described in some detail. The main features of the trigger system, data-acquisition, monitoring and set-up performances are also given
Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen
2006-01-01
We apply the technique of Hamiltonian reduction for the construction of three-dimensional N=4 supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional N=4 supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out
Connection between Dirac and matrix Schroedinger inverse-scattering transforms
International Nuclear Information System (INIS)
Jaulent, M.; Leon, J.J.P.
1978-01-01
The connection between two applications of the inverse scattering method for solving nonlinear equations is established. The inverse method associated with the massive Dirac system (D) : (iσ 3 d/dx - i q 3 σ 1 - q 1 σ 2 + mσ 2 )Y = epsilonY is rediscovered from the inverse method associated with the 2 x 2 matrix Schroedinger equation (S) : Ysub(xx) + (k 2 -Q)Y = 0. Here Q obeys a nonlinear constraint equivalent to a linear constraint on the reflection coefficient for (S). (author)
Dirac cosmology and the onset of galactic nucleosynthesis
International Nuclear Information System (INIS)
Adams, P.J.; Canuto, V.
1976-01-01
Recently Browne and Berman determined the onset of nucleosynthesis of heavy elements in the galaxy to be about 18 billion years ago based on the weak decay of rhenium 187 to osmium 187. This age is appreciably larger than the 13 billion years determined from the uranium decay chains. It is also larger than the 16 billion year age of the Universe determined from the standard model by the latest values of the Hubble constant and deceleration parameter. This letter points out that this discrepancy is predicted by Dirac's cosmology and derives from a time-varying weak coupling constant. (Auth.)
Lattice approximation of gauge theories with Dirac Kaehler fermions
International Nuclear Information System (INIS)
Joos, H.
1988-01-01
A program which tries to overcome the systematic difficulties caused by the lattice fermion problem by the consideration of models which describe Dirac fields by differential forms is reported. In the first lecture the formalism is developped and applied to the formulation of geometric QCD and of a Geometric Standard Model. The second lecture treats the characteristic symmetry problems which appear in the lattice approximation of geometric field theories. In the last lecture strong coupling dynamics of geometric QCD are considered with the final aim of a derivation of the quark model for the hadron spectrum. (author) [pt
From LHC physics to Dirac-Weyl materials
International Nuclear Information System (INIS)
Raya, Alfredo
2016-01-01
The quantum field theoretical description of particle physics under extreme conditions, namely, at finite temperature, density and in the presence of external magnetic fields, can naturally be extended to describe phenomenology in other branches of physics. In this contribution, I review some aspects of particle physics in the realm of condensed matter physics, particularly graphene and other Dirac-Weyl materials carried out in Mexico. I explore several features of the dynamics of fermions in (2+1)-dimensions which are relevant to heavy ion experiments, but that can be tested in table top experiments. (paper)
Minimax rational approximation of the Fermi-Dirac distribution
Moussa, Jonathan E.
2016-10-01
Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ɛ-1)) poles to achieve an error tolerance ɛ at temperature β-1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. This is particularly beneficial when Δ ≫ Δocc, such as in electronic structure calculations that use a large basis set.
Geometric phase of neutrinos: Differences between Dirac and Majorana neutrinos
Capolupo, A.; Giampaolo, S. M.; Hiesmayr, B. C.; Vitiello, G.
2018-05-01
We analyze the non-cyclic geometric phase for neutrinos. We find that the geometric phase and the total phase associated to the mixing phenomenon provide a theoretical tool to distinguish between Dirac and Majorana neutrinos. Our results hold for neutrinos propagating in vacuum and through the matter. We feed the values of the experimental parameters in our formulas in order to make contact with experiments. Although it remains an open question how the geometric phase of neutrinos could be detected, our theoretical results may open new scenarios in the investigation of the neutrino nature.
