How (not) to teach Lorentz covariance of the Dirac equation
International Nuclear Information System (INIS)
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)
How (not) to teach Lorentz covariance of the Dirac equation
Nikolic, H
2013-01-01
In the textbook proofs of 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 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.
Weak Dirac bracket construction and the superparticle covariant quantization problem
International Nuclear Information System (INIS)
The general procedure for constructing a consistent covariant Dirac-type bracket for the models with mixed first and second class constraints is presented. The proposed scheme essentially relies upon explicit separation of the initial constraints into infinitely reducible first and second class ones (by making use of some covariant projectors). Reducibility of the second class constraints involved manifests itself in weakening some properties of the bracket as compared to the standard Dirac one. In particular, a commutation of any quantity with the second class constraints and the Jacobi identity holds on the second class constraint surface only. The procedure developed is realized for a N=1 Brink-Schwarz superparticle in arbitrary dimension and for a N=1, D=9 massive superparticle with the Wess-Zumino term. The possibility to apply the bracket for quantizing the superparticles within the framework of the recent unified algebra approach by I.A.Batalin and I.V.Tyutin (1992,1993) is examined. It is shown, in particular, that for a D=9 massive superparticle it is impossible to construct a Dirac-type bracket possessing a (strong) Jacobi identity in a full phase space. (orig.)
Dirac oscillator in a Galilean covariant non-commutative space
International Nuclear Information System (INIS)
Full text: Even though Galilean kinematics is only an approximation of the relativistic kinematics, the structure of Galilean kinematics is more intricate than relativistic kinematics. For instance, the Galilean algebra admits a nontrivial central extension and projective representations, whereas the Poincare algebra does not. It is possible to construct representations of the Galilei algebra with three possible methods: (1) directly from the Galilei algebra, (2) from contractions of the Poincare algebra with the same space-time dimension, or (3) from the Poincare algebra in a space-time with one additional dimension. In this paper, we follow the third approach, which we refer to as 'Galilean covariance' because the equations are Lorentz covariant in the extended manifold. These equations become Galilean invariant after projection to the lower dimension. Our motivation is that this covariant approach provides one more unifying feature of field theory models. Indeed, particle physics (with Poincare kinematics) and condensed matter physics (with Galilean kinematics) share many tools of quantum field theory (e.g. gauge invariance, spontaneous symmetry breaking, Goldstone bosons), but the Galilean kinematics does not admit a metric structure. However, since the Galilean Lie algebra is a subalgebra of the Poincare Lie algebra if one more space-like dimension is added, we can achieve 'Galilean covariance' with a metric in an extended manifold; that makes non-relativistic models look similar to Lorentz-covariant relativistic models. In this context we study the Galilei covariant five-dimensional formulation applied to Galilean Dirac oscillator in a non-commutative situation, with space-space and momentum-momentum non-commutativity. The wave equation is obtained via a 'Galilean covariant' approach, which consists in projecting the covariant motion equations from a (4, l)-dimensional manifold with light-cone coordinates, to a (3, l
Dirac oscillator in a Galilean covariant non-commutative space
Energy Technology Data Exchange (ETDEWEB)
Melo, G.R. de [Universidade Federal do Reconcavo da Bahia, BA (Brazil); Montigny, M. [University of Alberta (Canada); Pompeia, P.J. [Instituto de Fomento e Coordecacao Industrial, Sao Jose dos Campos, SP (Brazil); Santos, Esdras S. [Universidade Federal da Bahia, Salvador (Brazil)
2013-07-01
Full text: Even though Galilean kinematics is only an approximation of the relativistic kinematics, the structure of Galilean kinematics is more intricate than relativistic kinematics. For instance, the Galilean algebra admits a nontrivial central extension and projective representations, whereas the Poincare algebra does not. It is possible to construct representations of the Galilei algebra with three possible methods: (1) directly from the Galilei algebra, (2) from contractions of the Poincare algebra with the same space-time dimension, or (3) from the Poincare algebra in a space-time with one additional dimension. In this paper, we follow the third approach, which we refer to as 'Galilean covariance' because the equations are Lorentz covariant in the extended manifold. These equations become Galilean invariant after projection to the lower dimension. Our motivation is that this covariant approach provides one more unifying feature of field theory models. Indeed, particle physics (with Poincare kinematics) and condensed matter physics (with Galilean kinematics) share many tools of quantum field theory (e.g. gauge invariance, spontaneous symmetry breaking, Goldstone bosons), but the Galilean kinematics does not admit a metric structure. However, since the Galilean Lie algebra is a subalgebra of the Poincare Lie algebra if one more space-like dimension is added, we can achieve 'Galilean covariance' with a metric in an extended manifold; that makes non-relativistic models look similar to Lorentz-covariant relativistic models. In this context we study the Galilei covariant five-dimensional formulation applied to Galilean Dirac oscillator in a non-commutative situation, with space-space and momentum-momentum non-commutativity. The wave equation is obtained via a 'Galilean covariant' approach, which consists in projecting the covariant motion equations from a (4, l)-dimensional manifold with light-cone coordinates, to a (3, l
Application of covariant analytic mechanics with differential forms to gravity with Dirac field
Nakajima, Satoshi
2015-01-01
We apply the covariant analytic mechanics with the differential forms to the Dirac field and the gravity with the Dirac field. The covariant analytic mechanics treats space and time on an equal footing regarding the differential forms as the basis variables. A significant feature of the covariant analytic mechanics is that the canonical equations, in addition to the Euler-Lagrange equation, are not only manifestly general coordinate covariant but also gauge covariant. Combining our study and the previous works (the scalar field, the abelian and non-abelian gauge fields and the gravity without the Dirac field), the applicability of the covariant analytic mechanics is checked for all fundamental fields. We study both the first and second order formalism of the gravitational field coupled with matters including the Dirac field. Although the first order formalism does not go well for the Hamilton formalism, the second order formalism can be successfully treated within the framework. It is suggested that the covar...
General-Covariant Quantum Mechanics of Dirac Particle in Curved Space-Times
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
We have employed the framework of Bethe–Salpeter equation under covariant instantaneous ansatz to calculate leptonic decay constants of unequal mass pseudoscalar mesons like π±, K, D, DS and B, and radiative decay constants of neutral pseudoscalar mesons like π0 and ηc into two photons. In the Dirac structure of hadronic Bethe–Salpeter wave function, the covariants are incorporated from their complete set in accordance with a recently proposed power counting rule. The contribution of both leading order and next-to-leading order Dirac covariants to decay constants are studied. The results are found to improve and hence validating the power counting rule which provides a practical means of incorporating Dirac covariants in the Bethe–Salpeter wave function for a hadron. (author)
On the covariance of the Dirac-Born-Infeld-Myers action
International Nuclear Information System (INIS)
A covariant version of the non-abelian Dirac-Born-Infeld-Myers action is presented. The non-abelian degrees of freedom are incorporated by adjoining to the (bosonic) worldvolume of the brane a number of anticommuting fermionic directions corresponding to boundary fermions in the string picture. The proposed action treats these variables as classical but can be given a matrix interpretation if a suitable quantisation prescription is adopted. After gauge-fixing and quantisation of the fermions, the action is shown to be in agreement with the Myers action derived from T-duality. It is also shown that the requirement of covariance in the above sense leads to a modified WZ term which also agrees with the one proposed by Myers
International Nuclear Information System (INIS)
We have employed the framework of Bethe-Salpeter equation under Covariant Instantaneous Ansatz to calculate the leptonic decay constants of unequal mass pseudoscalar mesons. In the Dirac structure of BS wave function, the covariants are incorporated from their complete set in accordance with a recently proposed power counting rule, order-by-order in powers of inverse of meson mass. The decay constants are calculated incorporating both Leading Order (LO) as well as Next-to-leading Order (NLO) Dirac covariants. The contribution of both LO as well as NLO covariants to decay constants are studied in detail in this paper. The results are found to improve dramatically, and hence validating the power counting rule which also provides a practical means of incorporating Dirac covariants in the BS wave function of a hadron. (author)
Wang, Yong-Jian; Shi, Xue-Ping; Meng, Xue-Feng; Wu, Xiao-Jing; Luo, Fang-Li; Yu, Fei-Hai
2016-01-01
Spatial heterogeneity in two co-variable resources such as light and water availability is common and can affect the growth of clonal plants. Several studies have tested effects of spatial heterogeneity in the supply of a single resource on competitive interactions of plants, but none has examined those of heterogeneous distribution of two co-variable resources. In a greenhouse experiment, we grew one (without intraspecific competition) or nine isolated ramets (with competition) of a rhizomatous herb Iris japonica under a homogeneous environment and four heterogeneous environments differing in patch arrangement (reciprocal and parallel patchiness of light and soil water) and patch scale (large and small patches of light and water). Intraspecific competition significantly decreased the growth of I. japonica, but at the whole container level there were no significant interaction effects of competition by spatial heterogeneity or significant effect of heterogeneity on competitive intensity. Irrespective of competition, the growth of I. japonica in the high and the low water patches did not differ significantly in the homogeneous treatments, but it was significantly larger in the high than in the low water patches in the heterogeneous treatments with large patches. For the heterogeneous treatments with small patches, the growth of I. japonica was significantly larger in the high than in the low water patches in the presence of competition, but such an effect was not significant in the absence of competition. Furthermore, patch arrangement and patch scale significantly affected competitive intensity at the patch level. Therefore, spatial heterogeneity in light and water supply can alter intraspecific competition at the patch level and such effects depend on patch arrangement and patch scale. PMID:27375630
Wang, Yong-Jian; Shi, Xue-Ping; Meng, Xue-Feng; Wu, Xiao-Jing; Luo, Fang-Li; Yu, Fei-Hai
2016-01-01
Spatial heterogeneity in two co-variable resources such as light and water availability is common and can affect the growth of clonal plants. Several studies have tested effects of spatial heterogeneity in the supply of a single resource on competitive interactions of plants, but none has examined those of heterogeneous distribution of two co-variable resources. In a greenhouse experiment, we grew one (without intraspecific competition) or nine isolated ramets (with competition) of a rhizomatous herb Iris japonica under a homogeneous environment and four heterogeneous environments differing in patch arrangement (reciprocal and parallel patchiness of light and soil water) and patch scale (large and small patches of light and water). Intraspecific competition significantly decreased the growth of I. japonica, but at the whole container level there were no significant interaction effects of competition by spatial heterogeneity or significant effect of heterogeneity on competitive intensity. Irrespective of competition, the growth of I. japonica in the high and the low water patches did not differ significantly in the homogeneous treatments, but it was significantly larger in the high than in the low water patches in the heterogeneous treatments with large patches. For the heterogeneous treatments with small patches, the growth of I. japonica was significantly larger in the high than in the low water patches in the presence of competition, but such an effect was not significant in the absence of competition. Furthermore, patch arrangement and patch scale significantly affected competitive intensity at the patch level. Therefore, spatial heterogeneity in light and water supply can alter intraspecific competition at the patch level and such effects depend on patch arrangement and patch scale. PMID:27375630
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.
Directory of Open Access Journals (Sweden)
Frieder Kleefeld
2013-01-01
Full Text Available According to some generalized correspondence principle the classical limit of a non-Hermitian quantum theory describing quantum degrees of freedom is expected to be the well known classical mechanics of classical degrees of freedom in the complex phase space, i.e., some phase space spanned by complex-valued space and momentum coordinates. As special relativity was developed by Einstein merely for real-valued space-time and four-momentum, we will try to understand how special relativity and covariance can be extended to complex-valued space-time and four-momentum. Our considerations will lead us not only to some unconventional derivation of Lorentz transformations for complex-valued velocities, but also to the non-Hermitian Klein-Gordon and Dirac equations, which are to lay the foundations of a non-Hermitian quantum theory.
Euclidean Supergravity in Terms of Dirac Eigenvalues
Vancea, I. V.
1997-01-01
It has been recently shown that the eigenvalues of the Dirac operator can be considered as dynamical variables of Euclidean gravity. The purpose of this paper is to explore the possiblity that the eigenvalues of the Dirac operator might play the same role in the case of supergravity. It is shown that for this purpose some primary constraints on covariant phase space as well as secondary constraints on the eigenspinors must be imposed. The validity of primary constraints under covariant transp...
Galilean covariant Lagrangian models
International Nuclear Information System (INIS)
We construct non-relativistic Lagrangian field models by enforcing Galilean covariance with a (4, 1) Minkowski manifold followed by a projection onto the (3, 1) Newtonian spacetime. We discuss scalar, Fermi and gauge fields, as well as interactions between these fields, preparing the stage for their quantization. We show that the Galilean covariant formalism provides an elegant construction of the Lagrangians which describe the electric and magnetic limits of Galilean electromagnetism. Similarly we obtain non-relativistic limits for the Proca field. Then we study Dirac Lagrangians and retrieve the Levy-Leblond wave equations when the Fermi field interacts with an Abelian gauge field
International Nuclear Information System (INIS)
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
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.
Euclidean Supergravity in Terms of Dirac Eigenvalues
Vancea, I V
1998-01-01
It has been recently shown by Landi and Rovelli that the eigenvalues of the Dirac operator can be considered as dynamical variables of Euclidean gravity. The purpose of this paper is to explore the possibility that the eigenvalues of the Dirac operator play the same role in the case of supergravity. It is shown that some constraints on the covariant phase space as well as on the eigenspinors must be imposed to this end.
Brown, Laurie M.
Paul Dirac was a brilliant and original thinker. He used his physical intuition and his ideal of mathematical beauty to construct bridges between major areas of physics. This article discusses several such important works, including the bridge between quantum mechanics and relativity that led to his prediction of the existence of antimatter.
Covariant approximation averaging
Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2014-01-01
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Particles and Dirac-type operators on curved spaces
International Nuclear Information System (INIS)
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)
Euclidean supergravity in terms of Dirac eigenvalues
Vancea, Ion V.
1998-08-01
It has been recently shown that the eigenvalues of the Dirac operator can be considered as dynamical variables of Euclidean gravity. The purpose of this paper is to explore the possibility that the eigenvalues of the Dirac operator might play the same role in the case of supergravity. It is shown that for this purpose some primary constraints on covariant phase space as well as secondary constraints on the eigenspinors must be imposed. The validity of primary constraints under covariant transport is further analyzed. It is shown that in this case restrictions on the tangent bundle and on the spinor bundle of spacetime arise. The form of these restrictions is determined under some simplifying assumptions. It is also shown that manifolds with flat curvature of tangent bundle and spinor bundle satisfy these restrictions and thus they support the Dirac eigenvalues as global observables.
Ultrarelativistic Decoupling Transformation for Generalized Dirac Equations
Noble, J H
2015-01-01
The Foldy--Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schr\\"{o}dinger--Pauli theory. We here discuss the opposite, ultrarelativistic limit which requires the use of a fundamentally different expansion where the leading kinetic term in the Dirac equation is perturbed by the mass of the particle and other interaction (potential) terms, rather than vice versa. The ultrarelativistic decoupling transformation is applied to free Dirac particles (in the Weyl basis) and to high-energy tachyons, which are faster-than-light particles described by a fully Lorentz-covariant equation. The effective gravitational interactions are found. For tachyons, the dominant gravitational interaction term in the high-energy limit is shown to be attractive, and equal to the leading term for subluminal Dirac particles (tardyons) in the high-energy limit.
Ultrarelativistic decoupling transformation for generalized Dirac equations
Noble, J. H.; Jentschura, U. D.
2015-07-01
The Foldy-Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schrödinger-Pauli theory. We here discuss the opposite, ultrarelativistic limit which requires the use of a fundamentally different expansion where the leading kinetic term in the Dirac equation is perturbed by the mass of the particle and other interaction (potential) terms, rather than vice versa. The ultrarelativistic decoupling transformation is applied to free Dirac particles (in the Weyl basis) and to high-energy tachyons, which are faster-than-light particles described by a fully Lorentz-covariant equation. The effective gravitational interactions are found. For tachyons, the dominant gravitational interaction term in the high-energy limit is shown to be attractive and equal to the leading term for subluminal Dirac particles (tardyons) in the high-energy limit.
On the spring and mass of the Dirac oscillator
Crawford, James P.
1993-01-01
The Dirac oscillator is a relativistic generalization of the quantum harmonic oscillator. In particular, the square of the Hamiltonian for the Dirac oscillator yields the Klein-Gordon equation with a potential of the form: (ar(sub 2) + b(L x S)), where a and b are constants. To obtain the Dirac oscillator, a 'minimal substitution' is made in the Dirac equation, where the ordinary derivative is replaced with a covariant derivative. However, an unusual feature of the covariant derivative in this case is that the potential is a non-trivial element of the Clifford algebra. A theory which naturally gives rise to gage potentials which are non-trivial elements of the Clifford algebra is that based on local automorphism invariance. An exact solution of the automorphism gage field equations which reproduces both the potential term and the mass term of the Dirac oscillator is presented.
Kursunoglu, Behram N.; Wigner, Eugene Paul
1990-04-01
Portrait R. Feyman; List of contributors; A memorial to P. A. M. Dirac B. N. Kursunoglu; Preface B. N. Kursunoglu and E. P. Wigner; Chronology; Part I. Human Side: 1. Thinking of my darling Paul M. Dirac; 2. Dirac in coral gables S. A. Kursunoglu; 3. Recollections of Paul Dirac at Florida State University J. E. Lannutti; 4. My association with Professor Dirac Harish-Chandra; 5. What Paul Dirac meant in my life N. Kemmer; 6. Dirac's way R. Peierls; 7. An experimenter's view of P. A. M. Dirac A. D. Krisch; 8. Dirac at the University of Miami H. K. Stanford; 9. Remembering Paul Dirac E. P. Wigner; Part II. More Scientific Ideas: 10. Another side to Paul Dirac R. H. Dalitz; 11. Playing with equations, the Dirac way A. Pais; 12. Paul Dirac and Werner Heisenberg - a partnership in science L. M. Brown and H. Rechenberg; 13. Dirac's magnetic monopole and the fine structure constant W. J. Marciano and M. Goldhaber; 14. Magnetic monopoles and the halos of galaxies F. Hoyle; 15. The inadequacies of quantum field theory P. A. M. Dirac; 16. Dirac and the foundation of quantum mechanics P. T. Matthews; Part III. Influenced and Inspired by Association: 17. At the feet of Dirac J. C. Polkinghorne; 18. Reminiscences of Paul Dirac N. Mott; 19. From relativistic quantum theory to the human brain H. J. Lipkin; 20. Dirac in 1962, weak and gravitational radiation interactions J. Weber; 21. Schrödinger's cat W. E. Lamb, Jr.; 22. Dirac and finite field theories A. Salam; 23. Dirac's influence on unified field theory B. N. Kursunoglu; Index.
Reality conditions for Ashtekar gravity from Lorentz-covariant formulation
Alexandrov, Sergei
2005-01-01
We show the equivalence of the Lorentz-covariant canonical formulation considered for the Immirzi parameter $\\beta=i$ to the selfdual Ashtekar gravity. We also propose to deal with the reality conditions in terms of Dirac brackets derived from the covariant formulation and defined on an extended phase space which involves, besides the selfdual variables, also their anti-selfdual counterparts.
Gravitational Gauge Interactions of Dirac Field
Institute of Scientific and Technical Information of China (English)
WU Ning
2004-01-01
Gravitational interactions of Dirac field are studied in this paper. Based on gauge principle, quantum gauge theory of gravity, which is perturbatively renormalizable, is formulated in the Minkowski space-time. In quantum gauge theory of gravity, gravity is treated as a kind of fundamental interactions, which is transmitted by gravitational gauge tield, and Dirac field couples to gravitational field through gravitational gauge covariant derivative. Based on this theory, we can easily explain gravitational phase effect, which has already been detected by COW experiment.
Electromagnetic Klein-Gordon and Dirac Equations in Scale Relativity
Célérier, Marie-Noëlle; Nottale, Laurent
We present a new step in the foundation of quantum field theory with the tools of scale relativity. Previously, quantum motion equations (Schrödinger, Klein-Gordon, Dirac, Pauli) have been derived as geodesic equations written with a quantum-covariant derivative operator. Then, the nature of gauge transformations, of gauge fields and of conserved charges have been given a geometric meaning in terms of a scale-covariant derivative tool. Finally, the electromagnetic Klein-Gordon equation has been recovered with a covariant derivative constructed by combining the quantum-covariant velocity operator and the scale-covariant derivative. We show here that if one tries to derive the electromagnetic Dirac equation from the Klein-Gordon one as for the free particle motion, i.e. as a square root of the time part of the Klein-Gordon operator, one obtains an additional term which is the relativistic analog of the spin-magnetic field coupling term of the Pauli equation. However, if one first applies the quantum covariance, then implements the scale covariance through the scale-covariant derivative, one obtains the electromagnetic Dirac equation in its usual form. This method can also be applied successfully to the derivation of the electromagnetic Klein-Gordon equation. This suggests it rests on more profound roots of the theory, since it encompasses naturally the spin-charge coupling.
Energy Technology Data Exchange (ETDEWEB)
Schanuss, Martin
2012-07-01
Optimum yields are only possible with a good flow through the collector array. With large-scale systems it is sometimes necessary to calculate several possible arrangements in order to find the best design. (orig.)
Connections on Clifford bundles and the Dirac operator
International Nuclear Information System (INIS)
It is shown, how - in the setting of Clifford bundles - the spin connection (or Dirac operator) may be obtained by averaging the Levi-Civita connection (or Kaehler-Dirac operator) over the finite group generated by an orthonormal frame of the base-manifold. The familiar covariance of the Dirac equation under a simultaneous transformation of spinors and matrix-representations emerges very naturally in this scheme, which can also be applied when the manifold does not possess a spin-structure. (Author)
On The Symplectic Two-Form of Gravity in Terms of Dirac Eigenvalues
Abdalla, Maria Christina B; Dos Santos, M A; Vancea, I V
2002-01-01
The Dirac eigenvalues form a subset of observables of the Euclidean gravity. The symplectic two-form in the covariant phase space could be expressed, in principle, in terms of the Dirac eigenvalues. We discuss the existence of the formal solution of the equation defining the components of the symplectic form in this framework.
The Dirac Eigenvalues as Observables of N=2 D=4 Euclidean Supergravity
Vancea, I V
2004-01-01
We generalize previous works on the Dirac eigenvalues as dynamical variables of the Euclidean gravity in four dimensions to N=2 D=4 Euclidean supergravity. We define the Poisson brackets in the covariant phase space of the theory and compute them for the Dirac eigenvalues.
On the symplectic two-form of gravity in terms of Dirac eigenvalues
International Nuclear Information System (INIS)
The Dirac eigenvalues form a subset of observables of the Euclidean gravity. The symplectic two-form in the covariant phase space could be expressed, in principle, in terms of the Dirac eigenvalues. We discuss the existence of the formal solution of the equations defining the components of the symplectic form in this framework
On the symplectic two-form of gravity in terms of Dirac eigenvalues
Abdalla, M. C. B.; De Andrade, M. A.; Santos, M. A.; Vancea, I. V.
2002-11-01
The Dirac eigenvalues form a subset of observables of the Euclidean gravity. The symplectic two-form in the covariant phase space could be expressed, in principle, in terms of the Dirac eigenvalues. We discuss the existence of the formal solution of the equations defining the components of the symplectic form in this framework.
On the symplectic two-form of gravity in terms of Dirac eigenvalues
Energy Technology Data Exchange (ETDEWEB)
Abdalla, M.C.B.; De Andrade, M.A.; Santos, M.A.; Vancea, I.V
2002-11-14
The Dirac eigenvalues form a subset of observables of the Euclidean gravity. The symplectic two-form in the covariant phase space could be expressed, in principle, in terms of the Dirac eigenvalues. We discuss the existence of the formal solution of the equations defining the components of the symplectic form in this framework.
International Nuclear Information System (INIS)
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.
Covariant Hamiltonian evolution in supersymmetric quantum systems
Schreiber, U
2003-01-01
We develop a general formalism for covariant Hamiltonian evolution of supersymmetric (field) theories by making use of the fact that these can be represented on the exterior bundle over their bosonic configuration space as generalized Dirac-Kaehler systems of the form $(d \\pm d^\\dag)\\ket{\\psi} = 0$. By using suitable deformations of the supersymmetry generators we find covariant Hamiltonians for target spaces with general gravitational and Kalb-Ramond field backgrounds and discuss their perturbation theory. Our results will be applied in another paper to the study of curvature corrections to superstring spectra in nontrivial backgrounds, such as ${\\rm AdS}$ close to its pp-wave limit.
Photoconductivity in Dirac materials
International Nuclear Information System (INIS)
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 structures on protobialgebroids
Institute of Scientific and Technical Information of China (English)
YIN; Yanbin; HE; Longguang
2006-01-01
Protobialgebroids include several kinds of algebroid structures such as Lie algebroid,Lie bialgebroid, Lie quasi-bialgebroid, etc. In this paper, the Dirac theories are generalized from Lie bialgebroid to protobialgebroid. We give the integrable conditions for a maximally isotropic subbundle being a Dirac structure for a protobialgebroid by the notion of a characteristic pair. From the integrable conditions, we found out that the Dirac structure has closed relations with the twisting of a protobialgebroid. At last, some special cases of the Dirac structures for protobialgebroids are discussed.
The (2 + 1) curved Dirac equation in polar coordinates in the presence of electromagnetic field
Panahi, H.; Jahangiri, L.
2015-03-01
In this work we study the covariant Dirac equation in (2 + 1) dimensional space-time in the presence of electromagnetic field. In polar coordinates, we show that by using a unitary transformation which implies a constraint between the components of gauge field, the covariant Dirac equation can be transformed into a Schrodinger-like differential equation for one of the spinor components. We also obtain the relativistic energy and spinor wave function for two different kinds of electrostatic potentials. The non-relativistic limit of the Dirac equation is also studied and it is shown that the upper spinor component satisfies the Pauli equation.
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.
Are the invariance principles really truly Lorentz covariant?