DIRAC: A High Resolution Spectrometer for Pionium Detection
Afanasiev, L G; Benelli, A; Berka, Z; Brekhovskikh, V; Caragheorgheopol, G; Cechák, T; Chiba, M; Cima, E; Constantinescu, S; Détraz, C; Dreossi, D; Drijard, Daniel; Dudarev, A; Evangelou, I; Ferro-Luzzi, M; Gallas, M V; Gerndt, J; Giacomich, R; Gianotti, P; Giardoni, M; Goldin, D; Gómez, F; Gorin, A; Gortchakov, O E; Guaraldo, C; Hansroul, M; Iliescu, M A; Zhabitsky, V M; Karpukhin, V V; Kluson, J; Kobayashi, M; Kokkas, P; Komarov, V; Kruglov, V; Kruglova, L; Kulikov, A; Kuptsov, A; Kurochkin, V; Kuroda, K I; Lamberto, A; Lanaro, A; Lapshin, V G; Lednicky, R; Leruste, P; Levisandri, P; López-Aguera, A; Lucherini, V; Mäki, T; Manthos, N; Manuilov, I V; Montanet, Lucien; Narjoux, J L; Nemenov, Leonid L; Nikitin, M; Núñez-Pardo de Vera, M T; Okada, K; Olchevskii, V; Orecchini, D; Pazos, A; Pentia, M; Penzo, Aldo L; Perreau, J M; Petrascu, C; Pló, M; Ponta, T; Pop, D; Rappazzo, G F; Riazantsev, A; Rodríguez, J M; Rodríguez-Fernández, A M; Romero, A; Rykalin, V I; Santamarina-Rios, C; Saborido, J; Schacher, J; Schütz, C P; Sidorov, A; Smolik, J; Steinacher, M; Takeutchi, F; Tarasov, A; Tauscher, Ludwig; Tobar, M J; Triantis, F A; Trusov, S V; Utkin, V; Vázquez-Doce, O; Vázquez, P; Vlachos, S; Yazkov, V; Yoshimura, Y; Zrelov, V P
2003-01-01
The DIRAC spectrometer has been commissioned at CERN with the aim of detecting $\\pi^+ \\pi^-$ atoms produced by a 24 GeV/$c$ high intensity proton beam in thin foil targets. A challenging apparatus is required to cope with the high interaction rates involved, the triggering of pion pairs with very low relative momentum, and the measurement of the latter with resolution around 0.6 MeV/$c$. The general characteristics of the apparatus are explained and each part is described in some detail. The main features of the trigger system, data-acquisition, monitoring and setup performances are also given.
κ-deformed Dirac oscillator in an external magnetic field
Chargui, Y.; Dhahbi, A.; Cherif, B.
2018-04-01
We study the solutions of the (2 + 1)-dimensional κ-deformed Dirac oscillator in the presence of a constant transverse magnetic field. We demonstrate how the deformation parameter affects the energy eigenvalues of the system and the corresponding eigenfunctions. Our findings suggest that this system could be used to detect experimentally the effect of the deformation. We also show that the hidden supersymmetry of the non-deformed system reduces to a hidden pseudo-supersymmetry having the same algebraic structure as a result of the κ-deformation.
Multiconfiguration Dirac-Fock method for atomic structure
International Nuclear Information System (INIS)
Sasaki, Ken
1982-02-01
The multiconfiguration Dirac-Fock method for calculating the atomic structure is reviewed in some detail. Being more comprehensive than the ones introduced in Desclaux's paper, the mathematical formulae derived in this review are more helpful to trace the thread of ideas and understand the algorithm in Desclaux's computer program which embodied the method. A detailed analysis is made on the restrictions on how the program is used, that is, on the fact that it does not apply to the problem where the configuration mixing occurs via the one-electron Hamiltonian. Finally, in conclusion, a way to overcome the difficulty is suggested. (author)
The bundles of algebraic and Dirac-Hestenes spinor fields
International Nuclear Information System (INIS)
Mosna, Ricardo A.; Rodrigues, Waldyr A. Jr.