International Nuclear Information System (INIS)
It is shown that some sections of the invariance (or symmetry) principles such as the space reversal symmetry (or parity P) and time reversal symmetry T (of elementary particle and condensed matter physics, etc.) are not really truly Lorentz covariant. Indeed, I find that the Dirac-Wigner sense of Lorentz invariance is not in full compliance with the Einstein-Minkowski reguirements of the Lorentz covariance of all physical laws (i.e., the world space Mach principle)
Octonion generalization of Pauli and Dirac matrices
Chanyal, B. C.
2015-10-01
Starting with octonion algebra and its 4 × 4 matrix representation, we have made an attempt to write the extension of Pauli's matrices in terms of division algebra (octonion). The octonion generalization of Pauli's matrices shows the counterpart of Pauli's spin and isospin matrices. In this paper, we also have obtained the relationship between Clifford algebras and the division algebras, i.e. a relation between octonion basis elements with Dirac (gamma), Weyl and Majorana representations. The division algebra structure leads to nice representations of the corresponding Clifford algebras. We have made an attempt to investigate the octonion formulation of Dirac wave equations, conserved current and weak isospin in simple, compact, consistent and manifestly covariant manner.
Sperling, J.; Vogel, W
2009-01-01
In 1927 the great physicist Paul A. M. Dirac failed to provide a consistent quantum description of the phase of a radiation field. Only one year later, he developed the famous Dirac theory of the electron, which led to the anti-particle -- the positron. We show that the reason for Dirac's failure with the phase problem bears a striking resemblance to his ingenious insight into the nature of the electron. For a correct quantum description of the phase of a radiation field it is necessary to ta...
International Nuclear Information System (INIS)
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
Muechler, Lukas; Alexandradinata, Aris; Neupert, Titus; Car, Roberto
2016-01-01
We introduce the notion of a band-inverted, topological semimetal in two-dimensional nonsymmorphic crystals. This notion is materialized in the monolayers of MTe$_2$ (M $=$ W, Mo) if spin-orbit coupling is neglected. We characterize the Dirac band touching topologically by the Wilson loop of the non-Abelian Berry gauge field. An additional feature of the Dirac cone in monolayer MTe$_2$ is that it tilts over in a Lifshitz transition to produce electron and hole pockets, a type-II Dirac cone. T...
Manifestly Covariant Relativity
Dalton, Kenneth
2006-01-01
According to Einstein's principle of general covariance, all laws of nature are to be expressed by manifestly covariant equations. In recent work, the covariant law of energy-momentum conservation has been established. Here, we show that this law gives rise to a fully covariant theory of gravitation and that Einstein's field equations yield total energy-momentum conservation.
Is the nucleon a dirac particle
Energy Technology Data Exchange (ETDEWEB)
Achtzehnter, J.; Wilets, L.
1988-01-01
A two-component Pauli equation for a composite model of the nucleon is derived using a relativistically covariant quark model. Results are presented as an expansion in the momentum and in derivatives for scalar-isoscalar, vector-isoscalar, vector-isovector and electromagnetic external potentials. The Dirac equation fails beginning with the magnetic moment and spin-orbit terms; the failure is modest for isoscalar potentials, but is large for the isovector case. For the vector fields we find anomalous ''magnetic moments'', which are simply related to the corresponding electromagnetic kappa. Preliminary results involving the fields quadratically are also presented. 13 refs.
DIRAC distributed computing services
International Nuclear Information System (INIS)
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.
International Nuclear Information System (INIS)
Conceptually there are a number of different contract models from which a country can select the most suitable for its social, political and economic requirements. These include: 1) the traditional concession, 2) production sharing contracts, 3) service contracts, and 4) equity sharing contracts, i.e. joint ventures. The joint venture arrangement, as it is most commonly used in uranium exploration and mining, is discussed in light of national objectives; geological and technical aspects; infrastructural aspects; and economic aspects. Topics covered include: the exploration phases; the exploration license; exploration area; minimum exploration commitment; host country investor relationship; financing of exploration expenditures; minerals other than uranium; feasibility studies; taxation and levies; and termination of the agreement. During the production phase consideration must be given to such aspects as: The operating company; participation ratio; financing of the participation share; export of production; fiscal regime; imports of goods and services; training of local personnel; provision of support by the host country; assignment of rights; duration of contract; disputes and arbitration procedures; decisions making; transfer of technology; safety; environmental protection and compensation; and restoration of sites. These considerations are all discussed, particularly in regard to the joint venture agreement. The paper emphasises the need, in a successful agreement, for openness and understanding between the parties. No agreement can cover every possible subject that can become a source of disagreement. Only by a sympathetic understanding of each others position and needs can a joint project be successful. (author). 11 refs
DIRAC Workload Management System
Paterson, S
2007-01-01
DIRAC (Distributed Infrastructure with Remote Agent Control) is the Workload and Data Management system (WMS) for the LHCb experiment. The DIRAC WMS offers a transparent way for LHCb users to submit jobs to the EGEE Grid as well as local clusters and individual PCs. This paper will describe workload management optimizations, which ensure high job efficiency and minimized job start times. The computing requirements of the LHCb experiment can only be fulfilled through the use of many distributed compute resources. DIRAC provides a robust platform to run data productions on all the resources available to LHCb including the EGEE Grid. More recently, user support was added to DIRAC that greatly simplifies the procedure of submitting, monitoring and retrieving output of Grid jobs for the LHCb user community. DIRAC submits Pilot Agents to the EGEE Grid via the gLite WMS as normal jobs. Pilot Agents then request jobs from the DIRAC Workload Management System after the local environment has been checked. Therefore DIR...
International Nuclear Information System (INIS)
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.
On radiation reaction and the Abraham-Lorentz-Dirac equation
de Oca, Alejandro Cabo Montes
2013-01-01
It is underlined that the Lienard-Wiechert solutions indicate that after the external force is instantly removed from a small charged particle, the field in its close neighborhood becomes a Lorentz boosted Coulomb field. It suggests that the force of the self-field on the particle should instantaneously vanish after a sudden removal of the external force. A minimal modification of Abraham-Lorentz-Dirac equation is searched seeking to implement this property. A term assuring this behavior is added to the equation by maintaining Lorentz covariance and vanishing scalar product with the four-velocity. The simple Dirac constant force example does not show runaway acceleration.
Atomic Kapitza-Dirac effect with quadrupole transitions
Sancho, Pedro
2013-01-01
Interactions between atoms and light fields are usually described in the electric-dipole approximation. We show that electric-quadrupole terms are important in the Kapitza-Dirac arrangement for light gratings on resonance with a quadrupole atomic transition. We derive the diffraction patterns, which in some cases are experimentally verifiable with the same techniques used with dipole transitions.
Sperling, J
2009-01-01
In 1927 the great physicist Paul A. M. Dirac failed to provide a consistent quantum description of the phase of a radiation field. Only one year later, he developed the famous Dirac theory of the electron, which led to the anti-particle -- the positron. We show that the reason for Dirac's failure with the phase problem bears a striking resemblance to his ingenious insight into the nature of the electron. For a correct quantum description of the phase of a radiation field it is necessary to take the polarisation into account. Similarly to the introduction of the anti-particle of the electron, the inclusion of the second polarisation resolves the inconsistency of the quantum phase problem. This also leads to new insight into the quantum measurement problem of time.
International Nuclear Information System (INIS)
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.)
Amorim, R G G; Silva, Edilberto O
2015-01-01
Symplectic unitary representations for the Poincar\\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space is constructed. The state of a quantum mechanics system is described by a quasi-probability amplitude that is in association with the Wigner function. As a result, the Klein-Gordon and Dirac equations are derived in phase space. As an application, we study the Dirac equation with electromagnetic interaction in phase space.
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.)
Quaternion Dirac Equation and Supersymmetry
Rawat, Seema; Negi, O. P. S.
2007-01-01
Quaternion Dirac equation has been analyzed and its supersymetrization has been discussed consistently. It has been shown that the quaternion Dirac equation automatically describes the spin structure with its spin up and spin down components of two component quaternion Dirac spinors associated with positive and negative energies. It has also been shown that the supersymmetrization of quaternion Dirac equation works well for different cases associated with zero mass, non zero mass, scalar pote...
Dirac Induction for loop groups
Posthuma, H.
2011-01-01
Using a coset version of the cubic Dirac operators for affine Lie algebras, we give an algebraic construction of the Dirac induction homomorphism for loop group representations. With this, we prove a homogeneous generalization of the Weyl-Kac character formula and show compatibility with Dirac induction for compact Lie groups.
Exact solutions of the Dirac equation in central backgrounds
International Nuclear Information System (INIS)
It is shown that the free Dirac equation in spherically symmetric static backgrounds of any dimensions can be put in a simple form using a special version of Cartesian gauge in Cartesian coordinates. This is manifestly covariant under the transformations of the isometry group so that the generalized spherical coordinates can be separated in terms of angular spinors like in the flat case, obtaining a pair of radial equations. In this approach the equation of the free Dirac field in some central backgrounds can be analytically solved obtaining the formula of the energy levels and the corresponding eigenspinors. The example we give are the solutions of the Dirac equation with mass term in AdSd+1 spacetimes and those formed by d-dimensional spheres with the time trivially added. (author)
On Local Constraints of D=4 Supergravity in Terms of Dirac Eigenvalues
Pauna, N.; Vancea, I. V.
1998-01-01
It has been recently shown that in order to have Dirac eigenvalues as observables of Euclidean supergravity, certain constraints should be imposed on the covariant phase space as well as on Dirac eigenspinors. We investigate the relationships among the constraints in the first set and argue that these relationships are not linear. We also derive a set of equations expressing the linear dependency of the constraints in order that the second set of constraints be linearly independent.
Electromagnetic Klein-Gordon and Dirac equations in scale relativity
Célérier, Marie-Noëlle; 10.1142/S0217751X10050615
2010-01-01
We present a new step in the foundation of quantum field theory with the tools of scale relativity. Previously, quantum motion equations (Schr\\"odinger, Klein-Gordon, Dirac, Pauli) have been derived as geodesic equations written with a quantum-covariant derivative operator. Then, the nature of gauge transformations, of gauge fields and of conserved charges have been given a geometric meaning in terms of a scale-covariant derivative tool. Finally, the electromagnetic Klein-Gordon equation has been recovered with a covariant derivative constructed by combining the quantum-covariant velocity operator and the scale-covariant derivative. We show here that if one tries to derive the electromagnetic Dirac equation from the Klein-Gordon one as for the free particle motion, i.e. as a square root of the time part of the Klein-Gordon operator, one obtains an additional term which is the relativistic analog of the spin-magnetic field coupling term of the Pauli equation. However, if one first applies the quantum covarianc...
Families of Dirac operators and quantum affine groups
Mickelsson, Jouko
2010-01-01
Twisted K-theory classes over compact Lie groups can be realized as families of Fredholm operators using the representation theory of loop groups. In this talk I want to show how to deform the Fredholm family, in the sense of quantum groups. The family of Dirac type operators is parametrized by vectors in the adjoint module for a quantum affine algebra and transform covariantly under a (central extension of) the algebra.
Abraham-Lorentz-Dirac Equation in 5D Stuekelberg Electrodynamics
Land, Martin
2016-01-01
We derive the Abraham-Lorentz-Dirac (ALD) equation in the framework of the electrodynamic theory associated with Stueckelberg manifestly covariant canonical mechanics. In this framework, a particle worldline is traced out through the evolution of an event $x^\\mu(\\tau)$. By admitting unconstrained commutation relations between the positions and velocities, the associated electromagnetic gauge fields are in general dependent on the parameter $\\tau$, which plays the role of time in Newtonian mec...
Directory of Open Access Journals (Sweden)
P. G. L. Leach
2014-04-01
Full Text Available Dirac devised his theory of Quantum Mechanics and recognised that his operators resembled the canonical coordinates of Hamiltonian Mechanics. This gave the latter a new lease of life. We look at what happens to Dirac’s Quantum Mechanics if one starts from Hamiltonian Mechanics.
Reconsideration of De Donder-Weyl theory by covariant analytic mechanics
Nakajima, Satoshi
2016-01-01
We show that the covariant analytic mechanics (CAM) is closely related to the De Donder-Weyl (DW) theory. To treat space and time on an equal footing, the DW theory introduces $D$ conjugate fields ($D$ is the dimension of space-time) for each field and the CAM regards the differential forms as the basic variables. The generalization of the canonical equations is called the DW equations. Although one of the DW equations is not correct for the gauge field and the gravitational field, we show the way to improve it. By rewriting the canonical equations of the CAM, which are manifestly general coordinate covariant and gauge covariant, using the components of the tensors, we show that these are equivalent to the improved DW equations. As an instance of constraint systems, we investigate the Dirac field. We present a modified Hamilton formalism which regards only the Dirac fields as the basic variables and show it provides the Dirac equations correctly.
Székely, Gábor J.; Rizzo, Maria L.
2009-01-01
Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but generalize and extend these classical bivariate measures of dependence. Distance correlation characterizes independence: it is zero if and only if the random vectors are independent. The notion of covariance with respect to a stochas...
Modelling Realized Covariances
Xin Jin; John M Maheu
2009-01-01
This paper proposes a new dynamic model of realized covariance (RCOV) matrices based on recent work in time-varying Wishart distributions. The specifications can be linked to returns for a joint multivariate model of returns and covariance dynamics that is both easy to estimate and forecast. Realized covariance matrices are constructed for 5 stocks using high-frequency intraday prices based on positive semi-definite realized kernel estimates. We extend the model to capture the strong persiste...
Adam, C.; Ekstrand, C.; Sykora, T.
2000-01-01
There exist two versions of the covariant Schwinger term in the literature. They only differ by a sign. However, we shall show that this is an essential difference. We shall carefully (taking all signs into account) review the existing quantum field theoretical computations for the covariant Schwinger term in order to determine the correct expression.
DIRAC Infrastructure for Distributed Analysis
Paterson, S
2006-01-01
DIRAC is the LHCb Workload and Data Management system for Monte Carlo simulation, data processing and distributed user analysis. Using DIRAC, a variety of resources may be integrated, including individual PC's, local batch systems and the LCG grid. We report here on the progress made in extending DIRAC for distributed user analysis on LCG. In this paper we describe the advances in the workload management paradigm for analysis with computing resource reservation by means of Pilot Agents. This approach allows DIRAC to mask any inefficiencies of the underlying Grid from the user thus increasing the effective performance of the distributed computing system. The modular design of DIRAC at every level lends the system intrinsic flexibility. The possible strategy for the evolution of the system will be discussed. The DIRAC API consolidates new and existing services and provides a transparent and secure way for users to submit jobs to the Grid. Jobs find their input data by interrogating the LCG File Catalogue which ...
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.
Algebraic and Dirac-Hestenes spinors and spinor fields
International Nuclear Information System (INIS)
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 (Ξu,ψΞu), where Ξu is a spinorial frame field and ψΞu 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
A detailed study of nonperturbative solutions of two-body Dirac equations
Energy Technology Data Exchange (ETDEWEB)
Crater, H.W.; Becker, R.L.; Wong, C.Y.; Van Alstine, P.
1992-12-01
In quark model calculations of the meson spectrums fully covariant two-body Dirac equations dictated by Dirac`s relativistic constraint mechanics gave a good fit to the entire meson mass spectrum for light quark mesons as well as heavy quark mesons with constituent world scalar and vector potentials depending on just one or two parameters. In this paper, we investigate the properties of these equations that made them work so well by solving them numerically for quantum electrodynamics (QED) and related field theories. The constraint formalism generates a relativistic quantum mechanics defined by two coupled Dirac equations on a sixteen component wave function which contain Lorentz covariant constituent potentials that are initially undetermined. An exact Pauli reduction leads to a second order relativistic Schroedinger-like equation for a reduced eight component wave function determined by an effective interaction -- the quasipotential. We first determine perturbatively to lowest order the relativistic quasipotential for the Schroedinger-like equation by comparing that form with one derived from the Bethe-Salpeter equation. Insertion of this perturbative information into the minimal interaction structures of the two-body Dirac equations then completely determines their interaction structures. Then we give a procedure for constructing the full sixteen component solution to our coupled first-order Dirac equations from a solution of the second order equation for the reduced wave function. Next, we show that a perturbative treatment of these equations yields the standard spectral results for QED and related interactions.
Discrete Dirac Structures and Variational Discrete Dirac Mechanics
Leok, Melvin
2008-01-01
We construct discrete analogues of Dirac structures by considering the geometry of symplectic maps and their associated generating functions, in a manner analogous to the construction of continuous Dirac structures in terms of the geometry of symplectic vector fields and their associated Hamiltonians. We demonstrate that this framework provides a means of deriving implicit discrete Lagrangian and Hamiltonian systems, while incorporating discrete Dirac constraints. In particular, this yields implicit nonholonomic Lagrangian and Hamiltonian integrators. We also introduce a discrete Hamilton-Pontryagin variational principle on the discrete Pontryagin bundle, which provides an alternative derivation of the same set of integration algorithms. In so doing, we explicitly characterize the discrete Dirac structures that are preserved by Hamilton-Pontryagin integrators. In addition to providing a unified treatment of discrete Lagrangian and Hamiltonian mechanics in the more general setting of Dirac mechanics, it provid...
Dirac operator, bicovariant differential calculus and gauge theory on κ-Minkowski space
International Nuclear Information System (INIS)
Connections between the κ-Poincare covariant space Γ of differential 1-forms on κ-Minkowski space, Dirac operator and Alain Connes formula are studied. The equations and Lagrangian of gauge theory are constructed. The appearance of an additional spin-0 gauge field according to the non-trivial structure of Γ is studied. (author)
De Leo, Stefano
2010-01-01
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.
Operator ordering in quantum optics theory and the development of Dirac's symbolic method
International Nuclear Information System (INIS)
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)
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...
Covariant Noncommutative Field Theory
International Nuclear Information System (INIS)
The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced
Covariance Applications with Kiwi
Elliott J.B.; Brown D.; Mattoon C.M.
2012-01-01
The Computational Nuclear Physics group at Lawrence Livermore National Laboratory (LLNL) is developing a new tool, named ‘Kiwi’, that is intended as an interface between the covariance data increasingly available in major nuclear reaction libraries (including ENDF and ENDL) and large-scale Uncertainty Quantification (UQ) studies. Kiwi is designed to integrate smoothly into large UQ studies, using the covariance matrix to generate multiple variations of nuclear data. The code has been tested u...
Dirac's Claim and the Chemists
Simões, Ana
In 1929 Paul A. M. Dirac claimed that ``the underlying physical laws necessary for the mathematical theory of ... the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.'' This sentence of Dirac's is cited frequently by historians and philosophers of chemistry in the context of discussions on the hypothetical reduction of chemistry to physics. But how did chemists themselves react to Dirac's claim? Did they feel threatened by physicists who felt they could do their job better than themselves? Did they feel indifferent, or did they simply not care? Was Dirac's paper often cited by chemists? Why was it cited? In this paper, I provide answers to these questions on the basis of an analysis of citations to Dirac's 1929 paper in the Science Citation Index.
Optical Arrangement and Method
DEFF Research Database (Denmark)
2010-01-01
Processing of electromagnetic radiation is described, said incoming electromagnetic radiation comprising radiation in a first wavelength interval and a plurality of spatial frequencies. An arrangement comprises a focusing arrangement for focusing the incoming electromagnetic radiation, a first ca...
Voluntary Environmental Governance Arrangements
J. van der Heijden
2012-01-01
Voluntary environmental governance arrangements have focal attention in studies on environmental policy, regulation and governance. The four major debates in the contemporary literature on voluntary environmental governance arrangements are studied. The literature falls short of sufficiently specify
Hosseinpour, Mansoureh; Silva, Edilberto O; Hassanabadi, Hassan
2016-01-01
We study the covariant Dirac equation in the space-time generated by a cosmic string in presence of vector and scalar potentials of electromagnetic field. We obtain the solution of the radial part of Dirac equation. We consider the scattering states under the Hulth\\'{e}n potential and obtain the phase shifts. From the poles of the scattering $S$-matrix the bound states energies are determined as well.
On the Dirac eigenvalues as observables of the on-shell N = 2D = 4 Euclidean supergravity
Vancea, Ion
2008-12-01
We generalize previous works on the Dirac eigenvalues as dynamical variables of Euclidean gravity and N =1 D = 4 supergravity to on-shell N = 2 D = 4 Euclidean supergravity. The covariant phase space of the theory is defined as the space of the solutions of the equations of motion modulo the on-shell gauge transformations. In this space we define the Poisson brackets and compute their value for the Dirac eigenvalues.
On the Dirac Eigenvalues as Observables of the on-shell N=2 D=4 Euclidean Supergravity
Vancea, Ion V.
2004-01-01
We generalize previous works on the Dirac eigenvalues as dynamical variables of the Euclidean gravity and N=1 D=4 supergravity to on-shell N=2 D=4 Euclidean supergravity. The covariant phase space of the theory is defined as as the space of the solutions of the equations of motion modulo the on-shell gauge transformations. In this space we define the Poisson brackets and compute their value for the Dirac eigenvalues.
International Nuclear Information System (INIS)
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.
Dirac Hamiltonian and Reissner-Nordstrom Metric: Coulomb Interaction in Curved Space-Time
Noble, J H
2016-01-01
We investigate the spin-1/2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordstrom space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordstrom geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational, and electro-gravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electro-gravitational correction terms to the potential proportional to alpha^n G, where alpha is the fine-structure constant, and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic c...
Lantsman, L
2006-01-01
We show that manifest superfluid properties of the Minkowskian Higgs model with vacuum BPS monopoles quantized by Dirac may be described in the framework of the Cauchy problem to the Gribov ambiguity equation. The latter equation specifies the ambiguity in choosing the covariant Coulomb (transverse) gauge for Yang-Mills fields represented as topological Dirac variables, may be treated as solutions to the Gauss law constraint at the removal of temporal components of these fields. We demonstrate that the above Cauchy problem comes just to fixing the covariant Coulomb gauge for topological Dirac variables in the given initial time instant $t_0$ and finding the solutions to the Gribov ambiguity equation in the shape of vacuum BPS monopoles and excitations over the BPS monopole vacuum referring to the class of multipoles. The next goal of the present study will be specifying the look of Gribov topological multipliers entering Dirac variables in the Minkowskian Higgs model quantized by Dirac, especially at the spat...
International Nuclear Information System (INIS)
In the extensive literature devoted to the Hamiltonian dynamics of constrained systems, the case when there are no second-class constraints has been thoroughly studied. In particular, the geometrical significance of the objects encountered in generalized Hamiltonian dynamics has been clarified. The foundation of the geometrical interpretation is the symplectic structure generated in the phase space by the Poisson bracket. It is this structure that permits the introduction of Hamiltonian vector fields isomorphic to the differentials of functions in the phase space and to elucidate the structure of the constraint surface. In this work, the possibility of giving a geometrical meaning to Hamiltonian dynamics in the presence of second-class constraints by using the Dirac bracket to define a symplectic structure on the phase space is discussed. 5 refs
Frasinski, Leszek J.
2016-08-01
Recent technological advances in the generation of intense femtosecond pulses have made covariance mapping an attractive analytical technique. The laser pulses available are so intense that often thousands of ionisation and Coulomb explosion events will occur within each pulse. To understand the physics of these processes the photoelectrons and photoions need to be correlated, and covariance mapping is well suited for operating at the high counting rates of these laser sources. Partial covariance is particularly useful in experiments with x-ray free electron lasers, because it is capable of suppressing pulse fluctuation effects. A variety of covariance mapping methods is described: simple, partial (single- and multi-parameter), sliced, contingent and multi-dimensional. The relationship to coincidence techniques is discussed. Covariance mapping has been used in many areas of science and technology: inner-shell excitation and Auger decay, multiphoton and multielectron ionisation, time-of-flight and angle-resolved spectrometry, infrared spectroscopy, nuclear magnetic resonance imaging, stimulated Raman scattering, directional gamma ray sensing, welding diagnostics and brain connectivity studies (connectomics). This review gives practical advice for implementing the technique and interpreting the results, including its limitations and instrumental constraints. It also summarises recent theoretical studies, highlights unsolved problems and outlines a personal view on the most promising research directions.
Misunderstanding analysis of covariance.
Miller, G A; Chapman, J P
2001-02-01
Despite numerous technical treatments in many venues, analysis of covariance (ANCOVA) remains a widely misused approach to dealing with substantive group differences on potential covariates, particularly in psychopathology research. Published articles reach unfounded conclusions, and some statistics texts neglect the issue. The problem with ANCOVA in such cases is reviewed. In many cases, there is no means of achieving the superficially appealing goal of "correcting" or "controlling for" real group differences on a potential covariate. In hopes of curtailing misuse of ANCOVA and promoting appropriate use, a nontechnical discussion is provided, emphasizing a substantive confound rarely articulated in textbooks and other general presentations, to complement the mathematical critiques already available. Some alternatives are discussed for contexts in which ANCOVA is inappropriate or questionable. PMID:11261398
Covariance Applications with Kiwi
Mattoon, C. M.; Brown, D.; Elliott, J. B.
2012-05-01
The Computational Nuclear Physics group at Lawrence Livermore National Laboratory (LLNL) is developing a new tool, named `Kiwi', that is intended as an interface between the covariance data increasingly available in major nuclear reaction libraries (including ENDF and ENDL) and large-scale Uncertainty Quantification (UQ) studies. Kiwi is designed to integrate smoothly into large UQ studies, using the covariance matrix to generate multiple variations of nuclear data. The code has been tested using critical assemblies as a test case, and is being integrated into LLNL's quality assurance and benchmarking for nuclear data.
Covariance Applications with Kiwi
Directory of Open Access Journals (Sweden)
Elliott J.B.
2012-05-01
Full Text Available The Computational Nuclear Physics group at Lawrence Livermore National Laboratory (LLNL is developing a new tool, named ‘Kiwi’, that is intended as an interface between the covariance data increasingly available in major nuclear reaction libraries (including ENDF and ENDL and large-scale Uncertainty Quantification (UQ studies. Kiwi is designed to integrate smoothly into large UQ studies, using the covariance matrix to generate multiple variations of nuclear data. The code has been tested using critical assemblies as a test case, and is being integrated into LLNL's quality assurance and benchmarking for nuclear data.
New scale-relativistic derivations of Pauli and Dirac equations
International Nuclear Information System (INIS)
In scale relativity, quantum mechanics is recovered by transcribing the classical equations of motion to fractal spaces and demanding, as dictated by the principle of scale relativity, that the form of these equations be preserved. In the framework of this theory, however, the form of the classical energy equations both in the relativistic and nonrelativistic cases are not preserved. Aiming to get full covariance, i.e., to restore to these equations their classical forms, we show that the scale-relativistic form of the Schroedinger equation yields the Pauli equation, whilst the Pissondes's scale-relativistic form of the Klein-Gordon equation gives the Dirac equation
New scale-relativistic derivations of Pauli and Dirac equations
Energy Technology Data Exchange (ETDEWEB)
Hammad, F [Departement TC-SETI, Universite A Mira de Bejaia, Route Targa Ouzemmour, 06000 Bejaia (Algeria)], E-mail: fayhammad@yahoo.fr
2008-02-22
In scale relativity, quantum mechanics is recovered by transcribing the classical equations of motion to fractal spaces and demanding, as dictated by the principle of scale relativity, that the form of these equations be preserved. In the framework of this theory, however, the form of the classical energy equations both in the relativistic and nonrelativistic cases are not preserved. Aiming to get full covariance, i.e., to restore to these equations their classical forms, we show that the scale-relativistic form of the Schroedinger equation yields the Pauli equation, whilst the Pissondes's scale-relativistic form of the Klein-Gordon equation gives the Dirac equation.
New scale-relativistic derivations of Pauli and Dirac equations
Hammad, F.
2008-02-01
In scale relativity, quantum mechanics is recovered by transcribing the classical equations of motion to fractal spaces and demanding, as dictated by the principle of scale relativity, that the form of these equations be preserved. In the framework of this theory, however, the form of the classical energy equations both in the relativistic and nonrelativistic cases are not preserved. Aiming to get full covariance, i.e., to restore to these equations their classical forms, we show that the scale-relativistic form of the Schrödinger equation yields the Pauli equation, whilst the Pissondes's scale-relativistic form of the Klein-Gordon equation gives the Dirac equation.
Aloisi, A M
2016-01-01
In 1931, Dirac advanced a startling prediction about the existence of a new elementary particle, characterized by a magnetic charge of a single polarity: the magnetic monopole. This prediction, that was not based on experimental reasons but on mathematical consistency considerations and the generalization of the formalism of quantum mechanics, illustrates emblematically the Dirac conception of the relationship between physics and mathematics. ----- Nel 1931 Dirac avanz\\`o una sorprendente previsione circa l'esistenza di una nuova particella elementare, caratterizzata da una carica magnetica di un'unica polarit\\`a: il monopolo magnetico. Questa previsione, che non era fondata su ragioni sperimentali ma su considerazioni di consistenza matematica e sulla generalizzazione del formalismo della meccanica quantistica, illustra emblematicamente la concezione di Dirac del rapporto tra fisica e matematica.
Brockmann, R.; Machleidt, R.
1996-01-01
In this review, we give a thorough introduction into the Dirac-Brueckner approach including the mathematical details of the formalism involved. Furthermore, we present results for nuclear matter, NN scattering in the nuclear medium, and finite nuclei.
Ambiguity of perturbative Dirac theory
International Nuclear Information System (INIS)
Degeneracy of parity even and odd electron solutions of the free Dirac equation may cause uncertainties in first order calculation of the perturbative energy. Choosing the even parity solution to start perturbation is though direct, not theoretically well supported. The arbitrariness in choosing lowest order electron wave functions causes uncertainties in the Foldy-Wouthuysen transformations and the reduction of the Pauli equation from the Dirac equation
Resonant Dirac leptogenesis on throats
Bechinger, Andreas; Seidl, Gerhart
2009-01-01
We consider resonant Dirac leptogenesis in a geometry with three five-dimensional throats in the flat limit. The baryon asymmetry in the universe is generated by resonant decays of heavy Kaluza-Klein scalars that are copies of the standard model Higgs. Discrete exchange symmetries between the throats are responsible for establishing two key features of the model. First, they ensure a near degeneracy of the scalar masses and thus a resonant decay of the scalars. This allows for Dirac leptogene...
A detailed study of nonperturbative solutions of two-body Dirac equations
Energy Technology Data Exchange (ETDEWEB)
Crater, H.W.; Becker, R.L.; Wong, C.Y.; Van Alstine, P.
1992-12-01
In quark model calculations of the meson spectrums fully covariant two-body Dirac equations dictated by Dirac's relativistic constraint mechanics gave a good fit to the entire meson mass spectrum for light quark mesons as well as heavy quark mesons with constituent world scalar and vector potentials depending on just one or two parameters. In this paper, we investigate the properties of these equations that made them work so well by solving them numerically for quantum electrodynamics (QED) and related field theories. The constraint formalism generates a relativistic quantum mechanics defined by two coupled Dirac equations on a sixteen component wave function which contain Lorentz covariant constituent potentials that are initially undetermined. An exact Pauli reduction leads to a second order relativistic Schroedinger-like equation for a reduced eight component wave function determined by an effective interaction -- the quasipotential. We first determine perturbatively to lowest order the relativistic quasipotential for the Schroedinger-like equation by comparing that form with one derived from the Bethe-Salpeter equation. Insertion of this perturbative information into the minimal interaction structures of the two-body Dirac equations then completely determines their interaction structures. Then we give a procedure for constructing the full sixteen component solution to our coupled first-order Dirac equations from a solution of the second order equation for the reduced wave function. Next, we show that a perturbative treatment of these equations yields the standard spectral results for QED and related interactions.
A detailed study of nonperturbative solutions of two-body Dirac equations
International Nuclear Information System (INIS)
In quark model calculations of the meson spectrums fully covariant two-body Dirac equations dictated by Dirac's relativistic constraint mechanics gave a good fit to the entire meson mass spectrum for light quark mesons as well as heavy quark mesons with constituent world scalar and vector potentials depending on just one or two parameters. In this paper, we investigate the properties of these equations that made them work so well by solving them numerically for quantum electrodynamics (QED) and related field theories. The constraint formalism generates a relativistic quantum mechanics defined by two coupled Dirac equations on a sixteen component wave function which contain Lorentz covariant constituent potentials that are initially undetermined. An exact Pauli reduction leads to a second order relativistic Schroedinger-like equation for a reduced eight component wave function determined by an effective interaction -- the quasipotential. We first determine perturbatively to lowest order the relativistic quasipotential for the Schroedinger-like equation by comparing that form with one derived from the Bethe-Salpeter equation. Insertion of this perturbative information into the minimal interaction structures of the two-body Dirac equations then completely determines their interaction structures. Then we give a procedure for constructing the full sixteen component solution to our coupled first-order Dirac equations from a solution of the second order equation for the reduced wave function. Next, we show that a perturbative treatment of these equations yields the standard spectral results for QED and related interactions
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...
Generalized Linear Covariance Analysis
Carpenter, James R.; Markley, F. Landis
2014-01-01
This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.
Energy Technology Data Exchange (ETDEWEB)
Dappiagi, Claudio; Hack, Thomas-Paul; Pinamonti, Nicola [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik
2009-03-15
We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We explicitly calculate its trace anomaly in particular. (orig.)
Dappiaggi, Claudio; Pinamonti, Nicola
2009-01-01
We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We shall explicitly calculate its trace anomaly in particular.
International Nuclear Information System (INIS)
We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We explicitly calculate its trace anomaly in particular. (orig.)
On Local Constraints of D=4 Euclidean Supergravity in Terms of Dirac Eigenvalues
Pauna, N.; Vancea, Ion V.
It has recently been shown that in order to have Dirac eigenvalues as observables of Euclidean supergravity, certain constraints should be imposed on the covariant phase space as well as on Dirac eigenspinors. We investigate the relationships among the constraints in the first set and argue that these relationships are not linear. We also derive a set of equations that should be satisfied by some arbitrary functions that enter as coefficients in the equation expressing the linear dependency of the constraints in order that the second set of constraints be linearly independent.
On arrangements of pseudohyperplanes
Indian Academy of Sciences (India)
PRIYAVRAT DESHPANDE
2016-08-01
To every realizable oriented matroid there corresponds an arrangement of real hyperplanes. The homeomorphism type of the complexified complement of such an arrangement is completely determined by the oriented matroid. In this paper we study arrangements of pseudohyperplanes; they correspond to non-realizable oriented matroids. These arrangements arise as a consequence of the Folkman--Lawrence topological representation theorem. We propose a generalization of the complexification process in this context. In particular we construct a space naturally associated with these pseudo-arrangements which is homeomorphic to the complexified complement in the realizable case. Further, we generalize the classical theorem of Salvetti and show that this space has the homotopy type of a cell complex defined in terms of the oriented matroid.
Mapping curved spacetimes into Dirac spinors
Sabín, Carlos
2016-01-01
We show how to transform a Dirac equation in curved spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1+1 dimensional flat spacetime can be transformed via a local phase transformation into a solution of the corresponding Dirac equation in a curved background, where the spacetime metric is encoded into the phase. In this way, the existing quantum simulators of the Dirac equation can naturally incorporate curved spacetimes. As a first example we use our technique to obtain solutions of the Dirac equation in a particular family of interesting spacetimes in 1+1 dimensions.
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...
Traffic disruption in PAM DIRAC road (Prévessin Site)
2003-01-01
From 8th September to 19th September, ST Division will be doing some road works to install HDPE ducts for optical fibre cables under the PAM DIRAC road. For this reason, the road will be closed during 2 days and alternative arrangements will be put in place to reroute the traffic. We kindly ask all users to respect these temporary arrangements. Thank you for your understanding in this matter. ST-EL Group Tel. 77779 - 160484 / 75498 - 163198
The Bragg regime of the two-particle KapitzaDirac effect
Sancho, Pedro
2011-01-01
Abstract We analyze the Bragg regime of the two-particle Kapitza-Dirac arrangement , completing the basic theory of this effect. We provide a detailed evaluation of the detection probabilities for multi-mode states, showing that a complete description must include the interaction time in addition to the usual dimensionless parameter w. The arrangement can be used as a massive two-particle beam splitter. In this respect, we present a comparison with Hong-Ou-Mandel-type experiments in quantu...
The Dirac equation applied to graphene in the presence of topological defects
International Nuclear Information System (INIS)
Full text: The Dirac equation was proposed by Paul Dirac in 1928, in an attempt to get a relativistic wave equation for particles of spin 1/2, because the Schroedinger equation does not remain invariant under Lorentz transformations and the Klein-Gordon only serves for spin 0 particles . Since then, it has been able to describe various systems, in several areas of physics, such as Field Theory, Condensed Matter, among others. Recently, some researchers have use this equation to study the graphene, a very promising material, that consist essentially in a monolayer of carbon atoms, with interesting electronic and transport properties and several possibilities of applications in Material Science and Engineering, for instance. In this work, we study the application of the Dirac equation in graphene, more specifically in the presence of topological defects, that change the physical properties of the material. This is possible because in the formalism of the Dirac equation, we can replace the derivative usual term by a term of covariant derivative, capable of describing the geometry of the space considered. From the job of Vozmediano a and others found in the literature, we write the dirac equation for graphene in presence of a defect, making a modification in the usual Dirac equation. (author)
International Nuclear Information System (INIS)
We investigate the Kondo effect in Dirac systems, where Dirac electrons interact with the localized spin via the s–d exchange coupling. The Dirac electron in solid state has the linear dispersion and is described typically by the Hamiltonian such as Hk = υk · σ for the wave number k where σj are Pauli matrices. We derived the formula of the Kondo temperature TK by means of the Green's function theory for small J. The TK is determined from a singularity of Green's functions in the form TK ≅D-bar exp(-const./ρ|J|) when the exchange coupling |J| is small where D-bar = D/√1+D2 /(2μ)2 for a cutoff D and ρ is the density of states at the Fermi surface. When |μ| << D, TK is proportional to |μ|: TK ≅ |μ| exp(-const./ρ|J|). The Kondo screening will, however, disappear when the Fermi surface shrinks to a point called the Dirac point, that is, TK vanishes when the chemical potential μ is just at the Dirac point. The resistivity and the specific heat exhibit a log-T singularity in the range TK < T << |μ|/kB. Instead, for T ∼ O(|μ|) or T > |μ|, they never show log-T. (author)
Gauge-covariant bimetric theory of gravitation and electromagnetism
Energy Technology Data Exchange (ETDEWEB)
Israelit, M.; Rosen, N.
1983-10-01
The Weyl theory of gravitation and electromagnetism, as modified by Dirac, contains a gauge-covariant scalar ..beta.. which has no geometric significance. This is a flaw if one is looking for a geometric description of gravitation and electromagnetism. A bimetric formalism is therefore introduced which enables one to replace ..beta.. by a geometric quantity. The formalism can be simplified by the use of a gauge-invariant physical metric. The resulting theory agrees with the general relativity for phenomena in the solar system.
Monitoring the DIRAC distributed system
Santinelli, R; Nandakumar, R
2010-01-01
DIRAC, the LHCb community Grid solution, 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 both by agents and services and collected by a logging system. This allows us to ensure that the components are running properly and to collect useful information regarding their operations. The process status monitoring is displayed using the SLS sensor mechanism that also automatically allows to plot various quantities and keep a history of the system. A dedicated GridMap interface (Service...
Institute of Scientific and Technical Information of China (English)
Ming; Zhao
2015-01-01
<正>Marriage is an important institution in our society,which binds men and women the most frequently.When men and women are together,the gender relationship becomes obvious.Most societies in the world are patriarchal,so men’s power penetrates everywhere,including the marriage institution.Marriage institution is built on men’s power,and at the same time,it contributes to men’s power.Arranged marriage is a good example to illustrate how men’s power is over women,which was prevailing in China.China also has arranged marriage today,but particularly in rural areas.Urban China develops a new form of arranged marriage recently,but whether traditional arranged
Institute of Scientific and Technical Information of China (English)
官琪
2004-01-01
Fiveyouthsfromdifferentcountriescometoapartyandsitaroundaroundtable.AisaChinesewhoalsospeaksEnglish;BisaFrenchWhohaslearnedJapanese;CcomesfromEnglandbutalsospeaksFrench;DisaJapanesewhoseforeignlanguageisChinese;EisaFrenchwhoalsospeaksSpanish(西班牙语).HowcanyouarrangetheirseatssothattheyCanspeakwiththepersonssittingnexttohim?(Keytobefound.)Arranging the Seats@官琪
Dirac Quantization of Some Singular Theories
Shirzad, A.; Moyassari, P.
2001-01-01
Analyzing the constraint structure of electrodynamics, massive vector bosons, Dirac fermions and electrodynamics coupled to fermions, we show that Dirac quantization method leads to appropriate creation-annihilation algebra among the Forier coefficients of the fields.
Directory of Open Access Journals (Sweden)
Fernando R. González Díaz
2007-01-01
Full Text Available En los años veinte, el físico inglés Paul Dirac ejemplificó de forma casi recreativa una de las partículas que componen la materia, conocido como espín. En este trabajo se muestra tanto la ejemplificación de Dirac, como algunas otras que se pueden encontrar en la literatura. Además, se presenta un esbozo de la demostración matemática del fenómeno utilizando topología algebraica.
Dirac Cat States in Relativistic Landau Levels
Bermudez, A.; Martin-Delgado, M. A.; Solano, E.
2007-01-01
We show that a relativistic version of Schrodinger cat states, here called Dirac cat states, can be built in relativistic Landau levels when an external magnetic field couples to a relativistic spin 1/2 charged particle. Under suitable initial conditions, the associated Dirac equation produces unitarily Dirac cat states involving the orbital quanta of the particle in a well defined mesoscopic regime. We demonstrate that the proposed Dirac cat states have a purely relativistic origin and cease...
Earth Observing System Covariance Realism
Zaidi, Waqar H.; Hejduk, Matthew D.
2016-01-01
The purpose of covariance realism is to properly size a primary object's covariance in order to add validity to the calculation of the probability of collision. The covariance realism technique in this paper consists of three parts: collection/calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics. An empirical cumulative distribution function (ECDF) Goodness-of-Fit (GOF) method is employed to determine if a covariance is properly sized by comparing the empirical distribution of Mahalanobis distance calculations to the hypothesized parent 3-DoF chi-squared distribution. To realistically size a covariance for collision probability calculations, this study uses a state noise compensation algorithm that adds process noise to the definitive epoch covariance to account for uncertainty in the force model. Process noise is added until the GOF tests pass a group significance level threshold. The results of this study indicate that when outliers attributed to persistently high or extreme levels of solar activity are removed, the aforementioned covariance realism compensation method produces a tuned covariance with up to 80 to 90% of the covariance propagation timespan passing (against a 60% minimum passing threshold) the GOF tests-a quite satisfactory and useful result.
Moduli Space of Integrable Dirac Structures
Milani, Vida
2009-01-01
In this paper we introduce the notion of integrable Dirac structures on Hermitian modules. The moduli space of the space of integrable Dirac structures is studied. Then a necessary and sufficient condition for the integrability of a Dirac structure is obtained as the solution of a certain partial differential equation.
Dirac constraint analysis and symplectic structure of anti-self-dual Yang–Mills equations
Indian Academy of Sciences (India)
U Camci; Z Can; Y Nutku; Y Sucu; D Yazici
2006-12-01
We present the explicit form of the symplectic structure of anti-self-dual Yang–Mills (ASDYM) equations in Yang's - and -gauges in order to establish the bi-Hamiltonian structure of this completely integrable system. Dirac's theory of constraints is applied to the degenerate Lagrangians that yield the ASDYM equations. The constraints are second class as in the case of all completely integrable systems which stands in sharp contrast to the situation in full Yang–Mills theory. We construct the Dirac brackets and the symplectic 2-forms for both - and -gauges. The covariant symplectic structure of ASDYM equations is obtained using the Witten–Zuckerman formalism. We show that the appropriate component of the Witten–Zuckerman closed and conserved 2-form vector density reduces to the symplectic 2-form obtained from Dirac's theory. Finally, we present the Bäcklund transformation between the - and -gauges in order to apply Magri's theorem to the respective two Hamiltonian structures.
Gauge-Invariant Formalism with Dirac-mode Expansion for Confinement and Chiral Symmetry Breaking
Gongyo, Shinya; Suganuma, Hideo
2012-01-01
We develop a manifestly gauge-covariant expansion of the QCD operator such as the Wilson loop, using the eigen-mode of the QCD Dirac operator $\\Slash D=\\gamma^\\mu D^\\mu$. With this method, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in lattice QCD Monte Carlo calculation on $6^4$ at $\\beta$=5.6. As a remarkable fact, the confinement force is almost unchanged even after removing the low-lying Dirac modes, which are responsible to chiral symmetry breaking. This indicates that one-to-one correspondence does not hold for between confinement and chiral symmetry breaking in QCD. In this analysis, we carefully amputate only the "essence of chiral symmetry breaking" by cutting off the low-lying Dirac modes, and can artificially realize the "confined but chiral restored situation" in QCD.
Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics
International Nuclear Information System (INIS)
Based on the accurate experimental data of energy-level differences in hydrogen-like atoms, especially the 1S—2S transitions of hydrogen and deuterium, the necessity of introducing a reduced Dirac equation with reduced mass as the substitution of original electron mass is stressed. Based on new cognition about the essence of special relativity, we provide a reasonable argument for the reduced Dirac equation to have two symmetries, the invariance under the (newly defined) space-time inversion and that under the pure space inversion, in a noninertial frame. By using the reduced Dirac equation and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated (at one-loop level) as the radiative correction on a bound electron staying in an off-mass-shell state—-a new approach eliminating the infrared divergence. Hence the whole calculation, though with limited accuracy, is simplified, getting rid of all divergences and free of ambiguity. (general)
Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics
Ni, Guang-Jiong; Xu, Jian-Jun; Lou, Sen-Yue
2011-02-01
Based on the accurate experimental data of energy-level differences in hydrogen-like atoms, especially the 1S—2S transitions of hydrogen and deuterium, the necessity of introducing a reduced Dirac equation with reduced mass as the substitution of original electron mass is stressed. Based on new cognition about the essence of special relativity, we provide a reasonable argument for the reduced Dirac equation to have two symmetries, the invariance under the (newly defined) space-time inversion and that under the pure space inversion, in a noninertial frame. By using the reduced Dirac equation and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated (at one-loop level) as the radiative correction on a bound electron staying in an off-mass-shell state—-a new approach eliminating the infrared divergence. Hence the whole calculation, though with limited accuracy, is simplified, getting rid of all divergences and free of ambiguity.
Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics
Institute of Scientific and Technical Information of China (English)
Ni Guang-Jiong; Xu Jian-Jun; Lou Sea-Yue
2011-01-01
Based on the accurate experimental data of energy-level differences in hydrogen-like atoms, especially the 1S-2S transitions of hydrogen and deuterium, the necessity of introducing a reduced Dirac equation with reduced mass as the substitution of original electron mass is stressed. Based on new cognition about the essence of special relativity, we provide a reasonable argument for the reduced Dirac equation to have two symmetries, the invariance under the (newly defined) space-time inversion and that under the pure space inversion, in a noninertial frame. By using the reduced Dirac equation and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated (at one-loop level) as the radiative correction on a bound electron staying in an off-mass-shell state-a new approach eliminating the infrared divergence. Hence the whole calculation, though with limited accuracy, is simplified, getting rid of all divergences and free of ambiguity.
Covariant Magnetic Connection Hypersurfaces
Pegoraro, F
2016-01-01
In the single fluid, nonrelativistic, ideal-Magnetohydrodynamic (MHD) plasma description magnetic field lines play a fundamental role by defining dynamically preserved "magnetic connections" between plasma elements. Here we show how the concept of magnetic connection needs to be generalized in the case of a relativistic MHD description where we require covariance under arbitrary Lorentz transformations. This is performed by defining 2-D {\\it magnetic connection hypersurfaces} in the 4-D Minkowski space. This generalization accounts for the loss of simultaneity between spatially separated events in different frames and is expected to provide a powerful insight into the 4-D geometry of electromagnetic fields when ${\\bf E} \\cdot {\\bf B} = 0$.
A new linear Dirac-like spin-3/2 wave equation using Clifford algebra
International Nuclear Information System (INIS)
A new linear Dirac-like wave equation for spin-3/2 is derived, employing four of the seven irreducible eight-dimensional matrices obeying the Clifford algebra C7 with the wave function having the needed eight components only. Though this wave equation is not manifestly covariant and the wave function employed is not locally covariant, it is relativistically invariant and by its very derivation is connected to the Weaver, Hammer and Good (Phys. Rev.; 135: B241 (1964)) formalism for spin-3/2 by a chain of transformations which can be arbitrarily chosen to be either unitary or non-unitary. (author)
A Tale of Three Equations: Breit, Eddington-Guant, and Two-Body Dirac
Van Alstine, Peter; Crater, Horace W.
1997-01-01
G.Breit's original paper of 1929 postulates the Breit equation as a correction to an earlier defective equation due to Eddington and Gaunt, containing a form of interaction suggested by Heisenberg and Pauli. We observe that manifestly covariant electromagnetic Two-Body Dirac equations previously obtained by us in the framework of Relativistic Constraint Mechanics reproduce the spectral results of the Breit equation but through an interaction structure that contains that of Eddington and Gaunt...
Mirrors for pion spectrometer DIRAC
Czech Academy of Sciences Publication Activity Database
Pech, Miroslav; Schovánek, Petr; Hrabovský, Miroslav; Řídký, Jan; Mandát, Dušan; Nožka, Libor; Palatka, Miroslav
1. Olomouc : Univerzita Palackého v Olomouci, 2006 - (Křepelka, J.), s. 109-110 ISBN 80-244-1544-5 R&D Projects: GA MŠk(CZ) 1M06002 Institutional research plan: CEZ:AV0Z10100522 Keywords : mirrors * pion spectrometer DIRAC Subject RIV: BH - Optics, Masers, Lasers
Dirac, Jordan and quantum fields
International Nuclear Information System (INIS)
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
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.
Patrice Loïez
2002-01-01
Photo 01: The DIRAC upstream vacuum channel placed between the target and the upstream detector region. Both the non-intracting primary proton beam and the seconday particle channel travel inside the shown vacuum channel. Photo 02: The DIRAC upstream detector region consisting of 4 planes of GEM/MSGC; 3 planes of Scintillating Fibres; 4 planes of Ionisation hodospope. The photo shows the cabling of GEM/MSGC (right end) and Scintillating Fibres (left end) detectors. Photo 03: Detailed view of the 4 GEM/MSGC planes. The secondary particle channel and the detectors are tilted by 5.7 degrees with respect to the primary proton beam channel visible on the bottom. Photo 04: View of the downstream part of the double arm DIRAC spectrometer, facing the direction of incoming particles. The Drift Chamber system, the scintillation hodoscopes and the threshold Cherenkov counters are shown in the picture. Photo 05: The DIRAC vacuum region between upstream detectors and the dipole magnet. The shielding around the primary pro...
Kocak, M.; Gonul, B.
2007-01-01
The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schrodinger like one. Earlier results are discussed in a unified framework and certain solutions of a large class of potentials are given.
Torsion Gravity for Dirac Fields
Fabbri, Luca
2016-01-01
In this article we will take into account the most complete back-ground with torsion and curvature, providing the most exhaustive coupling for the Dirac field: we will discuss the integrability of the interaction of the matter field and the reduction of the matter field equations.