2004-01-01
Our main objective in this paper is to clarify the ontology of Dirac-Hestenes spinor fields (DHSF) and its relationship with even multivector fields, on a Riemann-Cartan spacetime (RCST) M=(M,g,∇,τ g ,↑) admitting a spin structure, and to give a mathematically rigorous derivation of the so-called Dirac-Hestenes equation (DHE) in the case where M is a Lorentzian spacetime (the general case when M is a RCST will be discussed in another publication). To this aim we introduce the Clifford bundle of multivector fields (Cl(M,g)) and the left (Cl Spin 1,3 e l (M)) and right (Cl Spin 1,3 e r (M)) spin-Clifford bundles on the spin manifold (M,g). The relation between left ideal algebraic spinor fields (LIASF) and Dirac-Hestenes spinor fields (both fields are sections of Cl Spin 1,3 e l (M)) is clarified. We study in detail the theory of covariant derivatives of Clifford fields as well as that of left and right spin-Clifford fields. A consistent Dirac equation for a DHSF Ψ is a member of sec Cl Spin 1,3 e l (M) (denoted DECl l ) on a Lorentzian spacetime is found. We also obtain a representation of the DECl l in the Clifford bundle Cl(M,g). It is such equation that we call the DHE and it is satisfied by Clifford fields ψ Ξ is a member of sec Cl(M,g). This means that to each DHSF Ψ is a member of sec Cl Spin 1,3 e l (M) and spin frame Ξ is a member of sec P Spin 1,3 e (M), there is a well-defined sum of even multivector fields ψ Ξ isa member of sec Cl(M,g) (EMFS) associated with Ψ. Such an EMFS is called a representative of the DHSF on the given spin frame. And, of course, such a EMFS (the representative of the DHSF) is not a spinor field. With this crucial distinction between a DHSF and its representatives on the Clifford bundle, we provide a consistent theory for the covariant derivatives of Clifford and spinor fields of all kinds. We emphasize that the DECl l and the DHE, although related, are equations of different mathematical natures. We study also the
Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3
Fuhrer, Michael
2013-03-01
The three dimensional strong topological insulator (STI) is a new phase of electronic matter which is distinct from ordinary insulators in that it supports on its surface a conducting two-dimensional surface state whose existence is guaranteed by topology. I will discuss experiments on the STI material Bi2Se3, which has a bulk bandgap of 300 meV, much greater than room temperature, and a single topological surface state with a massless Dirac dispersion. Field effect transistors consisting of thin (3-20 nm) Bi2Se3 are fabricated from mechanically exfoliated from single crystals, and electrochemical and/or chemical gating methods are used to move the Fermi energy into the bulk bandgap, revealing the ambipolar gapless nature of transport in the Bi2Se3 surface states. The minimum conductivity of the topological surface state is understood within the self-consistent theory of Dirac electrons in the presence of charged impurities. The intrinsic finite-temperature resistivity of the topological surface state due to electron-acoustic phonon scattering is measured to be ~60 times larger than that of graphene largely due to the smaller Fermi and sound velocities in Bi2Se3, which will have implications for topological electronic devices operating at room temperature. As samples are made thinner, coherent coupling of the top and bottom topological surfaces is observed through the magnitude of the weak anti-localization correction to the conductivity, and, in the thinnest Bi2Se3 samples (~ 3 nm), in thermally-activated conductivity reflecting the opening of a bandgap.
A CPT-even and Lorentz-Violating nonminimal coupling in the Dirac equation
International Nuclear Information System (INIS)
Ferreira Junior, Manoel; Casana, M.R.; Santos, Frederico E.P. dos; Silva, E.O.; Passos, E.