Nuclear reactor internals arrangement
International Nuclear Information System (INIS)
A nuclear reactor internals arrangement is disclosed which facilitates reactor refueling. A reactor vessel and a nuclear core is utilized in conjunction with an upper core support arrangement having means for storing withdrawn control rods therein. The upper core support is mounted to the underside of the reactor vessel closure head so that upon withdrawal of the control rods into the upper core support, the closure head, the upper core support and the control rods are removed as a single unit thereby directly exposing the core for purposes of refueling
SU(2) loop quantum gravity seen from covariant theory
International Nuclear Information System (INIS)
Covariant loop gravity comes out of the canonical analysis of the Palatini action and the use of the Dirac brackets arising from dealing with the second class constraints ('simplicity' constraints). Within this framework, we underline a quantization ambiguity due to the existence of a family of possible Lorentz connections. We show the existence of a Lorentz connection generalizing the Ashtekar-Barbero connection and we loop quantize the theory showing that it leads to the usual SU(2) loop quantum gravity and to the area spectrum given by the SU(2) Casimir operator. This covariant point of view allows us to analyze closely the drawbacks of the SU(2) formalism: the quantization based on the (generalized) Ashtekar-Barbero connection breaks time diffeomorphisms and physical outputs depend nontrivially on the embedding of the canonical hypersurface into the space-time manifold. On the other hand, there exists a true space-time connection, transforming properly under all diffeomorphisms. We argue that it is this connection that should be used in the definition of loop variables. However, we are still not able to complete the quantization program for this connection giving a full solution of the second class constraints at the Hilbert space level. Nevertheless, we show how a canonical quantization of the Dirac brackets at a finite number of points leads to the kinematical setting of the Barrett-Crane model, with simple spin networks and an area spectrum given by the SL(2,C) Casimir operator
Bayes linear covariance matrix adjustment
Wilkinson, Darren J
1995-01-01
In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of random matrices is motivated and constructed. The inner-product on this space captures aspects of our beliefs about the relationship between covariance matrices of interest to us, providing a structure rich enough for us to adjust beliefs about unknown matrices in the light of data such as sample covariance matrices, exploiting second-order exchangeability and related specifications to obtain representations allowing analysis. Adjustment is associated with orthogonal projection, and illustrated with examples of adjustments for some common problems. The problem of adjusting the covariance matrices underlying exchangeable random vectors is tackled and discussed. Learning about the covariance matrices associated with multivariate time series dynamic linear models is shown to be a...
International Nuclear Information System (INIS)
We give an eight-dimensional realization of the Clifford algebra in the five-dimensional Galilean covariant spacetime by using a dimensional reduction from the (5 + 1) Minkowski spacetime to the (4 + 1) Minkowski spacetime which encompasses the Galilean covariant spacetime. A set of solutions of the Dirac-type equation in the five-dimensional Galilean covariant spacetime is obtained, based on the Pauli representation of 8 x 8 gamma matrices. In order to find an explicit solution, we diagonalize the Klein-Gordon divisor by using the Galilean boost
Modelling Realized Covariances and Returns
Xin Jin; John M Maheu
2010-01-01
This paper proposes new dynamic component models of realized covariance (RCOV) matrices based on recent work in time-varying Wishart distributions. The specifications are linked to returns for a joint multivariate model of returns and covariance dynamics that is both easy to estimate and forecast. Realized covariance matrices are constructed for 5 stocks using high-frequency intraday prices based on positive semi-definite realized kernel estimates. The models are compared based on a term-stru...
Deriving covariant holographic entanglement
Dong, Xi; Rangamani, Mukund
2016-01-01
We provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Renyi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.
National Planning Commission Arrangements
Watkins, Joanna
2009-01-01
Based on a review of relevant World Bank materials and outside sources, this note focuses on two questions of critical importance in discussions surrounding the establishment of a planning commission. These are: 1) what planning commission arrangements seem to be effective? 2) What should the role of a planning commission be in a quasi-federal system? It should be recognized that a plannin...
Power distribution arrangement
DEFF Research Database (Denmark)
2010-01-01
An arrangement and a method for distributing power supplied by a power source to two or more of loads (e.g., electrical vehicular systems) is disclosed, where a representation of the power taken by a particular one of the loads from the source is measured. The measured representation of the amount...
The bundles of algebraic and Dirac-Hestenes spinor fields
International Nuclear Information System (INIS)
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,∇,τg,↑) 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 (ClSpin1,3el(M)) and right (ClSpin1,3er(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 ClSpin1,3el(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 ClSpin1,3el(M) (denoted DECll) on a Lorentzian spacetime is found. We also obtain a representation of the DECll in the Clifford bundle Cl(M,g). It is such equation that we call the DHE and it is satisfied by Clifford fields ψΞ is a member of sec Cl(M,g). This means that to each DHSF Ψ is a member of sec ClSpin1,3el(M) and spin frame Ξ is a member of sec PSpin1,3e(M), there is a well-defined sum of even multivector fields ψΞ 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 DECll and the DHE, although related, are equations of different mathematical natures. We study also the local Lorentz invariance and the
Gravitational Repulsion and Dirac Antimatter
Kowitt, Mark E.
1996-03-01
Based on an analogy with electron and hole dynamics in semiconductors, Dirac's relativistic electron equation is generalized to include a gravitational interaction using an electromagnetic-type approximation of the gravitational potential. With gravitational and inertial masses decoupled, the equation serves to extend Dirac's deduction of antimatter parameters to include the possibility of gravitational repulsion between matter and antimatter. Consequences for general relativity and related “antigravity” issues are considered, including the nature and gravitational behavior of virtual photons, virtual pairs, and negative-energy particles. Basic cosmological implications of antigravity are explored—in particular, potential contributions to inflation, expansion, and the general absence of detectable antimatter. Experimental and observational tests are noted, and new ones suggested.
Batelaan, H
2000-01-01
The Kapitza - Dirac effect is the diffraction of a well - collimated particle beam by a standing wave of light. Why is this interesting? Comparing this situation to the introductory physics textbook example of diffraction of a laser beam by a grating, the particle beam plays the role of the incoming wave and the standing light wave the role of the material grating, highlighting particle - wave duality. Apart from representing such a beautiful example of particle - wave duality, the diffracted particle beams are coherent. This allows the construction of matter interferometers and explains why the Kapitza - Dirac effect is one of the workhorses in the field of atom optics. Atom optics concerns the manipulation of atomic waves in ways analogous to the manipulation of light waves with optical elements. The excitement and activity in this new field of physics stems for a part from the realisation that the shorter de Broglie wavelengths of matter waves allow ultimate sensitivities for diffractive and interferometri...
Stability of Dirac sheet configurations
International Nuclear Information System (INIS)
Using cooling for SU(2) lattice configurations, purely Abelian constant magnetic-field configurations were left over after the annihilation of constituents that formed metastable Q=0 configurations. These so-called Dirac sheet configurations were found to be stable if emerging from the confined phase, close to the deconfinement phase transition, provided their Polyakov loop was sufficiently nontrivial. Here we show how this is related to the notion of marginal stability of the appropriate constant magnetic-field configurations. We find a perfect agreement between the analytic prediction for the dependence of stability on the value of the Polyakov loop (the holonomy) in a finite volume and the numerical results studied on a finite lattice in the context of the Dirac sheet configurations
Renormalization of Dirac's Polarized Vacuum
Lewin, Mathieu
2010-01-01
We review recent results on a mean-field model for relativistic electrons in atoms and molecules, which allows to describe at the same time the self-consistent behavior of the polarized Dirac sea. We quickly derive this model from Quantum Electrodynamics and state the existence of solutions, imposing an ultraviolet cut-off $\\Lambda$. We then discuss the limit $\\Lambda\\to\\infty$ in detail, by resorting to charge renormalization.
Luo, Da-Wei; Pyshkin, P. V.; Yu, Ting; Lin, Hai-Qing; You, J. Q.; Wu, Lian-Ao
2016-01-01
We provide an alternative approach to relativistic dynamics based on the Feshbach projection technique. Instead of directly studying the Dirac equation, we derive a two-component equation for the upper spinor. This approach allows one to investigate the underlying physics in a different perspective. For particles with small mass such as the neutrino, the leading order equation has a Hermitian effective Hamiltonian, implying there is no leakage between the upper and lower spinors. In the weak ...
Dirac solutions for quaternionic potentials
De Leo, Stefano
2014-01-01
In this paper, the quaternionic Dirac equation is solved for quaternionic potentials, iV0+jW0. The study shows two different solutions. The first solution contains particles and anti-particles and leads to the diffusion, tunneling and Klein energy zones. The complex limit is recovered from this solution. The second solution, which does not have a complex counterpart, can be seen as a V0-antiparticle or |W0|-particle.
DIRAC: Secure web user interface
International Nuclear Information System (INIS)
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.
Revisiting pseudo-Dirac neutrinos
Balaji, K R S; Maalampi, J; Kalliomaki, Anna; Maalampi, Jukka
2002-01-01
We study the pseudo-Dirac mixing of left and right-handed neutrinos in the case where the Majorana masses M_L and M_R are small when compared with the Dirac mass, M_D. The light Majorana masses could be generated by a non-renormalizable operator reflecting effects of new physics at some high energy scale. In this context, we obtain a simple model independent closed bound for M_D. A phenomenologically consistent scenario is achieved with M_L,M_R ~ 10^{-7} eV and M_D ~ 10^{-5}-10^{-4} eV. This precludes the possibility of positive mass searches in the planned future experiments like GENIUS or in tritium decay experiments. If on the other hand, GENIUS does observe a positive signal for a Majorana mass \\geq 10^{-3} eV, then with very little fine tuning of neutrino parameters, the scale of new physics could be in the TeV range, but pseudo-Dirac scenario in that case is excluded. We briefly discuss the constraints from cosmology when a fraction of the dark matter is composed of nearly degenerate neutrinos.
Imaging arrangement and microscope
Pertsinidis, Alexandros; Chu, Steven
2015-12-15
An embodiment of the present invention is an imaging arrangement that includes imaging optics, a fiducial light source, and a control system. In operation, the imaging optics separate light into first and second tight by wavelength and project the first and second light onto first and second areas within first and second detector regions, respectively. The imaging optics separate fiducial light from the fiducial light source into first and second fiducial light and project the first and second fiducial light onto third and fourth areas within the first and second detector regions, respectively. The control system adjusts alignment of the imaging optics so that the first and second fiducial light projected onto the first and second detector regions maintain relatively constant positions within the first and second detector regions, respectively. Another embodiment of the present invention is a microscope that includes the imaging arrangement.
Coloring and Guarding Arrangements
Bose, Prosenjit; Collette, Sébastien; Hurtado, Ferran; Korman, Matias; Langerman, Stefan; Taslakian, Perouz
2012-01-01
Given an arrangement of lines in the plane, what is the minimum number $c$ of colors required to color the lines so that no cell of the arrangement is monochromatic? In this paper we give bounds on the number c both for the above question, as well as some of its variations. We redefine these problems as geometric hypergraph coloring problems. If we define $\\Hlinecell$ as the hypergraph where vertices are lines and edges represent cells of the arrangement, the answer to the above question is equal to the chromatic number of this hypergraph. We prove that this chromatic number is between $\\Omega (\\log n / \\log\\log n)$. and $O(\\sqrt{n})$. Similarly, we give bounds on the minimum size of a subset $S$ of the intersections of the lines in $\\mathcal{A}$ such that every cell is bounded by at least one of the vertices in $S$. This may be seen as a problem on guarding cells with vertices when the lines act as obstacles. The problem can also be defined as the minimum vertex cover problem in the hypergraph $\\Hvertexcell$...
Lagrangians for Massive Dirac Chiral Superfields
Jiménez, Enrique
2015-01-01
A new off-shell, $ 4D $, $ \\mathcal{N}=1 $ supersymmetric theory, based on massive Dirac superfields and carrying superspin one-half, is offered. In order to obtain the Dirac formalism for fermions, second order derivatives in the propagating component Dirac fields must be absent in the off-shell free Lagrangian. The bosonic sector is encoded in a tensor-spinor field and after studying its form, in the interaction picture, the propagating and auxiliary bosonic fields are identified. Besides the supersymmetric chiral condition, the Dirac superfields are not further constrained. In addition, an interaction super Yukawa potential, formed by Dirac and scalar chiral superfields, is given in terms of their component fields. Finally, in order to treat the case of neutral superparticles, the Majorana condition on the Dirac superfields is imposed.
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...
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...
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.
Bosonic symmetries of the Dirac equation
International Nuclear Information System (INIS)
We have found on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass the new physically meaningful features of this equation. The new bosonic symmetries of the Dirac equation in both the Foldy-Wouthuysen and the Pauli-Dirac representations are found, among which (together with the 32-dimensional pure matrix algebra of invariance) the new spin s=(1,0) multiplet Poincare symmetry is proved. In order to carry out the corresponding proofs a 64-dimensional extended real Clifford-Dirac algebra is put into consideration. -- Highlights: → The 64-dimensional extended real Clifford-Dirac algebra is put into consideration. → Maximal pure matrix algebra of invariance of the Foldy-Wouthuysen equation is found. → The spin (1,0) Lorentz and Poincare symmetries of the Dirac equation are proved.
Bosonic symmetries of the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Simulik, V.M., E-mail: vsimulik@gmail.com [Institute of Electron Physics, National Academy of Sciences of Ukraine, 21 Universitetska Str., 88000 Uzhgorod (Ukraine); Krivsky, I.Yu. [Institute of Electron Physics, National Academy of Sciences of Ukraine, 21 Universitetska Str., 88000 Uzhgorod (Ukraine)
2011-06-20
We have found on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass the new physically meaningful features of this equation. The new bosonic symmetries of the Dirac equation in both the Foldy-Wouthuysen and the Pauli-Dirac representations are found, among which (together with the 32-dimensional pure matrix algebra of invariance) the new spin s=(1,0) multiplet Poincare symmetry is proved. In order to carry out the corresponding proofs a 64-dimensional extended real Clifford-Dirac algebra is put into consideration. -- Highlights: → The 64-dimensional extended real Clifford-Dirac algebra is put into consideration. → Maximal pure matrix algebra of invariance of the Foldy-Wouthuysen equation is found. → The spin (1,0) Lorentz and Poincare symmetries of the Dirac equation are proved.
The stationary Maxwell-Dirac equations
International Nuclear Information System (INIS)
The Maxwell-Dirac equations are the equations for electronic matter, the 'classical' theory underlying QED. The system combines the Dirac equations with the Maxwell equations sourced by the Dirac current. A stationary Maxwell-Dirac system has ψ = e-iEtφ, with φ independent of t. The system is said to be isolated if the dependent variables obey quite weak regularity and decay conditions. In this paper, we prove the following strong localization result for isolated, stationary Maxwell-Dirac systems, - there are no embedded eigenvalues in the essential spectrum, i.e. -m ≤ E ≤ m; - if vertical bar E vertical bar < m then the Dirac field decays exponentially as vertical bar x vertical bar → ∞; - if vertical bar E vertical bar = m then the system is 'asymptotically' static and decays exponentially if the total charge is non-zero
Evaluation and processing of covariance data
International Nuclear Information System (INIS)
These proceedings of a specialists'meeting on evaluation and processing of covariance data is divided into 4 parts bearing on: part 1- Needs for evaluated covariance data (2 Papers), part 2- generation of covariance data (15 Papers), part 3- Processing of covariance files (2 Papers), part 4-Experience in the use of evaluated covariance data (2 Papers)
Emergent Dirac Hamiltonians in Quantum Gravity
Aastrup, Johannes; Paschke, Mario
2009-01-01
We modify the construction of the spectral triple over an algebra of holonomy loops by introducing additional parameters in form of families of matrices. These matrices generalize the already constructed Euler-Dirac type operator over a space of connections. We show that these families of matrices can naturally be interpreted as parameterizing foliations of 4-manifolds. The corresponding Euler-Dirac type operators then induce Dirac Hamiltonians associated to the corresponding foliation, in the previously constructed semi-classical states.
Emergent Dirac Hamiltonians in Quantum Gravity
Aastrup, Johannes; Grimstrup, Jesper M.; Paschke, Mario
2009-01-01
We modify the construction of the spectral triple over an algebra of holonomy loops by introducing additional parameters in form of families of matrices. These matrices generalize the already constructed Euler-Dirac type operator over a space of connections. We show that these families of matrices can naturally be interpreted as parameterizing foliations of 4-manifolds. The corresponding Euler-Dirac type operators then induce Dirac Hamiltonians associated to the corresponding foliation, in th...
The Dirac medals of the ICTP. 1993
International Nuclear Information System (INIS)
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
Stokes-Dirac structures through reduction of infinite-dimensional Dirac structures
Vankerschaver, Joris; Yoshimura, Hiroaki; Leok, Melvin; Marsden, Jerrold E
2010-01-01
We consider the concept of Stokes-Dirac structures in boundary control theory proposed by van der Schaft and Maschke. We introduce Poisson reduction in this context and show how Stokes-Dirac structures can be derived through symmetry reduction from a canonical Dirac structure on the unreduced phase space. In this way, we recover not only the standard structure matrix of Stokes-Dirac structures, but also the typical non-canonical advection terms in (for instance) the Euler equation.
Adjunctation and Scalar Product in the Dirac Equation - I
Dima, M.
2016-02-01
The Bargmann-Pauli adjunctator (hermitiser) of {C}{l}_{_{1,3}}(C) is derived in a representation independent way, circumventing the early derivations (Pauli, Ann. inst. Henri Poincaré 6, 109 and 121 1936) using representation-dependent arguments. Relations for the adjunctator's transformation with the scalar product and space generator set are given. The S U(2) adjunctator is shown to determine the {C}{l}_{_{1,3}}(C) adjunctator. Part-II of the paper will approach the problem of the two scalar products used in Dirac theory - an unphysical situation of "piece-wise physics" with erroneous results. The adequate usage of scalar product - via calibration - will be presented, in particular under boosts, yielding the known covariant transformations of physical quantities.
Dirac field on Moyal-Minkowski spacetime
Energy Technology Data Exchange (ETDEWEB)
Borris, Markus; Verch, Rainer [Inst. f. Theoretische Physik, Universitaet Leipzig, 04009 Leipzig (Germany)
2008-07-01
We present the Dirac field on Moyal-Minkowski spacetime as a model of quantum field theory on a Lorentzian non-commutative background spacetime. This provides an example for a quantum field theory on Lorentzian spectral geometries proposed by M. Paschke and R. Verch, and others. The scattering of the Dirac field coupled to a non-commutative potential term is investigated and it is shown that the scattering transformation is unitarily implementable in the vacuum Hilbert-space representation of the Dirac field. The way in which the scattering transformations induce observables of the Dirac field on Moyal-Minkowski spacetime, and their possible interpretation, will also be discussed.
Dirac field on Moyal-Minkowski spacetime
International Nuclear Information System (INIS)
We present the Dirac field on Moyal-Minkowski spacetime as a model of quantum field theory on a Lorentzian non-commutative background spacetime. This provides an example for a quantum field theory on Lorentzian spectral geometries proposed by M. Paschke and R. Verch, and others. The scattering of the Dirac field coupled to a non-commutative potential term is investigated and it is shown that the scattering transformation is unitarily implementable in the vacuum Hilbert-space representation of the Dirac field. The way in which the scattering transformations induce observables of the Dirac field on Moyal-Minkowski spacetime, and their possible interpretation, will also be discussed
The incredible shrinking covariance estimator
Theiler, James
2012-05-01
Covariance estimation is a key step in many target detection algorithms. To distinguish target from background requires that the background be well-characterized. This applies to targets ranging from the precisely known chemical signatures of gaseous plumes to the wholly unspecified signals that are sought by anomaly detectors. When the background is modelled by a (global or local) Gaussian or other elliptically contoured distribution (such as Laplacian or multivariate-t), a covariance matrix must be estimated. The standard sample covariance overfits the data, and when the training sample size is small, the target detection performance suffers. Shrinkage addresses the problem of overfitting that inevitably arises when a high-dimensional model is fit from a small dataset. In place of the (overfit) sample covariance matrix, a linear combination of that covariance with a fixed matrix is employed. The fixed matrix might be the identity, the diagonal elements of the sample covariance, or some other underfit estimator. The idea is that the combination of an overfit with an underfit estimator can lead to a well-fit estimator. The coefficient that does this combining, called the shrinkage parameter, is generally estimated by some kind of cross-validation approach, but direct cross-validation can be computationally expensive. This paper extends an approach suggested by Hoffbeck and Landgrebe, and presents efficient approximations of the leave-one-out cross-validation (LOOC) estimate of the shrinkage parameter used in estimating the covariance matrix from a limited sample of data.
A Short Biography of Paul A. M. Dirac and Historical Development of Dirac Delta Function
Debnath, Lokenath
2013-01-01
This paper deals with a short biography of Paul Dirac, his first celebrated work on quantum mechanics, his first formal systematic use of the Dirac delta function and his famous work on quantum electrodynamics and quantum statistics. Included are his first discovery of the Dirac relativistic wave equation, existence of positron and the intrinsic…
Covariant Electrodynamics in Vacuum
Wilhelm, H. E.
1990-05-01
The generalized Galilei covariant Maxwell equations and their EM field transformations are applied to the vacuum electrodynamics of a charged particle moving with an arbitrary velocity v in an inertial frame with EM carrier (ether) of velocity w. In accordance with the Galilean relativity principle, all velocities have absolute meaning (relative to the ether frame with isotropic light propagation), and the relative velocity of two bodies is defined by the linear relation uG = v1 - v2. It is shown that the electric equipotential surfaces of a charged particle are compressed in the direction parallel to its relative velocity v - w (mechanism for physical length contraction of bodies). The magnetic field H(r, t) excited in the ether by a charge e moving uniformly with velocity v is related to its electric field E(r, t) by the equation H=ɛ0(v - w)xE/[ 1 +w • (t>- w)/c20], which shows that (i) a magnetic field is excited only if the charge moves relative to the ether, and (ii) the magnetic field is weak if v - w is not comparable to the velocity of light c0 . It is remarkable that a charged particle can excite EM shock waves in the ether if |i> - w > c0. This condition is realizable for anti-parallel charge and ether velocities if |v-w| > c0- | w|, i.e., even if |v| is subluminal. The possibility of this Cerenkov effect in the ether is discussed for terrestrial and galactic situations
Inspection of Emergency Arrangements
International Nuclear Information System (INIS)
The Working Group on Inspection Practices (WGIP) was tasked by the NEA CNRA to examine and evaluate the extent to which emergency arrangements are inspected and to identify areas of importance for the development of good inspection practices. WGIP members shared their approaches to the inspection of emergency arrangements by the use of questionnaires, which were developed from the requirements set out in IAEA Safety Standards. Detailed responses to the questionnaires from WGIP member countries have been compiled and are presented in the appendix to this report. The following commendable practices have been drawn from the completed questionnaires and views provided by WGIP members: - RBs and their Inspectors have sufficient knowledge and information regarding operator's arrangements for the preparedness and response to nuclear emergencies, to enable authoritative advice to be given to the national coordinating authority, where necessary. - Inspectors check that the operator's response to a nuclear emergency is adequately integrated with relevant response organisations. - Inspectors pay attention to consider the integration of the operator's response to safety and security threats. - The efficiency of international relations is checked in depth during some exercises (e.g. early warning, assistance and technical information), especially for near-border facilities that could lead to an emergency response abroad. - RB inspection programmes consider the adequacy of arrangements for emergency preparedness and response to multi-unit accidents. - RBs assess the adequacy of arrangements to respond to accidents in other countries. - The RB's role is adequately documented and communicated to all agencies taking part in the response to a nuclear or radiological emergency. - Inspectors check that threat assessments for NPPs have been undertaken in accordance with national requirements and that up-to-date assessments have been used as the basis for developing emergency plans for
Bilinear covariants and spinor fields duality in quantum Clifford algebras
Abłamowicz, Rafał; Gonçalves, Icaro; da Rocha, Roldão
2014-10-01
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying {Z}-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, "The unpredictability of quantum gravity," Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.
Bilinear covariants and spinor fields duality in quantum Clifford algebras
International Nuclear Information System (INIS)
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying Z-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, “The unpredictability of quantum gravity,” Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived
Bilinear covariants and spinor fields duality in quantum Clifford algebras
Energy Technology Data Exchange (ETDEWEB)
Abłamowicz, Rafał, E-mail: rablamowicz@tntech.edu [Department of Mathematics, Box 5054, Tennessee Technological University, Cookeville, Tennessee 38505 (United States); Gonçalves, Icaro, E-mail: icaro.goncalves@ufabc.edu.br [Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, SP (Brazil); Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, SP (Brazil); Rocha, Roldão da, E-mail: roldao.rocha@ufabc.edu.br [Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, SP (Brazil); International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste (Italy)
2014-10-15
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying Z-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, “The unpredictability of quantum gravity,” Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.
Abraham-Lorentz-Dirac equation in 5D Stuekelberg electrodynamics
International Nuclear Information System (INIS)
We derive the Abraham-Lorentz-Dirac (ALD) equation in the framework of the electrodynamic theory associated with Stueckelberg manifestly covariant canonical mechanics. In this framework, a particle worldline is traced out through the evolution of an event xμ (τ). By admitting unconstrained commutation relations between the positions and velocities, the associated electromagnetic gauge fields are in general dependent on the parameter τ, which plays the role of time in Newtonian mechanics. Standard Maxwell theory emerges from this system as a τ-independent equilibrium limit. In this paper, we calculate the τ-dependent field induced by an arbitrarily evolving event, and study the long-range radiation part, which is seen to be an on-shell plane wave of the Maxwell type. Following Dirac's method, we obtain an expression for the finite part of the self-interaction, which leads to the ALD equation that generalizes the Lorentz force. This third-order differential equation is then converted to an integro-differential equation, identical to the standard Maxwell expression, except for the τ-dependence of the field. By studying this τ-dependence in detail, we show that field can be removed from the integration, so that the Lorentz force depends only on the instantaneous external field and an integral over dynamical variables of the event evolution. In this form, pre-acceleration of the event by future values of the field is not present.