2013-01-01
Full text: The Standard Model Extension (SME) has been the usual framework for investigating signals of Lorentz violation in physical systems. It is the natural framework for studying properties of physical systems with Lorentz-violation since it includes Lorentz-violating terms in all sectors of the minimal standard model. The Lorentz-violating (LV) terms are generated as vacuum expectation values of tensors defined in a high energy scale. This framework has inspired a great deal of investigation in recent years. Such works encompass several distinct aspects involving fermion systems and radiative corrections, CPT- probing experiments, the electromagnetic CPT- and Lorentz-odd term, the 19 electromagnetic CPT-even coefficients. Recently, some studies involving higher dimensional operators have also been reported with great interest, including nonminimal interactions. These many contributions have elucidated the effects induced by Lorentz violation and served to set up stringent upper bounds on the LV coefficients. In the present work, we propose a new CPT-even, dimension-five, nonminimal coupling linking the fermionic and gauge fields in the context of the Dirac equation, involving the CPT-even tensor of the gauge term of the SME. By considering the nonrelativistic limit of the modified Dirac equation, we explicitly evaluate the new contributions to the nonrelativistic Hamiltonian. These new terms imply a direct correction on the anomalous magnetic moment, a kind of electrical Zeeman-like effect on the atomic spectrum, and a Rashba-like coupling term. These effects are then used to impose upper bounds on the magnitude of the non minimally coupled LV coefficients at the level of 1 part in 10 16 . (author)
A CPT-even and Lorentz-Violating nonminimal coupling in the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Ferreira Junior, Manoel; Casana, M.R.; Santos, Frederico E.P. dos; Silva, E.O. [UFMA, Sao Luis (Brazil); Passos, E. [UFCG, Campina Grande, PB (Brazil)
2013-07-01
Full text: The Standard Model Extension (SME) has been the usual framework for investigating signals of Lorentz violation in physical systems. It is the natural framework for studying properties of physical systems with Lorentz-violation since it includes Lorentz-violating terms in all sectors of the minimal standard model. The Lorentz-violating (LV) terms are generated as vacuum expectation values of tensors defined in a high energy scale. This framework has inspired a great deal of investigation in recent years. Such works encompass several distinct aspects involving fermion systems and radiative corrections, CPT- probing experiments, the electromagnetic CPT- and Lorentz-odd term, the 19 electromagnetic CPT-even coefficients. Recently, some studies involving higher dimensional operators have also been reported with great interest, including nonminimal interactions. These many contributions have elucidated the effects induced by Lorentz violation and served to set up stringent upper bounds on the LV coefficients. In the present work, we propose a new CPT-even, dimension-five, nonminimal coupling linking the fermionic and gauge fields in the context of the Dirac equation, involving the CPT-even tensor of the gauge term of the SME. By considering the nonrelativistic limit of the modified Dirac equation, we explicitly evaluate the new contributions to the nonrelativistic Hamiltonian. These new terms imply a direct correction on the anomalous magnetic moment, a kind of electrical Zeeman-like effect on the atomic spectrum, and a Rashba-like coupling term. These effects are then used to impose upper bounds on the magnitude of the non minimally coupled LV coefficients at the level of 1 part in 10{sub 16}. (author)
Surface states of a system of Dirac fermions: A minimal model
International Nuclear Information System (INIS)
Volkov, V. A.; Enaldiev, V. V.
2016-01-01
A brief survey is given of theoretical works on surface states (SSs) in Dirac materials. Within the formalism of envelope wave functions and boundary conditions for these functions, a minimal model is formulated that analytically describes surface and edge states of various (topological and nontopological) types in several systems with Dirac fermions (DFs). The applicability conditions of this model are discussed.
The reactive content of the proton-nucleus impulse - approximation Dirac optical potential
International Nuclear Information System (INIS)
Carlson, B.V.; Isidro Filho, M.P.; Hussein, M.S.
1984-01-01
The total reaction cross sections for intermediate energy proton scattering on 40 Ca and 208 Pb are calculated within the Dirac-Eikonal formalism. Comparison with data indicate that the recently proposed impulse-approximation Dirac optical potential for nucleon-nucleus scattering, is not absorptive enough. (Author) [pt
Covariant differential calculus on quantum Minkowski space and the q-analogue of Dirac equation
International Nuclear Information System (INIS)
Song Xingchang; Academia Sinica, Beijing
1992-01-01
The covariant differential calculus on the quantum Minkowski space is presented with the help of the generalized Wess-Zumino method and the quantum Pauli matrices and quantum Dirac matrices are constructed parallel to those in the classical case. Combining these two aspects a q-analogue of Dirac equation follows directly. (orig.)
The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states
Energy Technology Data Exchange (ETDEWEB)
Finster, Felix E-mail: felix.finster@mis.mpg.de; Smoller, Joel E-mail: smoller@umich.edu; Yau, S.-T. E-mail: yau@math.harvard.edu
2000-09-18
We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.