Abraham-Lorentz-Dirac Equation in 5D Stuekelberg Electrodynamics
Land, Martin
2016-01-01
We derive the Abraham-Lorentz-Dirac (ALD) equation in the framework of the electrodynamic theory associated with Stueckelberg manifestly covariant canonical mechanics. In this framework, a particle worldline is traced out through the evolution of an event $x^\\mu(\\tau)$. By admitting unconstrained commutation relations between the positions and velocities, the associated electromagnetic gauge fields are in general dependent on the parameter $\\tau$, which plays the role of time in Newtonian mechanics. Standard Maxwell theory emerges from this system as a $\\tau$-independent equilibrium limit. In this paper, we calculate the $\\tau$-dependent field induced by an arbitrarily evolving event, and study the long-range radiation part, which is seen to be an on-shell plane wave of the Maxwell type. Following Dirac's method, we obtain an expression for the finite part of the self-interaction, which leads to the ALD equation that generalizes the Lorentz force. This third-order differential equation is then converted to an...
Seating arrangement in Althingi
Directory of Open Access Journals (Sweden)
Þorsteinn Magnússon
2014-12-01
Full Text Available Almost a century has passed since Althingi, the Parliament of Iceland, introduced, in 1916, the method of allocating seats to Members by drawing lots at the start of each session. This arrangement is not customary in any other national parliament in the world. It has never been established why this particular method of allocating seats was introduced in Althingi. Neither has it been mapped out how the allocation was conducted, what the Members thought of it nor what impact, if any, the arrangement had on the relations of Members and the workings of Althingi. This article therefore presents the first study of this subject in Iceland. The article also places the seat allocation procedure of Althingi in an international context, as the general rule in parliaments around the world is that Members are seated together in parliamentary party groups. The conclusions of the study are, among other things, that the seat allocation by lot was probably modelled on the House of Representatives of the United States Congress, where seats were allocated by lot from 1845-1913. The study also reveals that over 40 years passed until seat allocation by lot became fully established procedure in Althingi. In the Upper House seats were not allocated by lot at the great majority of sessions until 1959 and Members appear to have been mainly seated along party lines. In the Lower House it was common for some Members to exchange seats following the drawing of lots, and for some time attempts were made to introduce seating by parliamentary party, but the efforts were unsuccessful due to insufficient support. Since 1959 there has not been any disagreement regarding the drawing of lots for seats. Generally speaking, Members appear to hold the opinion that the seating arrangement in Althingi has a positive impact on personal relations, is a positive counterbalance to the division of Members into government supporters and opposition members and that the allocation of seats by
Covariant Stora-Zumino chain terms
Adam, C
1999-01-01
In a recent paper, Ekstrand proposed a simple expression from which covariant anomaly, covariant Schwinger term and higher covariant chain terms may be computed. We comment on the relation of his result to the earlier work of Tsutsui.
International Nuclear Information System (INIS)
The objective of the paper is to describe the safety scheme port authorities should establish to deal with any contingency that may result from the visit of a nuclear powered ship. The safety scheme should be devised to cover both normal operation and any accident conditions that could arise while the ship is in port. The paper is divided into three parts. The three parts being: background information, general instructions, and emergency procedures. The background information will describe the nature of the hazards a port authority has to be prepared to deal with, and the philosophical basis for a berthing policy. In the part dealing with general instructions the objective of the safety scheme will be described. Also this part will describe the composition of the Port Safety Panel, allocation of responsibilities, passage and berthing arrangements, general safety precautions, records required, and rescue arrangements. In the part dealing with emergency procedures the role of: the Ship's Master, Harbour Authorities, Local Police, and local Health Services are discussed. As an Appendix to the paper a copy of the safety scheme that has been devised for visits of nuclear merchant ships to Southampton is given
Phase-covariant quantum cloning
International Nuclear Information System (INIS)
Quantum cloning machines for equatorial qubits are studied. For a 1 to 2 phase-covariant quantum cloning machine, using Hilbert-Schmidt norm and Bures fidelity, we show that our transformation can achieve the bound of the fidelity. (author)
General covariance in computational electrodynamics
DEFF Research Database (Denmark)
Shyroki, Dzmitry; Lægsgaard, Jesper; Bang, Ole;
2007-01-01
We advocate the generally covariant formulation of Maxwell equations as underpinning some recent advances in computational electrodynamics—in the dimensionality reduction for separable structures; in mesh truncation for finite-difference computations; and in adaptive coordinate mapping as opposed...
Institute of Scientific and Technical Information of China (English)
LI Chang-Hui; DING Hao-Gang; DAI Jian; SONG Xing-Chang
2001-01-01
Several models in noncommutative geometry (NCG) with mild changes to the standard model are introduced to discuss the neutrino mass problem. We use two constraints, Poincaré duality and gauge anomaly free, to discuss the possibility of containing right-handed neutrinos in them. Our work shows that no model in this paper, with each generation containing a right-handed neutrino, can satisfy these two constraints at the same time. So, to consist with neutrino oscillation experiment results, maybe fundamental changes to the present version of NCG are usually needed to include Dirac massive neutrinos.
Superalgebraic representation of Dirac matrices
Monakhov, V. V.
2016-01-01
We consider a Clifford extension of the Grassmann algebra in which operators are constructed from products of Grassmann variables and derivatives with respect to them. We show that this algebra contains a subalgebra isomorphic to a matrix algebra and that it additionally contains operators of a generalized matrix algebra that mix states with different numbers of Grassmann variables. We show that these operators are extensions of spin-tensors to the case of superspace. We construct a representation of Dirac matrices in the form of operators of a generalized matrix algebra.
Symmetric Gini Covariance and Correlation
Sang, Yongli; Dang, Xin; Sang, Hailin
2016-01-01
Standard Gini covariance and Gini correlation play important roles in measuring the dependence of random variables with heavy tails. However, the asymmetry brings a substantial difficulty in interpretation. In this paper, we propose a symmetric Gini-type covariance and a symmetric Gini correlation ($\\rho_g$) based on the joint rank function. The proposed correlation $\\rho_g$ is more robust than the Pearson correlation but less robust than the Kendall's $\\tau$ correlation. We establish the rel...
Some exact solutions of the Dirac equation
International Nuclear Information System (INIS)
Exact analytic solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions. (author)
Option of three pseudo-Dirac neutrinos
Królikowski, W
2000-01-01
As an alternative for popular see-saw mechanism, the option of three pseudo% -Dirac neutrinos is discussed, where ${1/2}(m^{(L)} + m^{(R)}) \\ll m^{(D)}$ for their Majorana and Dirac masses. The actual neutrino mass matrix is assumed in the form of tensor product $ M^{(\
Dirac-Kahler Theory and Massless Fields
Pletyukhov, V A
2010-01-01
Three massless limits of the Dirac-Kahler theory are considered. It is shown that the Dirac-Kahler equation for massive particles can be represented as a result of the gauge-invariant mixture (topological interaction) of the above massless fields.
Quasi-exact Solvability of Dirac Equations
Ho, Choon-Lin
2007-01-01
We present a general procedure for determining quasi-exact solvability of the Dirac and the Pauli equation with an underlying $sl(2)$ symmetry. This procedure makes full use of the close connection between quasi-exactly solvable systems and supersymmetry. The Dirac-Pauli equation with spherical electric field is taken as an example to illustrate the procedure.
Katz, Mikhail G.; Tall, David
2012-01-01
The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.
Auspicious tatami mat arrangements
Erickson, Alejandro; Schurch, Mark; Woodcock, Jennifer
2011-01-01
An \\emph{auspicious tatami mat arrangement} is a tiling of a rectilinear region with two types of tiles, $1 \\times 2$ tiles (dimers) and $1 \\times 1$ tiles (monomers). The tiles must cover the region and satisfy the constraint that no four corners of the tiles meet; such tilings are called \\emph{tatami tilings}. The main focus of this paper is when the rectilinear region is a rectangle. We provide a structural characterization of rectangular tatami tilings and use it to prove that the tiling is completely determined by the tiles that are on its border. We prove that the number of tatami tilings of an $n \\times n$ square with $n$ monomers is $n2^{n-1}$. We also show that, for fixed-height, the generating function for the number of tatami tilings of a rectangle is a rational function, and outline an algorithm that produces the generating function.
Thermally actuated linkage arrangement
International Nuclear Information System (INIS)
A reusable thermally actuated linkage arrangement includes a first link member having a longitudinal bore therein adapted to receive at least a portion of a second link member therein, the first and second members being sized to effect an interference fit preventing relative movement there-between at a temperature below a predetermined temperature. The link members have different coefficients of thermal expansion so that when the linkage is selectively heated by heating element to a temperature above the predetermined temperature, relative longitudinal and/or rotational movement between the first and second link members is enabled. Two embodiments of a thermally activated linkage are disclosed which find particular application in actuators for a grapple head positioning arm in a nuclear reactor fuel handling mechanism to facilitate back-up safety retraction of the grapple head independently from the primary fuel handling mechanism drive system. (author)
Revisiting double Dirac delta potential
Ahmed, Zafar; Kumar, Sachin; Sharma, Mayank; Sharma, Vibhu
2016-07-01
We study a general double Dirac delta potential to show that this is the simplest yet still versatile solvable potential to introduce double wells, avoided crossings, resonances and perfect transmission (T = 1). Perfect transmission energies turn out to be the critical property of symmetric and anti-symmetric cases wherein these discrete energies are found to correspond to the eigenvalues of a Dirac delta potential placed symmetrically between two rigid walls. For well(s) or barrier(s), perfect transmission (or zero reflectivity, R(E)) at energy E=0 is non-intuitive. However, this has been found earlier and called the ‘threshold anomaly’. Here we show that it is a critical phenomenon and we can have 0≤slant R(0)\\lt 1 when the parameters of the double delta potential satisfy an interesting condition. We also invoke a zero-energy and zero curvature eigenstate (\\psi (x)={Ax}+B) of the delta well between two symmetric rigid walls for R(0)=0. We resolve that the resonant energies and the perfect transmission energies are different and they arise differently.
On supersymmetric Dirac delta interactions
Guilarte, J Mateos; Castaneda, J M Munoz
2014-01-01
In this paper we construct $\\mathcal{N}=2$ supersymmetric quantum mechanics over several configurations of Dirac delta potentials from one single delta to a Dirac "comb". We show in detail how the building of supersymmetry on potentials with delta interactions placed in two or more points on the real line requires the inclusion of quasi-square wells. We find an scenario of either unbroken supersymmetry with Witten index one or supersymmetry breaking when there is one "bosonic" and one "fermionic" ground state such that the Witten index is zero. We explain next the different structure of the scattering waves produced by three $\\delta/\\theta$ potentials with respect to the the eigenfunctions arising in the non-SUSY case. In particular, much more bound states paired by supersymmetry exist within the supersymmetric framework as compared with the non-SUSY problem. An infinite array of equally spaced $\\delta$-interactions of the same strength but alternatively attractive and repulsive are susceptible of being promo...
Nuclear decommissioning: Funding arrangements
International Nuclear Information System (INIS)
This statement describes the United Kingdom's approach to funding civil nuclear decommissioning activities and explain proposed changes to the current arrangements. The UK has nuclear operators both in the private and public sectors and the approach to decommissioning funding differs. British Energy (BE), which operates a fleet of AGR power stations and a PWR, is in the private sector. On privatization, a segregated fund was established to cover BE's future decommissioning costs. Money paid into the fund is invested and the accumulated assets used to meet future decommissioning and cleanup costs. The precise amount of money that will be required to cover decommissioning costs is not an exact science. That is why the performance of the segregated fund is reviewed at five yearly intervals, at which stage BE's annual contribution can be adjusted as appropriate. To ensure that the fund is managed effectively and investments are made wisely, the fund is managed by independent trustees jointly appointed by the Government and the company. So far, the fund is performing as expected and it is on target to cover BE's decommissioning costs. Operators in the public sector include British Nuclear Fuels Limited (BNFL) and the United Kingdom Atomic Energy Authority (UKAEA). BNFL operates the fleet of Magnox power stations, a number of which are in various stages of decommissioning. BNFL also operates Sellafield (reprocessing, MOX and other operations) and Springfields (fuel manufacture). UKAEA is responsible for decommissioning the UK's former research reactor sites at Dounreay, Windscale (Cumbria), Harwell and Winfrith (Dorset). Under current arrangements, taxpayers meet the cost of decommissioning and cleanup at UKAEA sites; taxpayers will also meet the costs associated with the decommissioning of Magnox power stations from 2008 onwards
Dirac Coupled Channel Analyses of the high-lying excited states at $^{22}$Ne(p,p$'$)$^{22}$Ne
Shim, Sugie
2015-01-01
Dirac phenomenological coupled channel analyses are performed using an optical potential model for the high-lying excited vibrational states at 800 MeV unpolarized proton inelastic scatterings from $^{22}$Ne nucleus. Lorentz-covariant scalar and time-like vector potentials are used as direct optical potentials and the first-order vibrational collective model is used for the transition optical potentials to describe the high-lying excited vibrational collective states. The complicated Dirac coupled channel equations are solved phenomenologically using a sequential iteration method by varying the optical potential and the deformation parameters. Relativistic Dirac coupled channel calculations are able to describe the high-lying excited states of the vibrational bands in $^{22}$Ne clearly better than the nonrelativistic coupled channel calculations. The channel-coupling effects of the multistep process for the excited states of the vibrational bands are investigated. The deformation parameters obtained from the ...
Shrinkage estimators for covariance matrices.
Daniels, M J; Kass, R E
2001-12-01
Estimation of covariance matrices in small samples has been studied by many authors. Standard estimators, like the unstructured maximum likelihood estimator (ML) or restricted maximum likelihood (REML) estimator, can be very unstable with the smallest estimated eigenvalues being too small and the largest too big. A standard approach to more stably estimating the matrix in small samples is to compute the ML or REML estimator under some simple structure that involves estimation of fewer parameters, such as compound symmetry or independence. However, these estimators will not be consistent unless the hypothesized structure is correct. If interest focuses on estimation of regression coefficients with correlated (or longitudinal) data, a sandwich estimator of the covariance matrix may be used to provide standard errors for the estimated coefficients that are robust in the sense that they remain consistent under misspecification of the covariance structure. With large matrices, however, the inefficiency of the sandwich estimator becomes worrisome. We consider here two general shrinkage approaches to estimating the covariance matrix and regression coefficients. The first involves shrinking the eigenvalues of the unstructured ML or REML estimator. The second involves shrinking an unstructured estimator toward a structured estimator. For both cases, the data determine the amount of shrinkage. These estimators are consistent and give consistent and asymptotically efficient estimates for regression coefficients. Simulations show the improved operating characteristics of the shrinkage estimators of the covariance matrix and the regression coefficients in finite samples. The final estimator chosen includes a combination of both shrinkage approaches, i.e., shrinking the eigenvalues and then shrinking toward structure. We illustrate our approach on a sleep EEG study that requires estimation of a 24 x 24 covariance matrix and for which inferences on mean parameters critically
Covariant approach of perturbations in Lovelock type brane gravity
Norma, Bagatella-Flores; Miguel, Cruz; Efrain, Rojas
2016-01-01
We develop a covariant scheme to describe the dynamics of small perturbations on Lovelock type branes probing a Minkowski spacetime. The higher-dimensional analogue of the Jacobi equation in this theory becomes a wave type equation for a scalar field $\\Phi$. Whithin this framework, we analyse the stability of spherically symmetric branes with a de Sitter geometry floating in a flat Minkowski spacetime where we find that the Jacobi equation specializes to a Klein-Gordon equation for a scalar field possessing a tachyonic mass. This fact shows that, to some extent, these type of branes share the symmetries of the usual Dirac-Nambu-Goto (DNG) action which is by no means coincidental because the DNG model is the simplest included in the Lovelock type brane gravity.
Chowdhury, Debashree; B. Basu
2013-01-01
We have studied the spin dependent force and the associated momentum space Berry curvature in an accelerating system. The results are derived by taking into consideration the non relativistic limit of a generally covariant Dirac equation under the presence of electromagnetic field where the methodology of Foldy-Wouthuysen transformation is applied to achieve the non relativistic limit. Spin currents appear due to the combined action of the external electric field, crystal field and the induce...
Covariant jump conditions in electromagnetism
International Nuclear Information System (INIS)
A generally covariant four-dimensional representation of Maxwell’s electrodynamics in a generic material medium can be achieved straightforwardly in the metric-free formulation of electromagnetism. In this setup, the electromagnetic phenomena are described by two tensor fields, which satisfy Maxwell’s equations. A generic tensorial constitutive relation between these fields is an independent ingredient of the theory. By use of different constitutive relations (local and non-local, linear and non-linear, etc.), a wide area of applications can be covered. In the current paper, we present the jump conditions for the fields and for the energy–momentum tensor on an arbitrarily moving surface between two media. From the differential and integral Maxwell equations, we derive the covariant boundary conditions, which are independent of any metric and connection. These conditions include the covariantly defined surface current and are applicable to an arbitrarily moving smooth curved boundary surface. As an application of the presented jump formulas, we derive a Lorentzian type metric as a condition for existence of the wave front in isotropic media. This result holds for ordinary materials as well as for metamaterials with negative material constants. - Highlights: ► Covariant metric-free jump conditions for the electromagnetic field are derived. ► Covariantly defined surface current is considered. ► Lorentzian type metric from existence of the wave front in isotropic media. ► The result holds for ordinary materials as well as for metamaterials.
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.)
On the structure of the energy-momentum and the spin currents in Dirac's electron theory
Hehl, F W; Mielke, E W; Obukhov, Yu N; Obukhov, Yu.N.
1997-01-01
We consider a classical Dirac field in flat Minkowski spacetime. We perform a Gordon decomposition of its canonical energy-momentum and spin currents, respectively. Thereby we find for each of these currents a convective and a polarization piece. The polarization pieces can be expressed as exterior covariant derivatives of the two-forms $\\check M_\\alpha$ and $M_{\\alpha\\beta}=-M_{\\beta\\alpha}$, respectively. In analogy to the magnetic moment in electrodynamics, we identify these two-forms as gravitational moments connected with the translation group and the Lorentz group, respectively. We point out the relation between the Gordon decomposition of the energy-momentum current and its Belinfante-Rosenfeld symmetrization. In the non-relativistic limit, the translational gravitational moment of the Dirac field is found to be proportional to the spin covector of the electron.
LHCbDirac: distributed computing in LHCb
International Nuclear Information System (INIS)
We present LHCbDirac, an extension of the DIRAC community Grid solution that handles 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 handling 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. Before putting in production a new release, a number of certification tests are run in a dedicated setup. This contribution highlights the versatility of the system, also presenting the experience with real data processing, data and resources management, monitoring for activities and resources.
LHCbDirac: distributed computing in LHCb
Stagni, F.; Charpentier, P.; Graciani, R.; Tsaregorodtsev, A.; Closier, J.; Mathe, Z.; Ubeda, M.; Zhelezov, A.; Lanciotti, E.; Romanovskiy, V.; Ciba, K. D.; Casajus, A.; Roiser, S.; Sapunov, M.; Remenska, D.; Bernardoff, V.; Santana, R.; Nandakumar, R.
2012-12-01
We present LHCbDirac, an extension of the DIRAC community Grid solution that handles 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 handling 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. Before putting in production a new release, a number of certification tests are run in a dedicated setup. This contribution highlights the versatility of the system, also presenting the experience with real data processing, data and resources management, monitoring for activities and resources.
Paul Dirac: the purest soul in physics
International Nuclear Information System (INIS)
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)
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.
Dirac's theorem for random graphs
Lee, Choongbum
2011-01-01
A classical theorem of Dirac from 1952 asserts that every graph on $n$ vertices with minimum degree at least $\\lceil n/2 \\rceil$ is Hamiltonian. In this paper we extend this result to random graphs. Motivated by the study of resilience of random graph properties we prove that if $p \\gg \\log n /n$, then a.a.s. every subgraph of $G(n,p)$ with minimum degree at least $(1/2+o(1))np$ is Hamiltonian. Our result improves on previously known bounds, and answers an open problem of Sudakov and Vu. Both, the range of edge probability $p$ and the value of the constant 1/2 are asymptotically best possible.
Covariant jump conditions in electromagnetism
Itin, Yakov
2014-01-01
A generally covariant four-dimensional representation of Maxwell's electrodynamics in a generic material medium can be achieved straightforwardly in the metric-free formulation of electromagnetism. In this setup, the electromagnetic phenomena described by two tensor fields, which satisfy Maxwell's equations. A generic tensorial constitutive relation between these fields is an independent ingredient of the theory. By use of different constitutive relations (local and non-local, linear and non-linear, etc.), a wide area of applications can be covered. In the current paper, we present the jump conditions for the fields and for the energy-momentum tensor on an arbitrarily moving surface between two media. From the differential and integral Maxwell equations, we derive the covariant boundary conditions, which are independent of any metric and connection. These conditions include the covariantly defined surface current and are applicable to an arbitrarily moving smooth curved boundary surface. As an application of ...
The Dirac equation and its solutions
International Nuclear Information System (INIS)
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.
Dirac's Equation in $R$-Minkowski Spacetime
Foughali, T
2016-01-01
We recently constructed the $R$-Poincar\\'e algebra from an appropriate deformed Poisson brackets which reproduce the Fock coordinate transformation. We showed then that the spacetime of this transformation is the de Sitter one. In this paper, we derive in the $R$-Minkowski spacetime the Dirac equation and show that this is none other than the Dirac equation in the de Sitter spacetime given by its conformally flat metric. Furthermore, we propose a new approach for solving Dirac's equation in the de Sitter spacetime using the Schr\\"{o}dinger picture.
Dirac's Equation in R-Minkowski Spacetime
Foughali, T.; Bouda, A.
2016-04-01
We recently constructed the R-Poincaré algebra from an appropriate deformed Poisson brackets which reproduce the Fock coordinate transformation. We showed then that the spacetime of this transformation is the de Sitter one. In this paper, we derive in the R-Minkowski spacetime the Dirac equation and show that this is none other than the Dirac equation in the de Sitter spacetime given by its conformally flat metric. Furthermore, we propose a new approach for solving Dirac's equation in the de Sitter spacetime using the Schrödinger picture.
On the local structure of Dirac manifolds
Dufour, Jean-Paul; Wade, Aissa
2004-01-01
We give a local normal form for Dirac structures. As a consequence, we show that the dimensions of the pre-symplectic leaves of a Dirac manifold have the same parity. We also show that, given a point $m$ of a Dirac manifold $M$, there is a well-defined transverse Poisson structure to the pre-symplectic leaf $P$ through $m$. Finally, we describe the neighborhood of a pre-symplectic leaf in terms of geometric data. This description agrees with that given by Vorobjev for the Poisson case
Helicity oscillations of Dirac and Majorana neutrinos
Dobrynina, Alexandra; Raffelt, Georg
2016-01-01
The helicity of a Dirac neutrino with mass $m$ evolves under the influence of a $B$-field because it has a magnetic dipole moment proportional to $m$. Moreover, it was recently shown that a polarized or anisotropic medium engenders the same effect for both Dirac and Majorana neutrinos. Because a $B$-field polarizes a background medium, it instigates helicity oscillations even for Majorana neutrinos unless the medium is symmetric between matter and antimatter. Motivated by these observations, we review the impact of a $B$-field and of an anisotropic or polarized medium on helicity oscillations for Dirac and Majorana neutrinos from the common perspective of in-medium dispersion.
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.
Quasi-Dirac neutrinos at the LHC
Anamiati, G; Nardi, E
2016-01-01
Lepton number violation is searched for at the LHC using same-sign leptons plus jets. The standard lore is that the ratio of same-sign lepton to opposite-sign lepton events, $R_{ll}$, is equal to $R_{ll}=1$ ($R_{ll}=0$) for Majorana (Dirac) neutrinos. We argue that for "quasi-Dirac" neutrinos, $R_{ll}$ can have any value between 0 and 1, the precise value being controlled by the mass splitting versus the width of the quasi-Dirac resonances. A measurement of $R_{ll}\
GLq(N)-covariant quantum algebras and covariant differential calculus
International Nuclear Information System (INIS)
GLq(N)-covariant quantum algebras with generators satisfying quadratic polynomial relations are considered. It is that, up to some innessential arbitrariness, there are only two kinds of such quantum algebras, namely, the algebras with q-deformed commutation and q-deformed anticommutation relations. 25 refs
Cosmic censorship conjecture revisited: covariantly
International Nuclear Information System (INIS)
In this paper we study the dynamics of the trapped region using a frame independent semi-tetrad covariant formalism for general locally rotationally symmetric (LRS) class II spacetimes. We covariantly prove some important geometrical results for the apparent horizon, and state the necessary and sufficient conditions for a singularity to be locally naked. These conditions bring out, for the first time in a quantitative and transparent manner, the importance of the Weyl curvature in deforming and delaying the trapped region during continual gravitational collapse, making the central singularity locally visible. (paper)
Cosmic Censorship Conjecture revisited: Covariantly
Hamid, Aymen I M; Maharaj, Sunil D
2014-01-01
In this paper we study the dynamics of the trapped region using a frame independent semi-tetrad covariant formalism for general Locally Rotationally Symmetric (LRS) class II spacetimes. We covariantly prove some important geometrical results for the apparent horizon, and state the necessary and sufficient conditions for a singularity to be locally naked. These conditions bring out, for the first time in a quantitative and transparent manner, the importance of the Weyl curvature in deforming and delaying the trapped region during continual gravitational collapse, making the central singularity locally visible.
k-Parabolic Subspace Arrangements
Severs, Christopher; White, Jacob
2009-01-01
Nous généralisons les arrangements k-égaux à tous les groupes de réflexions finis réels. Les arrangements ainsi obtenus sont dits k-paraboliques. Dans le cas où k = 2 nous retrouvons les arrangements de Coxeter qui sont bien connus. En 1971, Brieskorn démontra que le groupe fondamental associé au complément (complexe) de l'arrangement de Coxeter de type W est en fait isomorphe au groupe pure d'Artin de type W . En 1996, Khovanov donne une description algébrique du groupe fondamental du complé...
Fermi-Bose duality of the Dirac equation and extended real Clifford-Dirac algebra
Directory of Open Access Journals (Sweden)
I.Yu. Krivsky
2010-01-01
Full Text Available We have proved on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass that this equation may describe not only fermions of spin 1/2 but also bosons of spin 1. The new bosonic symmetries of the Dirac equation in both the Foldy-Wouthuysen and the Pauli-Dirac representations are found. Among these symmetries (together with the 32-dimensional pure matrix algebra of invariance the new, physically meaningful, spin 1 Poincare symmetry of equation under consideration is proved. In order to provide the corresponding proofs, a 64-dimensional extended real Clifford-Dirac algebra is put into consideration.
Quasi-classical derivation of the Dirac and one-particle Schroedinger equations
International Nuclear Information System (INIS)
The quasi-classical approach, in which particles are regarded as extended periodic excitations of a classical nonlinear field, is for the first time applied quantitatively in the quantum domain. It is shown that the twofold intrinsic 'spin' degree of freedom possessed by an electron can be interpreted in a purely classical way, and that the Lorentz covariant incorporation of this degree of freedom requires that the spacetime evolution of an electron excitation in a prescribed external field be given by the Dirac equation and hence, in the nonrelativistic limit, by the Pauli or Schroedinger one-particle equations. 17 refs
International Nuclear Information System (INIS)
A method for expressing spinor amplitudes M=vectorμ(p1sigma1)GAMMAsubMμ(psigma) in a formal covariant way and calculating them by trace calculations is described. By means of complex Lorentz transformations an expression for μ(psigma)vectorμ(p1sigma1) in terms of Dirac γ-matrices, four vectors and the complex Lorentz transformation coefficients is obtained. M can then be written as a trace of γ-matrices similar to the expression for Σsub(pol)matrixM2. The method is easily extended to cases when higher spin spinors and matrices are involved. (Auth.)
Covariation Neglect among Novice Investors
Hedesstrom, Ted Martin; Svedsater, Henrik; Garling, Tommy
2006-01-01
In 4 experiments, undergraduates made hypothetical investment choices. In Experiment 1, participants paid more attention to the volatility of individual assets than to the volatility of aggregated portfolios. The results of Experiment 2 show that most participants diversified even when this increased risk because of covariation between the returns…
Relativistic covariance of Ohm's law
Starke, R
2014-01-01
The derivation of relativistic generalizations of Ohm's law has been a long-term issue in theoretical physics with deep implications for the study of relativistic plasmas in astrophysics and cosmology. Here we propose an alternative route to this problem by introducing the most general Lorentz covariant first order response law, which is written in terms of the fundamental response tensor $\\chi^\\mu_{~\
Uncertainty covariances in robotics applications
International Nuclear Information System (INIS)
The application of uncertainty covariance matrices in the analysis of robot trajectory errors is explored. First, relevant statistical concepts are reviewed briefly. Then, a simple, hypothetical robot model is considered to illustrate methods for error propagation and performance test data evaluation. The importance of including error correlations is emphasized
Investigating Student Difficulties with Dirac Notation
Singh, Chandralekha
2015-01-01
Quantum mechanics is challenging even for advanced undergraduate and graduate students. Dirac notation is a convenient notation used extensively in quantum mechanics. We have been investigating the difficulties that the advanced undergraduate and graduate students have with Dirac notation. We administered written free response and multiple-choice questions to students and also conducted semi-structured individual interviews with 23 students using a think-aloud protocol to obtain a better understanding of the rationale behind their responses. We find that many students struggle with Dirac notation and they are not consistent in using this notation across various questions in a given test. In particular, whether they answer questions involving Dirac notation correctly or not is context dependent.
On the level order for Dirac operators
International Nuclear Information System (INIS)
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)
Duality between coordinates and Dirac field
Abdalla, Maria Christina B; Vancea, I V
2000-01-01
The duality between the Cartesian coordinates on the Minkowski space-time andthe Dirac field is investigated. Two distinct possibilities to define thisduality are shown to exist. In both cases, the equations satisfied byprepotentials are of second order.
SO(10) grand unified theory in generalized covariant derivative formalism
International Nuclear Information System (INIS)
The SO(10) grand unified theory is reformulated in a new field theory with a unified field strength for both the gauge and Higgs fields, and the fine-tuning problem and the condition for the symmetry breakings are investigated. The unified field strength for the gauge and Higgs fields, which takes values in the Dirac algebra, is defined by means of the commutator of the generalized covariant derivative for a multi-spinor field decreasing all families of quarks and leptons. The bosonic Lagrangian is constructed from a general sum of quadratic invariants of the field strength. Among the Yukawa coupling constants and other parameters related to the Higgs field self-couplings, there exist additional relations that are interpreted as initial conditions for renormalization equations. The grand unified symmetry is broken down to the low energy symmetry by the 210-, 45-, 126- and 10-dimensional Higgs fields. The Higgs potential turns out to have a discrete symmetry among Higgs fields. This symmetry makes it subtle and difficult to solve the fine-tuning problem, which required accurate adjustments of the parameters included in the generalized covariant derivative. It is shown that the 45-dimensional Higgs field plays an essential role to break the discrete symmetry and to solve the fine-tuning problem. (author)
Two Qubits in the Dirac Representation
Rajagopal, A K; Rendell, R. W.
2000-01-01
A general two qubit system expressed in terms of the complete set of unit and fifteen traceless, Hermitian Dirac matrices, is shown to exhibit novel features of this system. The well-known physical interpretations associated with the relativistic Dirac equation involving the symmetry operations of time-reversal T, charge conjugation C, parity P, and their products are reinterpreted here by examining their action on the basic Bell states. The transformation properties of the Bell basis states ...
The degeneracy of the free Dirac equation
International Nuclear Information System (INIS)
Parity-mixed solutions of the free Dirac equation with the same 4-momentum are considered. The first-order EM energy has an electric dipole moment term whose value depends on the mixing angle. Further implications of this degeneracy to perturbative calculations are discussed. It is argued that the properties of the Dirac equation with the Coulomb potential can be used to decide the mixing angle, which should be zero
Polyakov loop fluctuations in Dirac eigenmode expansion
Doi, Takahiro M.; Redlich, Krzysztof; Sasaki, Chihiro; Suganuma, Hideo
2015-01-01
We investigate correlations of the Polyakov loop fluctuations with eigenmodes of the lattice Dirac operator. Their analytic relations are derived on the temporally odd-number size lattice with the normal non-twisted periodic boundary condition for the link-variables. We find that the low-lying Dirac modes yield negligible contributions to the Polyakov loop fluctuations. This property is confirmed to be valid in confined and deconfined phase by numerical simulations in SU(3) quenched QCD. Thes...
Dirac particle spin in strong gravitational fields
Obukhov, Yu. N.; Silenko, A. J.; Teryaev, O. V.
2014-01-01
Dynamics of the Dirac particle spin in general strong gravitational fields is discussed. The Hermitian Dirac Hamiltonian is derived and transformed to the Foldy-Wouthuysen (FW) representation for an arbitrary metric. The quantum mechanical equations of spin motion are found. These equations agree with corresponding classical ones. The new restriction on the anomalous gravitomagnetic moment (AGM) by the reinterpretation of Lorentz invariance tests is obtained.
Dirac Neutrino Masses from Generalized Supersymmetry Breaking
Demir, Durmus A.; Everett, Lisa L.; Langacker, Paul
2007-01-01
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 nonana...
On the Dirac Monopole Mass Scale
Caruso, Francisco
2013-01-01
It is shown, by a semi-classical argument, that the Dirac charge quantization is still valid in the (classical) Born-Infeld electromagnetic theory. Then it is possible to calculate Dirac's monopole mass in the framework of this theory, which is not possible in Maxwell's theory. The existence of an upper limit for the field intensities in this theory plays an important role in this proof.
Data acquisition software for DIRAC experiment
International Nuclear Information System (INIS)
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
Pathways to Naturally Small Dirac Neutrino Masses
Ma, Ernest
2016-01-01
If neutrinos are truly Dirac fermions, the smallness of their masses may still be natural if certain symmetries exist beyond those of the standard model of quarks and leptons. We perform a systematic study of how this may occur at tree level and in one loop. We also propose a scotogenic version of the left-right gauge model with naturally small Dirac neutrino masses in one loop.
An algorithm for multiplication of Dirac numbers
Aleksandr Cariow; Galina Cariowa
2013-01-01
In this work a rationalized algorithm for Dirac numbers multiplication is presented. This algorithm has a low computational complexity feature and is well suited to parallelization of computations. The computation of two Dirac numbers product using the naïve method takes 256 real multiplications and 240 real additions, while the proposed algorithm can compute the same result in only 128 real multiplications and 160 real additions. During synthesis of the discussed algorithm we use the fact th...
Ultrarelativistic Decoupling Transformation for Generalized Dirac Equations
Noble, J. H.; Jentschura, U. D.
2015-01-01
The Foldy--Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schr\\"{o}dinger--Pauli theory. We here discuss the opposite, ultrarelativistic limit which requires the use of a fundamentally different expansion where the leading kinetic term in the Dirac equation is perturbed by the mass of the particle and other interaction (potential) terms, rather than vice ...
Split-Quaternions and the Dirac Equation
Antonuccio, Francesco
2014-01-01
We show that Dirac 4-spinors admit an entirely equivalent formulation in terms of 2-spinors defined over the split-quaternions. In this formalism, a Lorentz transformation is represented as a $2 \\times 2$ unitary matrix over the split-quaternions. The corresponding Dirac equation is then derived in terms of these 2-spinors. In this framework the $SO(3,2; {\\bf R})$ symmetry of the Lorentz invariant scalar $\\overline{\\psi}\\psi$ is manifest.
Quantum Dirac field without vacuum energy divergence
Wang, Ruo Peng
2001-01-01
A quantum Dirac field theory with no divergences of vacuum energy is presented. The vacuum energy divergence is eliminated by removing a extra degree of freedom of the Dirac fields. The conditions for removing the extra degree of freedom, expressed in the form of a conservation law and an orthogonality relation, define another spin 1/2 field with the same rest mass that is just the antifermion field. The anticommutation relations for fermion and antifermion fields are imposed by this conserva...
Pseudo-Dirac Scenario for Neutrino Oscillations
Kobayashi, Makoto; Lim, C. S.
2000-01-01
We argue how pseudo-Dirac scenario for neutrinos leads to rich neutrino oscillation phenomena, including oscillation inside each generation. The pseudo-Dirac scenario is generalized by incorporating generation mixings and formulae for the various neutrino oscillations are derived. As the application we compare the formulae with the corresponding data. We find that observed pattern of mixings, such as almost maximal mixing in the atmospheric neutrino oscillation, is naturally explained in the ...
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.
Phenomenology of Dirac Neutralino Dark Matter
Energy Technology Data Exchange (ETDEWEB)
Buckley, Matthew R.; Hooper, Dan; Kumar, Jason
2013-09-01
In supersymmetric models with an unbroken R-symmetry (rather than only R-parity), the neutralinos are Dirac fermions rather than Majorana. In this article, we discuss the phenomenology of neutralino dark matter in such models, including the calculation of the thermal relic abundance, and constraints and prospects for direct and indirect searches. Due to the large elastic scattering cross sections with nuclei predicted in R-symmetric models, we are forced to consider a neutralino that is predominantly bino, with very little higgsino mixing. We find a large region of parameter space in which bino-like Dirac neutralinos with masses between 10 and 380 GeV can annihilate through slepton exchange to provide a thermal relic abundance in agreement with the observed cosmological density, without relying on coannihilations or resonant annihilations. The signatures for the indirect detection of Dirac neutralinos are very different than predicted in the Majorana case, with annihilations proceeding dominately to $\\tau^+ \\tau^-$, $\\mu^+ \\mu^-$ and $e^+ e^-$ final states, without the standard chirality suppression. And unlike Majorana dark matter candidates, Dirac neutralinos experience spin-independent scattering with nuclei through vector couplings (via $Z$ and squark exchange), leading to potentially large rates at direct detection experiments. These and other characteristics make Dirac neutralinos potentially interesting within the context of recent direct and indirect detection anomalies. We also discuss the case in which the introduction of a small Majorana mass term breaks the $R$-symmetry, splitting the Dirac neutralino into a pair of nearly degenerate Majorana states.
Localized form of Fock terms in nuclear covariant density functional theory
Liang, Haozhao; Ring, Peter; Roca-Maza, Xavier; Meng, Jie
2012-01-01
In most of the successful versions of covariant density functional theory in nuclei, the Fock terms are not included explicitly, which leads to local functionals and forms the basis of their widespread applicability at present. However, it has serious consequences for the description of Gamow-Teller resonances (GTR) and spin-dipole resonances (SDR) which can only be cured by adding further phenomenological parameters. Relativistic Hartree-Fock models do not suffer from these problems. They can successfully describe the GTR and SDR as well as the isovector part of the Dirac effective mass without any additional parameters. However, they are non-local and require considerable numerical efforts. By the zero-range reduction and the Fierz transformation, a new method is proposed to take into account the Fock terms in local functionals, which retains the simplicity of conventional models and provides proper descriptions of the spin-isospin channels and the Dirac masses.
IAEA paper on institutional arrangements
International Nuclear Information System (INIS)
At its fifth series of meetings, Working Group 3 received a background paper prepared by the IAEA which had a threefold purpose: firstly, to provide an overview on institutional arrangements under consideration by the INFCE Working Groups; secondly, to explore potential relationships between the various institutional arrangements under consideration; and thirdly, to identify areas where further analysis might be desirable
Graphene wormholes: A condensed matter illustration of Dirac fermions in curved space
International Nuclear Information System (INIS)
We study the properties of graphene wormholes in which a short nanotube acts as a bridge between two graphene sheets, where the honeycomb carbon lattice is curved from the presence of 12 heptagonal defects. By taking the nanotube bridge with very small length compared to the radius, we develop an effective theory of Dirac fermions to account for the low-energy electronic properties of the wormholes in the continuum limit, where the frustration induced by the heptagonal defects is mimicked by a line of fictitious gauge flux attached to each of them. We find in particular that, when the effective gauge flux from the topological defects becomes maximal, the zero-energy modes of the Dirac equation can be arranged into two triplets, that can be thought as the counterpart of the two triplets of zero modes that arise in the dual instance of the continuum limit of large spherical fullerenes. We further investigate the graphene wormhole spectra by performing a numerical diagonalization of tight-binding Hamiltonians for very large lattices realizing the wormhole geometry. The correspondence between the number of localized electronic states observed in the numerical approach and the effective gauge flux predicted in the continuum limit shows that graphene wormholes can be consistently described by an effective theory of two Dirac fermion fields in the curved geometry of the wormhole, opening the possibility of using real samples of the carbon material as a playground to experiment with the interaction between the background curvature and the Dirac fields.
Hyperplane Arrangements and Diagonal Harmonics
Armstrong, Drew
2010-01-01
In 2003, Haglund's {\\sf bounce} statistic gave the first combinatorial interpretation of the $q,t$-Catalan numbers and the Hilbert series of diagonal harmonics. In this paper we propose a new combinatorial interpretation in terms of the affine Weyl group of type $A$. In particular, we define two statistics on affine permutations; one in terms of the Shi hyperplane arrangement, and one in terms of a new arrangement - which we call the Ish arrangement. We prove that our statistics are equivalent to the {\\sf area'} and {\\sf bounce} statistics of Haglund and Loehr. In this setting, we observe that {\\sf bounce} is naturally expressed as a statistic on the root lattice. We extend our statistics in two directions: to "extended" Shi arrangements and to the bounded chambers of these arrangements. This leads to a (conjectural) combinatorial interpretation for all integral powers of the Bergeron-Garsia nabla operator applied to the elementary symmetric functions.
Quasi-exact solvability of Dirac-Pauli equation and generalized Dirac oscillators
Ho, Choon-Lin; Roy, Pinaki
2003-01-01
We demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasi-exactly solvable systems. Electric field configurations permitting quasi-exact solvability of the system based on the $sl(2)$ symmetry are discussed separately in spherical, cylindrical, and Cartesian coordinates. Some exactly solvable field configurations are also exhibited.
Quasi-exact solvability of Dirac-Pauli equation and generalized Dirac oscillators
International Nuclear Information System (INIS)
In this paper we demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasi-exactly solvable systems. Electric field configurations permitting quasi-exact solvability of the system based on the sl(2) symmetry are discussed separately in the spherical, cylindrical, and Cartesian coordinates. Some exactly solvable field configurations are also exhibited
Glinka, Yuri D; Babakiray, Sercan; Johnson, Trent A; Lederman, David
2015-02-11
We report on a >100-fold enhancement of Raman responses from Bi2Se3 thin films if laser photon energy switches from 2.33 eV (532 nm) to 1.58 eV (785 nm), which is due to direct optical coupling to Dirac surface states (SS) at the resonance energy of ∼1.5 eV (a thickness-independent enhancement) and due to nonlinearly excited Dirac plasmon (a thickness-dependent enhancement). Owing to the direct optical coupling, we observed an in-plane phonon mode of hexagonally arranged Se-atoms associated with a continuous network of Dirac SS. This mode revealed a Fano lineshape for films interference between surface phonon and Dirac plasmon states. PMID:25614684
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.
Shrinkage Estimators for Covariance Matrices
Daniels, Michael J.; Kass, Robert E.
2001-01-01
Estimation of covariance matrices in small samples has been studied by many authors. Standard estimators, like the unstructured maximum likelihood estimator (ML) or restricted maximum likelihood (REML) estimator, can be very unstable with the smallest estimated eigenvalues being too small and the largest too big. A standard approach to more stably estimating the matrix in small samples is to compute the ML or REML estimator under some simple structure that involves estimation of fewer paramet...
Alexandrov, Sergei
2007-01-01
We generalize the covariant c-map found in hep-th/0701214 including perturbative quantum corrections. We also perform explicitly the superconformal quotient from the hyperkahler cone obtained by the quantum c-map to the quaternion-Kahler space, which is the moduli space of hypermultiplets. As a result, the perturbatively corrected metric on the moduli space is found in a simplified form comparing to the expression known in the literature.
The H-Covariant Strong Picard Groupoid
Jansen, Stefan; Waldmann, Stefan
2004-01-01
The notion of H-covariant strong Morita equivalence is introduced for *-algebras over C = R(i) with an ordered ring R which are equipped with a *-action of a Hopf *-algebra H. This defines a corresponding H-covariant strong Picard groupoid which encodes the entire Morita theory. Dropping the positivity conditions one obtains H-covariant *-Morita equivalence with its H-covariant *-Picard groupoid. We discuss various groupoid morphisms between the corresponding notions of the Picard groupoids. ...
Covariant Perturbations of Schwarzschild Black Holes
Clarkson, Chris A.; Barrett, Richard K.
2002-01-01
We present a new covariant and gauge-invariant perturbation formalism for dealing with spacetimes having spherical symmetry (or some preferred spatial direction) in the background, and apply it to the case of gravitational wave propagation in a Schwarzschild black hole spacetime. The 1+3 covariant approach is extended to a `1+1+2 covariant sheet' formalism by introducing a radial unit vector in addition to the timelike congruence, and decomposing all covariant quantities with respect to this....
Are Maxwell's equations Lorentz-covariant?
Redzic, D V
2016-01-01
The statement that Maxwell's electrodynamics in vacuum is already covariant under Lorentz transformations is commonplace in the literature. We analyse the actual meaning of that statement and demonstrate that Maxwell's equations are perfectly fit to be Lorentz-covariant; they become Lorentz-covariant if we construct to be so, by postulating certain transformation properties of field functions. In Aristotelian terms, the covariance is a plain potentiality, but not necessarily entelechy.
Covariant jump conditions in electromagnetism
Itin, Yakov
2012-02-01
A generally covariant four-dimensional representation of Maxwell's electrodynamics in a generic material medium can be achieved straightforwardly in the metric-free formulation of electromagnetism. In this setup, the electromagnetic phenomena are described by two tensor fields, which satisfy Maxwell's equations. A generic tensorial constitutive relation between these fields is an independent ingredient of the theory. By use of different constitutive relations (local and non-local, linear and non-linear, etc.), a wide area of applications can be covered. In the current paper, we present the jump conditions for the fields and for the energy-momentum tensor on an arbitrarily moving surface between two media. From the differential and integral Maxwell equations, we derive the covariant boundary conditions, which are independent of any metric and connection. These conditions include the covariantly defined surface current and are applicable to an arbitrarily moving smooth curved boundary surface. As an application of the presented jump formulas, we derive a Lorentzian type metric as a condition for existence of the wave front in isotropic media. This result holds for ordinary materials as well as for metamaterials with negative material constants.
The Bragg regime of the two-particle Kapitza-Dirac effect
Sancho, Pedro
2011-07-01
We analyse the Bragg regime of the two-particle Kapitza-Dirac arrangement, completing the basic theory of this effect. We provide a detailed evaluation of the detection probabilities for multi-mode states, showing that a complete description must include the interaction time in addition to the usual dimensionless parameter w. The arrangement can be used as a massive two-particle beam splitter. In this respect, we present a comparison with Hong-Ou-Mandel-type experiments in quantum optics. The analysis reveals the presence of dips for massive bosons and a differentiated behaviour of distinguishable and identical particles in an unexplored scenario. We suggest that the arrangement can provide the basis for symmetrization verification schemes.
The Bragg regime of the two-particle Kapitza-Dirac effect
Sancho, Pedro
2011-01-01
We analyze the Bragg regime of the two-particle Kapitza-Dirac arrangement, completing the basic theory of this effect. We provide a detailed evaluation of the detection probabilities for multi-mode states, showing that a complete description must include the interaction time in addition to the usual dimensionless parameter w. The arrangement can be used as a massive two-particle beam splitter. In this respect, we present a comparison with Hong-Ou-Mandel-type experiments in quantum optics. The analysis reveals the presence of dips for massive bosons and a differentiated behavior of distinguishable and identical particles in an unexplored scenario. We suggest that the arrangement can provide the basis for symmetrization verification schemes.
The Bragg regime of the two-particle Kapitza-Dirac effect
Energy Technology Data Exchange (ETDEWEB)
Sancho, Pedro, E-mail: psanchos@aemet.es [Centro de Laseres Pulsados, CLPU, E-37008 Salamanca (Spain)
2011-07-28
We analyse the Bragg regime of the two-particle Kapitza-Dirac arrangement, completing the basic theory of this effect. We provide a detailed evaluation of the detection probabilities for multi-mode states, showing that a complete description must include the interaction time in addition to the usual dimensionless parameter w. The arrangement can be used as a massive two-particle beam splitter. In this respect, we present a comparison with Hong-Ou-Mandel-type experiments in quantum optics. The analysis reveals the presence of dips for massive bosons and a differentiated behaviour of distinguishable and identical particles in an unexplored scenario. We suggest that the arrangement can provide the basis for symmetrization verification schemes.
Covariant Quantization of D-branes
Kallosh, Renata
1997-01-01
We have found that kappa-symmetry allows a covariant quantization provided the ground state of the theory is strictly massive. For D-p-branes a Hamiltonian analysis is performed to explain the existence of a manifestly supersymmetric and Lorentz covariant description of the BPS states of the theory. The covariant quantization of the D-0-brane is presented as an example.
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
Quaternions, Lorentz group and the Dirac theory
International Nuclear Information System (INIS)
It is shown that a subgroup of SL(2,H), denoted Spin (2,H) in this paper, which is defined by two conditions in addition to unit quaternionic determinant, is locally isomorphic to the restricted Lorentz group, L+↑. On the basis of the Dirac theory using the spinor group Spin (2,H), in which the charge conjugation transformation becomes linear in the quaternionic Dirac spinor, it is shown that the Hermeticity requirement of the Dirac Lagrangian, together with the persistent presence of the Pauli-Guersey SU(2) group, requires an additional imaginary unit (taken to be the ordinary one, i) that commutes with Hamilton's units, in the theory. A second quantization is performed with this i incorporated into the theory, and we recover the conventional Dirac theory with an automatic anti-symmetrization' of the field operators. It is also pointed out that we are naturally led to the scheme of complex quaternions, Hc, in which a space-time point is represented by a Hermitian quaternion, and that the isomorphism SL(1,Hc)/Z2 ≅ L+↑ is a direct consequence of the fact Spin (2,H)/Z2 ≅ L+↑. Using SL(1,Hc) ≅ SL(2,C), we make explicit the Weyl spinor indices of the spinor-quaternion, which is the Dirac spinor defined over Hc. (author)
International Nuclear Information System (INIS)
Within the standard electroweak theory ''wrong-helicity'' neutrinos are produced in a nascent neutron star by ''spin-flip'' processes (at a rate proportional to mν2), freely escape, and can lead to an excessively rapid cooling of the newly born neutron star. Previous work, based upon the neutrino-nucleon spin-flip scattering process alone, has shown that the observed cooling of the neutron star associated with SN 1987A excludes a Dirac-neutrino mass greater than ∼20 keV for either νe, νμ, or ντ. We reexamine the emission of ''wrong-helicity'' Dirac neutrinos from SN 1987A and conclude that due to neutrino degeneracy and additional emission processes (N+N→N+N+ν bar ν, π-+p→n+ν bar ν) the effect of a Dirac neutrino on the cooling of SN 1987A has been IunderestimatedP. While a precise Dirac-mass limit awaits the incorporation of our new rates into detailed numerical cooling models, we believe that the limit that follows from the cooling of SN 1987A is better, probably much better, than 10 keV. In particular, we believe that SN 1987A definitely excludes a 17-keV (purely) Dirac-mass neutrino that mixes with the electron neutrino at the 1% level
Gravitationally Coupled Dirac Equation for Antimatter
Jentschura, U D
2013-01-01
The coupling of antimatter to gravity is of general interest because of conceivable cosmological consequences ("surprises") related to dark energy and the cosmological constant. Here, we revisit the derivation of the gravitationally coupled Dirac equation and find that the prefactor of a result given previously in [D.R. Brill and J.A. Wheeler, Rev. Mod. Phys., vol. 29, p. 465 (1957)] for the affine connection matrix is in need of a correction. We also discuss the conversion the curved-space Dirac equation from East-Coast to West-Coast conventions, in order to bring the gravitationally coupled Dirac equation to a form where it can easily be unified with the electromagnetic coupling as it is commonly used in modern particle physics calculations. The Dirac equation describes anti-particles as negative-energy states. We find a symmetry of the gravitationally coupled Dirac equation, which connects particle and antiparticle solutions for a general space-time metric of the Schwarzschild type and implies that particl...
Determinants of flexible work arrangements
Sarbu, Miruna
2014-01-01
Flexible work arrangements such as allowing employees to work at home are used in firms, especially since information and communication technologies have become so widespread. Using individual-level data from 10,884 German employees, this paper analyses the determinants of working at home as a form of flexible work arrangements. The analysis is based on descriptive analyses and a discrete choice model using a probit estimation approach. The results reveal that men have a higher...
Covariance Evaluation Methodology for Neutron Cross Sections
Energy Technology Data Exchange (ETDEWEB)
Herman,M.; Arcilla, R.; Mattoon, C.M.; Mughabghab, S.F.; Oblozinsky, P.; Pigni, M.; Pritychenko, b.; Songzoni, A.A.
2008-09-01
We present the NNDC-BNL methodology for estimating neutron cross section covariances in thermal, resolved resonance, unresolved resonance and fast neutron regions. The three key elements of the methodology are Atlas of Neutron Resonances, nuclear reaction code EMPIRE, and the Bayesian code implementing Kalman filter concept. The covariance data processing, visualization and distribution capabilities are integral components of the NNDC methodology. We illustrate its application on examples including relatively detailed evaluation of covariances for two individual nuclei and massive production of simple covariance estimates for 307 materials. Certain peculiarities regarding evaluation of covariances for resolved resonances and the consistency between resonance parameter uncertainties and thermal cross section uncertainties are also discussed.
Dirac eigenvalues and eigenvectors at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Goeckeler, M.; Hehl, H.; Rakow, P.E.L.; Schaefer, A.; Soeldner, W.; Wettig, T
2001-03-01
We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local correlations. In the chirally symmetric phase, the local correlations in the bulk of the spectrum are still described by random matrix theory, and we investigate the dependence of the bulk Thouless energy on the simulation parameters. At and above the critical point, the properties of the low-lying Dirac eigenvalues depend on the Z{sub 3}-phase of the Polyakov loop. In the real phase, they are no longer described by chiral random matrix theory. We also investigate the localization properties of the Dirac eigenvectors in the different Z{sub 3}-phases.
Dirac eigenvalues and eigenvectors at finite temperature
Göckeler, M; Rakow, P E L; Schäfer, A; Söldner, W; Wettig, T
2001-01-01
We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local correlations. In the chirally symmetric phase, the local correlations in the bulk of the spectrum are still described by random matrix theory, and we investigate the dependence of the bulk Thouless energy on the simulation parameters. At and above the critical point, the properties of the low-lying Dirac eigenvalues depend on the $Z_3$-phase of the Polyakov loop. In the real phase, they are no longer described by chiral random matrix theory. We also investigate the localization properties of the Dirac eigenvectors in the different $Z_3$-phases.
Student Difficulties with the Dirac Delta Function
Wilcox, Bethany R
2014-01-01
The Dirac delta function is a standard mathematical tool used in multiple topical areas in the undergraduate physics curriculum. While Dirac delta functions are usually introduced in order to simplify a problem mathematically, students often struggle to manipulate and interpret them. To better understand student difficulties with the delta function at the upper-division level, we examined responses to traditional exam questions 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 physics. Here, we focus on student difficulties using the delta function to express charge distributions in the context of junior-level electrostatics. Challenges included: invoking the delta function spontaneously, constructing two- and three-dimensional delta functions, integrating novel delta function expressions, and recognizing that the delta function can have units.
Dirac zero modes in hyperdiamond model
International Nuclear Information System (INIS)
Using the SU(5) symmetry of the 4D hyperdiamond and results on the study of 4D graphene given in Drissi et al.[Phys. Rev. D 84, 014504 (2011)], we engineer a class of 4D lattice QCD fermions whose Dirac operators have two zero modes. We show that generally the zero modes of the Dirac operator in hyperdiamond fermions are captured by a tensor Ωμl with 4x5 complex components linking the Euclidean SO(4) vector μ; and the 5-dimensional representation of SU(5). The Borici-Creutz (BC) and the Karsten-Wilzeck (KW) models as well as their Dirac zero modes are rederived as particular realizations of Ωμl. Other features are also given.
The supersymmetric Dirac operator on noncommutative geometry
International Nuclear Information System (INIS)
In order to incorporate supersymmetry, we extend naturally the spectral triple which defines noncommutative geometry and obtain a supersymmetric Dirac operator DM which acts on a Minkowskian manifold. Inversely, we can also construct a projection which reduces DM to the Dirac operator of the original spectral triple. We investigate properties of DM, some of which are inherited from the original Dirac operator. Z/2 grading and real structure are also supersymmetrically extended. We introduce a supersymmetric bilinear form and the form with DM provides the kinetic terms of chiral and antichiral supermultiplets which represent the wave functions of matter particles and their superpartners. Fluctuations of DM will be expected to produce vector supermultiplets with gauge degrees of freedom and will then lead to Super Yang–Mills theory
Flavour models with Dirac and fake gluinos
International Nuclear Information System (INIS)
In the context of supersymmetric models where the gauginos may have both Majorana and Dirac masses we investigate the general constraints from flavour-changing processes on the scalar mass matrices. One finds that the chirality-flip suppression of flavour-changing effects usually invoked in the pure Dirac case holds in the mass insertion approximation but not in the general case, and fails in particular for inverted hierarchy models. We quantify the constraints in several flavour models which correlate fermion and scalar superpartner masses. We also discuss the limit of very large Majorana gaugino masses compared to the chiral adjoint and Dirac masses, where the remaining light eigenstate is the “fake” gaugino, including the consequences of suppressed couplings to quarks beyond flavour constraints
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 ...
Analytic Representation of the Dirac Equation
Gill, T L; Zachary, W W
2006-01-01
In this paper we construct an analytical separation (diagonalization) of the full (minimal coupling) Dirac equation into particle and antiparticle components. The diagonalization is analytic in that it is achieved without transforming the wave functions, as is done by the Foldy-Wouthuysen method, and reveals the nonlocal time behavior of the particle-antiparticle relationship. We then show explicitly that the Pauli equation is not completely valid for the study of the Dirac hydrogen atom problem in s-states (hyperfine splitting). We conclude that there are some open mathematical problems with any attempt to explicitly show that the Dirac equation is insufficient to explain the full hydrogen spectrum. If the perturbation method can be justified, our analysis suggests that the use of cutoffs in QED is already justified by the eigenvalue analysis that supports it. Using a new method, we are able to effect separation of variables for full coupling, solve the radial equation and provide graphs of the probability d...
Supersymmetry in 6d Dirac Action
Fujimoto, Yukihiro; Nishiwaki, Kenji; Sakamoto, Makoto; Tatsumi, Kentaro
2016-01-01
We investigate a 6d Dirac fermion on a rectangle. It is found that the 4d spectrum is governed by $N = 2$ supersymmetric quantum mechanics. Then we demonstrate that the supersymmetry is very useful to classify all allowed boundary conditions and to expand the 6d Dirac field in Kaluza-Klein modes. A striking feature of the model is that even though the 6d Dirac fermion has non-vanishing bulk mass, the 4d mass spectrum can contain degenerate massless chiral fermions, which may provide a hint to solve the generation problem of the quarks and leptons. It is pointed out that zero energy solutions are not affected by the presence of the boundaries, while the boundary conditions work well for determining the positive energy solutions.
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...
Higher Dirac cohomology of modules with generalized infinitesimal character
Pandžić, Pavle; Somberg, Petr
2013-01-01
We modify the definition of Dirac cohomology in such a way that the standard properties of the usual Dirac cohomology, valid for modules with infinitesimal character, become valid also for modules with only generalized infinitesimal character.
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...
On Spin Structures and Dirac Operators on the Noncommutative Torus
Paschke, Mario; Sitarz, Andrzej
2006-01-01
We find and classify possible equivariant spin structures with Dirac operators on the noncommutative torus, proving that similarly as in the classical case the spectrum of the Dirac operator depends on the spin structure.
Asymptotic formula for eigenvalues of one dimensional Dirac system
Ulusoy, Ismail; Penahlı, Etibar
2016-06-01
In this paper, we study the spectral problem for one dimensional Dirac system with Dirichlet boundary conditions. By using Counting lemma, we give an asymptotic formulas of eigenvalues of Dirac system.
Time-dependent constrained Hamiltonian systems and Dirac brackets
International Nuclear Information System (INIS)
In this paper the canonical Dirac formalism for time-dependent constrained Hamiltonian systems is globalized. A time-dependent Dirac bracket which reduces to the usual one for time-independent systems is introduced. (author)
A five-dimensional form of the Dirac equation
International Nuclear Information System (INIS)
A Dirac equation in a covariant form with respect to proper orthochronous rotations in (4+1)-dimensional pseudo-orthogonal space, i.e. Minkowski space extended by one real dimension is introduced. It contains a five-vector potential with a non-electromagnetic fifth component. The invariance of this equation under the CPT transformation is conditioned by the assumption that the real fifth coordinate changes its sign under charge conjugation, and that it simultaneously changes its sign either under time reversal or under space inversion. The energy levels of an electron under the simultaneous action of Coulomb and central gravitational fields are determined. To this end, (1) new eigenspinors of the total angular momentum operator are derived, with non-zero entries in the first and fourth or in the second and third row of the column matrix and (2) a scalar function is constructed from doubly-periodic Jacobian elliptic functions which, in the limit of the vanishing modulus of the elliptic functions, replaces the function exp(iωt) in the stationary-state solutions. The iterated five-dimensional equation contains the ten components of the antisymmetric field tensor. It also contains a term determining the potential energy operator of electron spin density in a non-electromagnetic field. The Pauli equation is derived from the five-dimensional equation, with the transformational characteristics of the original equation. It contains a spin-orbit coupling term depending on the non-electromagnetic potential. (author)
A five-dimensional form of the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Kocinski, J. [Institute of Physics, Warsaw University of Technology, Warsaw (Poland)]. E-mail: kocinsk@if.pw.edu.pl
1999-06-11
A Dirac equation in a covariant form with respect to proper orthochronous rotations in (4+1)-dimensional pseudo-orthogonal space, i.e. Minkowski space extended by one real dimension is introduced. It contains a five-vector potential with a non-electromagnetic fifth component. The invariance of this equation under the CPT transformation is conditioned by the assumption that the real fifth coordinate changes its sign under charge conjugation, and that it simultaneously changes its sign either under time reversal or under space inversion. The energy levels of an electron under the simultaneous action of Coulomb and central gravitational fields are determined. To this end, (1) new eigenspinors of the total angular momentum operator are derived, with non-zero entries in the first and fourth or in the second and third row of the column matrix and (2) a scalar function is constructed from doubly-periodic Jacobian elliptic functions which, in the limit of the vanishing modulus of the elliptic functions, replaces the function exp(i{omega}t) in the stationary-state solutions. The iterated five-dimensional equation contains the ten components of the antisymmetric field tensor. It also contains a term determining the potential energy operator of electron spin density in a non-electromagnetic field. The Pauli equation is derived from the five-dimensional equation, with the transformational characteristics of the original equation. It contains a spin-orbit coupling term depending on the non-electromagnetic potential. (author)
Cloud flexibility using DIRAC interware
International Nuclear Information System (INIS)
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
Fermi-Bose duality of the Dirac equation and extended real Clifford-Dirac algebra
I.Yu. Krivsky; Simulik, V. M.
2010-01-01
We have proved on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass that this equation may describe not only fermions of spin 1/2 but also bosons of spin 1. The new bosonic symmetries of the Dirac equation in both the Foldy-Wouthuysen and the Pauli-Dirac representations are found. Among these symmetries (together with the 32-dimensional pure matrix algebra of invariance) the new, physically meaningful, spin 1 Poincare symmetry of equation under consideration ...
Polyakov loop fluctuations in Dirac eigenmode expansion
Doi, Takahiro M; Sasaki, Chihiro; Suganuma, Hideo
2015-01-01
We investigate correlations of the Polyakov loop fluctuations with eigenmodes of the lattice Dirac operator. Their analytic relations are derived on the temporally odd-number size lattice with the normal non-twisted periodic boundary condition for the link-variables. We find that the low-lying Dirac modes yield negligible contributions to the Polyakov loop fluctuations. This property is confirmed to be valid in confined and deconfined phase by numerical simulations in quenched QCD. These results indicate that there is no direct, one-to-one correspondence between confinement and chiral symmetry breaking in QCD in the context of different properties of the Polyakov loop fluctuation ratios.
D-Instanton Generated Dirac Neutrino Masses
Cvetic, Mirjam; Langacker, Paul
2008-01-01
We present a stringy mechanism to generate Dirac neutrino masses by D-instantons in an experimentally relevant mass scale without fine-tuning. Within Type IIA string theory with intersecting D6-branes, we spell out specific conditions for the emergence of such couplings and provide a class of supersymmetric local SU(5) Grand Unified models, based on the Z_2 x Z'_2 orientifold compactification, where perturbatively absent Dirac neutrino masses can be generated by D2-brane instantons in the exp...
D-instanton generated Dirac neutrino masses
International Nuclear Information System (INIS)
We present a stringy mechanism to generate Dirac neutrino masses by D-instantons in an experimentally relevant mass scale without fine-tuning. Within type IIA string theory with intersecting D6-branes, we spell out specific conditions for the emergence of such couplings and provide a class of supersymmetric local SU(5) grand unified models, based on the Z2xZ2' orientifold compactification, where perturbatively absent Dirac neutrino masses can be generated by D2-brane instantons in the experimentally observed mass regime, while Majorana masses remain absent, thus providing an intriguing mechanism for the origin of small neutrino masses due to nonperturbative stringy effects.
Dirac Neutrino Masses from Generalized Supersymmetry Breaking
International Nuclear Information System (INIS)
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 superpotential neutrino Yukawa terms are forbidden by the gauge symmetry [such as a U(1)'], sub-eV scale effective Dirac mass terms can arise at tree level from hard supersymmetry breaking Yukawa couplings, or at one loop due to nonanalytic soft supersymmetry breaking trilinear scalar couplings. The radiative neutrino magnetic and electric dipole moments vanish at one-loop order
On singular lagrangians and Dirac's method
J.U. Cisneros-Parra
2012-01-01
Se presentan algunos lagrangianos singulares del ámbito de la mecánica clásica de partículas, y se les aplica el método de Dirac para construir las ecuaciones canónicas. Se halla la razón de la singularidad, y, con ello, se obtienen las ecuaciones de Hamilton por el camino acostumbrado, esto es, sin necesidad del método de Dirac. Se presentan también casos conocidos de lagrangianos singulares en la relatividad especial y sus alternativas no singulares.
PERSAMAAN MEDAN DIRAC DALAM PENGARUH MEDAN MAGNETIK YANG SERAGAM
Directory of Open Access Journals (Sweden)
Andrias Widiantoro, Erika Rani
2012-03-01
Full Text Available Telah dilakukan perlakuan khusus terhadap persamaan gerak partikel elementer yaitu Persamaan Dirac dengan dipengaruhi oleh medan magnet eksternal yang seragam untuk mendapat solusi Persamaan Dirac dalam pengaruh medan magnetic. Penambahan pengaruh potensial magnetik terhadap momentum dan energi total suatu partikel bermuatan dalam kajian teoritis terhadap persamaan gerak yaitu persamaan Dirac telah memberikan solusi persamaan medan Dirac yang baru, dan kuantisasi kedua yang terdapat konstanta tambahan serta propagasi fermioniknya terdapat suku pengali baru.
Dirac equations for generalised Yang-Mills systems
International Nuclear Information System (INIS)
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.)
Dirac equations for generalised Yang-Mills systems
International Nuclear Information System (INIS)
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.)
Generalized Dirac and Klein-Gordon equations for spinor wavefunctions
Huegele, R.; Musielak, Z. E.; Fry, J. L.
2013-01-01
A novel method is developed to derive the original Dirac equation and demonstrate that it is the only Poincare invariant dynamical equation for 4-component spinor wavefunctions. New Poincare invariant generalized Dirac and Klein-Gordon equations are also derived. In the non-relativistic limit the generalized Dirac equation gives the generalized Levy-Leblond equation and the generalized Pauli-Schrodinger equation. The main difference between the original and generalized Dirac equations is that...
Maxwell and Dirac theories as an already unified theory
Vaz, Jr., Jayme; Rodrigues, Jr., Waldyr A.
1995-01-01
In this paper we formulate Maxwell and Dirac theories as an already unified theory (in the sense of Misner and Wheeler). We introduce Dirac spinors as "Dirac square root" of the Faraday bivector, and use this in order to find a spinorial representation of Maxwell equations. Then we show that under certain circunstances this spinor equation reduces to an equation formally identical to Dirac equation. Finally we discuss certain conditions under which this equation can be really interpreted as D...
Dirac cohomology for the degenerate affine Hecke Clifford algebra
Chan, Kei Yuen
2013-01-01
We define an analogue of the Dirac operator for the degenerate affine Hecke-Clifford algebra. A main result is to relate the central characters of the degenerate affine Hecke-Clifford algebra with the central characters of the Sergeev algebra via Dirac cohomology. The action of the Dirac operator on certain modules is also computed. Results in this paper could be viewed as a projective version of the Dirac cohomology of the degenerate affine Hecke algebra.
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 th
Arranged marriages annulled by law.
Zhu, H
1996-06-01
The arranged marriages of 210 young people in Yongle Town in Zunyi County of Guizhou Province were dissolved in 1995. The proportion of child betrothals, which generally happens among close relatives, is as high as 85% in the town. Some engagements, known as fetus betrothals or belt betrothals, are arranged before the children are born or while they are still infants strapped (belted) to their mothers. Dissemination of information from the Constitution, the Marriage Law, and the Regulations on the Registration of Marriage concerning marriage, healthier births, and good upbringing of children, and other information on reproductive health, has shown young people that they have the freedom to love and marry of their own free will, that their marriage is protected by law, and that consanguineous marriage is harmful to the health of future generations. Some convinced their parents that their arranged marriages should be annulled. PMID:12291696
Transitional arrangements for ITER started
International Nuclear Information System (INIS)
Negotiations by the ITER Parties on the Agreement on the Establishment of the International Fusion Energy Organization for the Joint Implementation of the ITER Project (ITER Implementation Agreement, or simply 'the Agreement') and on the site selection for construction of the ITER machine are making good progress. Therefore, the ITER Parties decided that subsequent to the ITER Co-ordinated Technical Activities (CTA), the Transitional Arrangements for ITER (ITA or 'the Arrangements') will start on 1 January 2003, conducted under the auspices of the IAEA, and will terminate upon the entry into force of the Agreement, or at such earlier date as the Participants may decide. The Parties to the ITER Engineering Design Activities and the participants in the Negotiations on the ITER Joint Implementation wishing to co-operate in the ITER Transitional Arrangements will be the ITA Participants ('the Participants'). All four current ITER Parties, namely Canada, the European Union, Japan, and the Russian Federation confirmed, before the end of 2002, in their letters to the IAEA Director General their intention to participate in the ITA. The Arrangements are also open to new Participants acceding the Negotiations. The purpose of the ITA is to prepare for an efficient start of the Agreement, if and when so decided, and to maintain the integrity of the ITER Project. The overall direction of the Arrangements, as well as the supervision of their implementation will be exercised by the ITER Preparatory Committee ('the Committee'). It will be composed of two members from each Participant to the Arrangements. In exercising its functions, the Committee shall work for a smooth transition towards the organization and structure for ITER construction being developed in the frame of the ITER Negotiations. The first meeting of the Committee is scheduled for St. Petersburg, RF, on 17 February 2003
Lu, Wei; Liu, Xuefeng; Lu, Hong; Li, Caizhen; Lai, Jiawei; Zhao, Chuan; Tian, Ye; Liao, Zhimin; Jia, Shuang; Sun, Dong
2016-01-01
Three dimensional (3D) Dirac semimetal exhibiting ultrahigh mobility has recently attracted enormous research interests as 3D analogues of graphene. From the prospects of future application toward electronic/optoelectronic devices with extreme performance, it is crucial to understand the relaxation dynamics of photo-excited carriers and their coupling with lattice. In this work, we report ultrafast transient reflection measurements of photo-excited carrier dynamics in cadmium arsenide (Cd3As2), which is among the most stable Dirac semimetals that have been confirmed experimentally. With low energy probe photon of 0.3 eV, photo-excited Dirac Fermions dynamics closing to Dirac point are probed. Through transient reflection measurements on bulk and nanoplate samples that have different doping intensities, and systematic probe wavelength, pump power and lattice temperature dependent measurements, the dynamical evolution of carrier distributions can be retrieved qualitatively using a two-temperature model. The pho...
Hyperplane Arrangements and Diagonal Harmonics
Armstrong, Drew
2011-01-01
En 2003, la statistique bounce de Haglund a donné la première interprétation combinatoire de la somme des nombres q,t-Catalan et de la série de Hilbert des harmoniques diagonaux. Dans cet article nous proposons une nouvelle interprétation combinatoire à partir du groupe de Weyl affine de type A. En particulier, nous définissons deux statistiques sur les permutations affines; l'une à partir de l'arrangement d'hyperplans Shi, et l'autre à partir d'un nouvel arrangement — que nous appelons l'arr...
Patient positioning and supporting arrangement
International Nuclear Information System (INIS)
This patent specification describes an E.M.I. claim relating to a patient positioning and support arrangement for a computerised axial tomography system, the arrangement comprising a curved platter upon which the patient can be disposed, a table having a curved groove to accommodate the platter, and means for driving the platter slidably along the groove; the platter being formed of a substantially rigid platform shaped to conform to the groove, and a shroud, secured to the platter and disposed between the platter and the surface of the groove, so as to permit the platter to slide smoothly. (U.K.)
International Nuclear Information System (INIS)
A 64-dimensional extended real Clifford-Dirac algebra is introduced. On its basis, new pure matrix symmetries of the Dirac equation in the Foldy-Wouthuysen representation was found. Finally, spin 1 Poincare symmetries both for the Foldy-Wouthuysen and standard Dirac equations with nonzero mass are found.
Supersymmetric Dirac particles in external fields
International Nuclear Information System (INIS)
A classical Lagrangian is proposed for a relativistic particle with spin. It is supersymmetric under transformations between position and spin variables. The theory can be quantized and becomes identical with conventional Dirac theory. This correspondence continues to be valid when the particle interacts with external electromagnetic or gravitational fields as long as its coupling to these fields conserves the supersymmetry. (Auth.)
Distance preconditioning for lattice Dirac operators
de Divitiis, G M; Tantalo, N
2010-01-01
We propose a preconditioning of the Dirac operator based on the factorisation of a predefined function related to the decay of the propagator with the distance. We show that it can improve the accuracy of correlators involving heavy quarks at large distances and accelerate the computation of light quark propagators.
Path Integral for the Dirac Equation
Polonyi, Janos
1998-01-01
A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the spin and the chirality flips.
An infinite algebra of quantum Dirac brackets
International Nuclear Information System (INIS)
A new algebraic approach to the theory with second-class constraints is proposed. The operator equations that generate automatically the infinite algebra of quantum Dirac brackets are formulated. First-class constraints are naturally involved into the new algebraic scheme. (orig.)
Paul Dirac:. Building Bridges of the Mind
Brown, Laurie M.
2003-12-01
Paul Dirac was a brilliant and original thinker. He used his physical intuition and his ideal of mathematical beauty to construct bridges between major areas of physics. This article discusses several such important works, including the bridge between quantum mechanics and relativity that led to his prediction of the existence of antimatter.
Quantum simulation of the Dirac equation.
Gerritsma, R; Kirchmair, G; Zähringer, F; Solano, E; Blatt, R; Roos, C F
2010-01-01
The Dirac equation successfully merges quantum mechanics with special relativity. It provides a natural description of the electron spin, predicts the existence of antimatter and is able to reproduce accurately the spectrum of the hydrogen atom. The realm of the Dirac equation-relativistic quantum mechanics-is considered to be the natural transition to quantum field theory. However, the Dirac equation also predicts some peculiar effects, such as Klein's paradox and 'Zitterbewegung', an unexpected quivering motion of a free relativistic quantum particle. These and other predicted phenomena are key fundamental examples for understanding relativistic quantum effects, but are difficult to observe in real particles. In recent years, there has been increased interest in simulations of relativistic quantum effects using different physical set-ups, in which parameter tunability allows access to different physical regimes. Here we perform a proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion set to behave as a free relativistic quantum particle. We measure the particle position as a function of time and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states, as well as the crossover from relativistic to non-relativistic dynamics. The high level of control of trapped-ion experimental parameters makes it possible to simulate textbook examples of relativistic quantum physics. PMID:20054392
Analytic representation of the Dirac equation
International Nuclear Information System (INIS)
In this paper, we construct an analytical separation (diagonalization) of the full (minimal coupling) Dirac equation into particle and antiparticle components. The diagonalization is analytic in that it is achieved without transforming the wavefunctions, as is done by the Foldy-Wouthuysen method, and reveals the nonlocal time behaviour of the particle-antiparticle relationship. We then show explicitly that the Pauli equation is not completely valid for the study of the Dirac hydrogen atom problem in s-states (hyperfine splitting). We conclude that there are some open mathematical problems with any attempt to explicitly show that the Dirac equation is insufficient to explain the full hydrogen spectrum. If the perturbation method can be justified, our analysis suggests that the use of cut-offs in QED is already justified by the eigenvalue analysis that supports it. Using a new method, we are able to effect separation of variables for full coupling, solve the radial equation and provide graphs of the probability density function for the 2p- and 2s-states, and compare them with those of the Dirac-Coulomb case
Analytic representation of the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Gill, Tepper L [Department of Electrical and Computer Engineering, Howard University, Washington, DC 20059 (United States); Zachary, W W [Department of Electrical and Computer Engineering, Howard University, Washington, DC 20059 (United States); Alfred, Marcus [Computational Physics Laboratory, Howard University, Washington, DC 20059 (United States)
2005-08-05
In this paper, we construct an analytical separation (diagonalization) of the full (minimal coupling) Dirac equation into particle and antiparticle components. The diagonalization is analytic in that it is achieved without transforming the wavefunctions, as is done by the Foldy-Wouthuysen method, and reveals the nonlocal time behaviour of the particle-antiparticle relationship. We then show explicitly that the Pauli equation is not completely valid for the study of the Dirac hydrogen atom problem in s-states (hyperfine splitting). We conclude that there are some open mathematical problems with any attempt to explicitly show that the Dirac equation is insufficient to explain the full hydrogen spectrum. If the perturbation method can be justified, our analysis suggests that the use of cut-offs in QED is already justified by the eigenvalue analysis that supports it. Using a new method, we are able to effect separation of variables for full coupling, solve the radial equation and provide graphs of the probability density function for the 2p- and 2s-states, and compare them with those of the Dirac-Coulomb case.
Emeritus trio scoops the 2013 Dirac Medal
Dacey, James
2013-09-01
The 2013 Dirac Medal has been awarded to three scientists whose wide-ranging work has brought profound advances in cosmology, astrophysics and fundamental physics. Thomas Kibble, James Peebles and Martin Rees all receive the honour, which is bestowed annually by the Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste, Italy.
Duality between coordinates and Dirac field
Abdalla, M. C. B.; Gadelha, A. L.; Vancea, I. V.
2000-01-01
The duality between the Cartesian coordinates on the Minkowski space-time and the Dirac field is investigated. Two distinct possibilities to define this duality are shown to exist. In both cases, the equations satisfied by prepotentials are of second order.
Duality between coordinates and Dirac field
Abdalla, M. C. B.; Gadelha, A. L.; Vancea, I. V.
2000-07-01
The duality between the Cartesian coordinates on the Minkowski space-time and the Dirac field is investigated. Two distinct possibilities to define this duality are shown to exist. In both cases, the equations satisfied by prepotentials are of second order.
Understanding Quaternions and the Dirac Belt Trick
Staley, Mark
2010-01-01
The Dirac belt trick is often employed in physics classrooms to show that a 2n rotation is not topologically equivalent to the absence of rotation whereas a 4n 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…
Probabilistic solution of the Dirac equation
International Nuclear Information System (INIS)
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.)
Eigenvalue asymptotics for Dirac-Bessel operators
Hryniv, Rostyslav O.; Mykytyuk, Yaroslav V.
2016-06-01
In this paper, we establish the eigenvalue asymptotics for non-self-adjoint Dirac-Bessel operators on (0, 1) with arbitrary real angular momenta and square integrable potentials, which gives the first step for solution of the related inverse problem. The approach is based on a careful examination of the corresponding characteristic functions and their zero distribution.
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...
Principle of general covariance and quantum theory
International Nuclear Information System (INIS)
The authors emphasise the distinction between formal and operational notions of general covariance. Classical, formal covariance implies operational covariance. This is not true in quantum theory. Two observers may not agree on the results of measurement of a tensorial object like T/sub ik/ (stress tensor) in quantum theory. In particular, one observer might conclude that the measured value is zero while another might attribute non-zero value to it
Balancing Covariates via Propensity Score Weighting
Li, Fan; Morgan, Kari Lock; Zaslavsky, Alan M.
2014-01-01
Covariate balance is crucial for an unconfounded descriptive or causal comparison. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of weights-the balancing weights-that balance the weighted distributions of the covariates between treatment groups. These weights incorporate the propensity score to weight each group to an analyst-selected target population. This class unifies existing we...
Adaptive covariance estimation of locally stationary processes
Mallat, Stéphane; Papanicolaou, George; Zhang, Zhifeng
1998-01-01
It is shown that the covariance operator of a locally stationary process has approximate eigenvectors that are local cosine functions. We model locally stationary processes with pseudo-differential operators that are time-varying convolutions. An adaptive covariance estimation is calculated by searching first for a "best" local cosine basis which approximates the covariance by a band or a diagonal matrix. The estimation is obtained from regularized versions of the diagonal coefficients in the...
Kalman Filtering with Unknown Noise Covariances
Nilsson, Martin
2006-01-01
Since it is often difficult to identify the noise covariances for a Kalman filter, they are commonly considered design variables. If so, we can as well try to choose them so that the corresponding Kalman filter has some nice form. In this paper, we introduce a one-parameter subfamily of Kalman filters with the property that the covariance parameters cancel in the expression for the Kalman gain. We provide a simple criterion which guarantees that the implicitly defined process covariance matri...
Competing risks and time-dependent covariates
DEFF Research Database (Denmark)
Cortese, Giuliana; Andersen, Per K
2010-01-01
classified by Kalbfleisch and Prentice [The Statistical Analysis of Failure Time Data, Wiley, New York, 2002] with the intent of clarifying their role and emphasizing the limitations in standard survival models and in the competing risks setting. If random (internal) time-dependent covariates are to be......Time-dependent covariates are frequently encountered in regression analysis for event history data and competing risks. They are often essential predictors, which cannot be substituted by time-fixed covariates. This study briefly recalls the different types of time-dependent covariates, as...
Synge's covariant conservation laws for general relativity
International Nuclear Information System (INIS)
Following Synge, the covariant formulas for the total four-momentum and angular momentum of an isolated physical system in general relativity are derived. These formulas ar first obtained in the weak-field approximation, for which they are shown to be expressible in surface integral form, to be unique, and to represent covariantly conserved quantities. The covariant expressions for the general case are then shown to be identical to those for the weak-field case. The uniquely determined and covariantly conserved quantities so obtained are found to agree with the corresponding canonical, noncovariant surface integral expressions
Conformal covariance and the split property
Morinelli, Vincenzo; Weiner, Mihály
2016-01-01
We show that for a conformal local net of observables on the circle, the split property is automatic. Both full conformal covariance (i.e. diffeomorphism covariance) and the circle-setting play essential roles in this fact, while by previously constructed examples it was already known that even on the circle, M\\"obius covariance does not imply the split property. On the other hand, here we also provide an example of a local conformal net living on the two-dimensional Minkowski space, which - although being diffeomorphism covariant - does not have the split property.
Wu, Yun; Wang, Lin-Lin; Mun, Eundeok; Johnson, D. D.; Mou, Daixiang; Huang, Lunan; Lee, Yongbin; Bud'Ko, S. L.; Canfield, P. C.; Kaminski, Adam
2016-07-01
In topological quantum materials the conduction and valence bands are connected at points or along lines in the momentum space. A number of studies have demonstrated that several materials are indeed Dirac/Weyl semimetals. However, there is still no experimental confirmation of materials with line nodes, in which the Dirac nodes form closed loops in the momentum space. Here we report the discovery of a novel topological structure--Dirac node arcs--in the ultrahigh magnetoresistive material PtSn4 using laser-based angle-resolved photoemission spectroscopy data and density functional theory calculations. Unlike the closed loops of line nodes, the Dirac node arc structure arises owing to the surface states and resembles the Dirac dispersion in graphene that is extended along a short line in the momentum space. We propose that this reported Dirac node arc structure is a novel topological state that provides an exciting platform for studying the exotic properties of Dirac fermions.
Spinorial Reduction of the Superdimensional Dual-covariant Field Theory
Derbenev, Yaroslav
2015-01-01
In this paper we produce further specification of the geometric and algebraic properties of the earlier introduced superdimensional dual-covariant field theory (SFT) in a N-dimensional manifold [1] as an approach to a unified field theory (UFT). Considerations in the present paper are directed by a requirement of transformational invariance of connections of derivatives of dual state vector (DSV) and unified gauge field (UGF matrices) to these objects themselves established by mean of N split metric matrices of a rank {\\mu} (SM, an extended analog of Dirac matrices) in frame of the related Euler-Lagrange equations for DSV, UGF and SM derived in [1]. This requirement is posed on SFT as one of the aspects of the general demand of irreducibility claimed to UFT; it leads to rotational invariance of SM and grand metric tensor (GM) as being structured on SM. Study in this work has led to explication of geometrical nature of SM and DSV as spin-affinors (variable in space of the unified manifold) and dual spin-field,...
Dirac equation for massive neutrinos in a non-rotating SdS black hole from a 5D vacuum
Sánchez, Pablo Alejandro; Bellini, Mauricio
2011-01-01
Starting from a Dirac equation for massless neutrino in a 5D Ricci-flat background metric, we obtain the effective 4D equation for massive neutrino in a Schwarzschild-de Sitter (SdS) background metric from an extended SdS 5D Ricci-flat metric. We use the fact that the spin connection is defined to an accuracy of a vector, so that the covariant derivative of the spinor field is strongly dependent of the background geometry. We show that the mass of the neutrino can be induced from the extra space-like dimension.
Reduced vibration motor winding arrangement
Energy Technology Data Exchange (ETDEWEB)
Slavik, Charles J. (Rexford, NY); Rhudy, Ralph G. (Scotia, NY); Bushman, Ralph E. (Lathem, NY)
1997-01-01
An individual phase winding arrangement having a sixty electrical degree phase belt width for use with a three phase motor armature includes a delta connected phase winding portion and a wye connected phase winding portion. Both the delta and wye connected phase winding portions have a thirty electrical degree phase belt width. The delta and wye connected phase winding portions are each formed from a preselected number of individual coils each formed, in turn, from an unequal number of electrical conductor turns in the approximate ratio of .sqroot.3. The individual coils of the delta and wye connected phase winding portions may either be connected in series or parallel. This arrangement provides an armature winding for a three phase motor which retains the benefits of the widely known and utilized thirty degree phase belt concept, including improved mmf waveform and fundamental distribution factor, with consequent reduced vibrations and improved efficiency.
Treatment Effects with Many Covariates and Heteroskedasticity
DEFF Research Database (Denmark)
Cattaneo, Matias D.; Jansson, Michael; Newey, Whitney K.
propose a new heteroskedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroskedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: (i) parametric linear models with many covariates, (ii...
MUSICAL ARRANGEMENT OF MEDIA ADS
Chernyshov Alexander V.
2015-01-01
The music-compositional principles of commercial and political advertising and also the self-promotion of electronic media (radio, television, Internet) are considered in this mediatext: from the elementary beeps, symbolic functions, emblems/logos and musical brands to the sound engineering technology to underscore the product's name and the complex synthesis between music and intra movements and color-light design of frames. Simultaneously examines, how the musical arrangement of ethereal ad...
International Nuclear Information System (INIS)
A technique for ensuring the rapid correction of both amplitude and offset errors in the deflectional movement of an electron beam along an X-ray emissive target is described. The movement is monitored at at least two positions during a sweep and differences, between the two movements and a desired movement, at these positions are combined in different proportions to produce a corrective servo signal. Such arrangements find application, for example, in computerised tomographic scanners. (author)
Effect modification by time-varying covariates.
Robins, James M; Hernán, Miguel A; Rotnitzky, Andrea
2007-11-01
Marginal structural models (MSMs) allow estimation of effect modification by baseline covariates, but they are less useful for estimating effect modification by evolving time-varying covariates. Rather, structural nested models (SNMs) were specifically designed to estimate effect modification by time-varying covariates. In their paper, Petersen et al. (Am J Epidemiol 2007;166:985-993) describe history-adjusted MSMs as a generalized form of MSM and argue that history-adjusted MSMs allow a researcher to easily estimate effect modification by time-varying covariates. However, history-adjusted MSMs can result in logically incompatible parameter estimates and hence in contradictory substantive conclusions. Here the authors propose a more restrictive definition of history-adjusted MSMs than the one provided by Petersen et al. and compare the advantages and disadvantages of using history-adjusted MSMs, as opposed to SNMs, to examine effect modification by time-dependent covariates. PMID:17875581
Dirac Geometry of the Holonomy Fibration
Cabrera, Alejandro; Meinrenken, Eckhard
2015-01-01
In this paper, we solve the problem of giving a gauge-theoretic description of the natural Dirac structure on a Lie Group which plays a prominent role in the theory of D- branes for the Wess-Zumino-Witten model as well as the theory of quasi-Hamiltonian spaces. We describe the structure as an infinite-dimensional reduction of the space of connections over the circle. Our insight is that the formal Poisson structure on the space of connections is not an actual Poisson structure, but is itself a Dirac structure, due to the fact that it is defined by an unbounded operator. We also develop general tools for reducing Courant algebroids and morphisms between them, allowing us to give a precise correspondence between Hamiltonian loop group spaces and quasi- Hamiltonian spaces.
Dirac phenomenology and hyperon-nucleus interactions
International Nuclear Information System (INIS)
We discuss various aspects of hyperon-nucleus interactions in the relativistic mean field theory. First, characteristics of Λ, Σ and ≡ 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 fωy. Second, optical potentials for Λ and Σ 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 Λ hypernuclei. The large discrepancy between the decay rates and data suggests the need for additional meson exchanges. (authors). 62 refs.,7 figs., 6 tabs
Dirac neutrino masses from generalized supersymmetry breaking
International Nuclear Information System (INIS)
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.)
Dirac Equations with Linear Confining Potentials
Noble, J H
2014-01-01
This paper is devoted to a study of relativistic eigenstates of Dirac particles which are simultaneously bound by a static Coulomb potential and added linear confining potentials. It has recently been shown that, despite the addition of radially symmetric, linear confining potentials, some specific bound-state energies surprisingly retain their exact Dirac-Coulomb values (in the sense of an "exact symmetry"). This observation raises pertinent questions as to the generality of the cancellation mechanism. A Foldy-Wouthuysen transformation is used to find the relevant nonrelativistic physical degrees of freedom, which include additional spin-orbit couplings induced by the linear confining potentials. The matrix elements of the effective operators obtained from the scalar, and time-like confining potentials mutually cancel for specific ratios of the prefactors of the effective operators, which must be tailored to the cancellation mechanism. The result of the Foldy-Wouthuysen transformation is used to explicitly s...
Dirac Neutrino Masses from Generalized Supersymmetry Breaking
Demir, Durmus A; Langacker, Paul
2007-01-01
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.
Dirac structures and Dixmier-Douady bundles
Alekseev, A
2009-01-01
A Dirac structure on a vector bundle V is a maximal isotropic subbundle E of the direct sum of V with its dual. We show how to associate to any Dirac structure a Dixmier-Douady bundle A, that is, a Z/2Z-graded bundle of C*-algebras with typical fiber the compact operators on a Hilbert space. The construction has good functorial properties, relative to Morita morphisms of Dixmier-Douady bundles. As applications, we show that the `spin' Dixmier-Douady bundle over a compact, connected Lie group (as constructed by Atiyah-Segal) is multiplicative, and we obtain a canonical `twisted Spin-c-structure' on spaces with group valued moment maps.
Gauge identities and the Dirac conjecture
International Nuclear Information System (INIS)
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonian or a Lagrangian approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first class constraints. In the latter approach such local symmetries are reflected in the existence of so called gauge identities. The connection between the two becomes apparent, if one works with a first order Lagrangian formulation. Our analysis applies to purely first class systems. We show that Dirac's conjecture applies to first class constraints which are generated in a particular iterative way, regardless of the possible existence of bifurcations or multiple zeroes of these constraints. We illustrate these statements in terms of several examples
Dirac gauginos in low scale supersymmetry breaking
International Nuclear Information System (INIS)
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
Dirac Gauginos in Low Scale Supersymmetry Breaking
Goodsell, Mark D
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.
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.
Quaternion solution of the Dirac equation
International Nuclear Information System (INIS)
A technique for the solution in quaternions of the Dirac equation for particles having anomalous magnetic moment in the field of a flat electromagnetic wave, has been considered. The Lorentz group representation is realized on the wave function being the complex quaternion. The complex numbers are limited to the requirement of invariance relative to P-, C- and T transformations. Equation for a spinor particle interacting with an external magnetic field is easily solved in the case of linear and circular polarizations
High Scale Mixing Unification for Dirac Neutrinos
Abbas, Gauhar; Gupta, Saurabh; Rajasekaran, G.; Srivastava, Rahul(The Institute of Mathematical Sciences, Chennai, 600 113, India)
2013-01-01
Starting with high scale mixing unification hypothesis, we investigate the renormalization group evolution of mixing parameters and masses for Dirac type neutrinos. Following this hypothesis, the PMNS mixing angles and phase are taken to be identical to the CKM ones at a unifying high scale. Then, they are evolved to a low scale using renormalization-group equations. The notable feature of this hypothesis is that renormalization group evolution with quasi-degenerate mass pattern can explain l...
Two-particle Kapitza-Dirac diffraction
Sancho, Pedro
2010-01-01
We extend the study of Kapitza-Dirac diffraction to the case of two-particle systems. Due to the exchange effects the shape and visibility of the two-particle detection patterns show important differences for identical and distinguishable particles. We also identify a novel quantum statistics effect present in momentum space for some values of the initial particle momenta, which is associated with different numbers of photon absorptions compatible with the final momenta.
Dirac particles in a gravitational field
International Nuclear Information System (INIS)
The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metric leads to new contributions to the in-band energy operator in comparison to previous works in the static case. In particular we find a new coupling term between the linear momentum and the spin, as well as couplings that contribute to the breaking of the particle-antiparticle symmetry. (orig.)
Emergent tilt order in Dirac polymer liquids
Souslov, Anton; Loewe, Benjamin; Goldbart, Paul M.
2014-01-01
We study a liquid of zigzagging two-dimensional directed polymers with bending rigidity, i.e., polymers whose conformations follow checkerboard paths. In the continuum limit the statistics of such polymers obey the Dirac equation for particles of imaginary mass. We exploit this observation to investigate a liquid of these polymers via a quantum many-fermion analogy. A self-consistent approximation predicts a phase of tilted order, in which the polymers may develop a preference to zig rather t...
Dirac neutrinos from a second Higgs doublet
Davidson, Shainen M.; Logan, Heather E.
2009-01-01
We propose a minimal extension of the Standard Model in which neutrinos are Dirac particles and their tiny masses are explained without requiring tiny Yukawa couplings. A second Higgs doublet with a tiny vacuum expectation value provides neutrino masses while simultaneously improving the naturalness of the model by allowing a heavier Standard Model-like Higgs boson consistent with electroweak precision data. The model predicts a mu to e gamma rate potentially detectable in the current round o...
The Dirac equation and the Lamb shift
International Nuclear Information System (INIS)
In this paper we show that the Pauli equation does not contain all the essential information of the full, completely separated Dirac equation. We point out that the term which is quadratic in the vector potential is small in all but s-states, where it diverges. A simplistic analysis shows that this term can be used to account for the Lamb shift. (orig./HSI)
Flat band superconductivity in strained Dirac materials
Kauppila, V. J.; Aikebaier, F.; Heikkilä, T. T.
2016-01-01
We consider superconducting properties of a two-dimensional Dirac material such as graphene under strain that produces a flat band spectrum in the normal state. We show that in the superconducting state, such a model results in a highly increased critical temperature compared to the case without the strain, inhomogenous order parameter with two-peak shaped local density of states and yet a large and almost uniform and isotropic supercurrent. This model could be realized in strained graphene o...
Resonant valley filtering of massive Dirac electrons
Moldovan, D.; Masir, M. Ramezani; Covaci, L.; Peeters, F. M.
2013-01-01
Electrons in graphene, in addition to their spin, have two pseudospin degrees of freedom: sublattice and valley pseudospin. Valleytronics uses the valley degree of freedom as a carrier of information similar to the way spintronics uses electron spin. We show how a double barrier structure consisting of electric and vector potentials can be used to filter massive Dirac electrons based on their valley index. We study the resonant transmission through a finite number of barriers and we obtain th...
Dirac particle in a pseudoscalar potential
Energy Technology Data Exchange (ETDEWEB)
Moreno, M. [Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Ap. Postal 20-364, 01000 (Mexico), D.F.; Zentella-Dehesa, A. [Departamento de Fisicoquimica, Intituto de Quimica, UNAM Ap. Postal 70-213, 04510 (Mexico), D.F.
1996-02-01
We study the problem of a Dirac particle with a pseudoscalar interaction in the potential approximation. It is shown how nonperturbative relativistic solutions arise. The case of the central pseudoscalar potential is explicitly worked out also in a closed form. The angular functions are worked out in general for this central case. Finally for the special case of the spherical well the radial solutions are shown to behave like Bessel-type functions. {copyright} {ital 1996 American Institute of Physics.}
Quaternion solution of the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Berezin, A.V.; Tolkachev, E.A.; Fedorov, F.I. (AN Belorusskoj SSR, Minsk. Inst. Fiziki)
1981-10-01
A technique for the solution in quaternions of the Dirac equation for particles having anomalous magnetic moment in the field of a flat electromagnetic wave, has been considered. The Lorentz group representation is realized on the wave function being the complex quaternion. The complex numbers are limited to the requirement of invariance relative to P-, C- and T transformations. Equation for a spinor particle interacting with an external magnetic field is easily solved in the case of linear and circular polarizations.
Dynamical seesaw mechanism for Dirac neutrinos
Directory of Open Access Journals (Sweden)
José W.F. Valle
2016-04-01
Full Text Available So far we have not been able to establish that, as theoretically expected, neutrinos are their own anti-particles. Here we propose a dynamical way to account for the Dirac nature of neutrinos and the smallness of their mass in terms of a new variant of the seesaw paradigm in which the energy scale of neutrino mass generation could be accessible to the current LHC experiments.
Membrane fluids and Dirac membrane fluids
Ivanov, M G
2004-01-01
The relation between two different methods of membrane fluid description is clarified by construction of combined method. Dirac membrane field appears naturally in new approach. It provides a possibility to consider new aspects of electrodynamics-type theories with electric and magnetic sources. The membrane fluid models automatically prohibit simulatenos existence of electric and magnetic currents. Possible applications to the dark energy problem are mentioned.
Dirac operators and Killing spinors with torsion
International Nuclear Information System (INIS)
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.
General covariance and quantum theory
International Nuclear Information System (INIS)
The extension of the principle of relativity to general coordinate systems is based on the hypothesis that an accelerated observer is locally equivalent to a hypothetical inertial observer with the same velocity as the noninertial observer. This hypothesis of locality is expected to be valid for classical particle phenomena as well as for classical wave phenomena but only in the short-wavelength approximation. The generally covariant theory is therefore expected to be in conflict with the quantum theory which is based on wave-particle duality. This is explicitly demonstrated for the frequency of electromagnetic radiation measured by a uniformly rotating observer. The standard Doppler formula is shown to be valid only in the geometric optics approximation. A new definition for the frequency is proposed, and the resulting formula for the frequency measured by the rotating observer is shown to be consistent with expectations based on the classical theory of electrons. A tentative quantum theory is developed on the basis of the generalization of the Bohr frequency condition to include accelerated observers. The description of the causal sequence of events is assumed to be independent of the motion of the observer. Furthermore, the quantum hypothesis is supposed to be valid for all observers. The implications of this theory are critically examined. The new formula for frequency, which is still based on the hypothesis of locality, leads to the observation of negative energy quanta by the rotating observer and is therefore in conflict with the quantum theory
Tunneling times with covariant measurements
Kiukas, J; Werner, R F; 10.1007/s10701-009-9275-z
2009-01-01
We consider the time delay of massive, non-relativistic, one-dimensional particles due to a tunneling potential. In this setting the well-known Hartman effect asserts that often the sub-ensemble of particles going through the tunnel seems to cross the tunnel region instantaneously. An obstacle to the utilization of this effect for getting faster signals is the exponential damping by the tunnel, so there seems to be a trade-off between speedup and intensity. In this paper we prove that this trade-off is never in favor of faster signals: the probability for a signal to reach its destination before some deadline is always reduced by the tunnel, for arbitrary incoming states, arbitrary positive and compactly supported tunnel potentials, and arbitrary detectors. More specifically, we show this for several different ways to define ``the same incoming state'' and ''the same detector'' when comparing the settings with and without tunnel potential. The arrival time measurements are expressed in the time-covariant appr...
Quantum transport through 3D Dirac materials
International Nuclear Information System (INIS)
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
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
Salehi, M.; Jafari, S. A.
2015-08-01
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.
Manipulation of Dirac Cones in Mechanical Graphene.
Kariyado, Toshikaze; Hatsugai, Yasuhiro
2015-01-01
Recently, quantum Hall state analogs in classical mechanics attract much attention from topological points of view. Topology is not only for mathematicians but also quite useful in a quantum world. Further it even governs the Newton's law of motion. One of the advantages of classical systems over solid state materials is its clear controllability. Here we investigate mechanical graphene, which is a spring-mass model with the honeycomb structure as a typical mechanical model with nontrivial topological phenomena. The vibration spectrum of mechanical graphene is characterized by Dirac cones serving as sources of topological nontriviality. We find that the spectrum has dramatic dependence on the spring tension at equilibrium as a natural control parameter, i.e., creation and annihilation of the Dirac particles are realized as the tension increases. Just by rotating the system, the manipulated Dirac particles lead to topological transition, i.e., a jump of the "Chern number" occurs associated with flipping of propagating direction of chiral edge modes. This is a bulk-edge correspondence governed by the Newton's law. A simple observation that in-gap edge modes exist only at the fixed boundary, but not at the free one, is attributed to the symmetry protection of topological phases. PMID:26667580
One real function instead of the Dirac spinor function
International Nuclear Information System (INIS)
Three out of four complex components of the Dirac spinor can be algebraically eliminated from the Dirac equation (if some linear combination of electromagnetic fields does not vanish), yielding a partial differential equation of the fourth order for the remaining complex component. This equation is generally equivalent to the Dirac equation. Furthermore, following Schroedinger [Nature (London), 169, 538 (1952)], the remaining component can be made real by a gauge transform, thus extending to the Dirac field the Schroedinger conclusion that charged fields do not necessarily require complex representation. One of the two resulting real equations for the real function describes current conservation and can be obtained from the Maxwell equations in spinor electrodynamics (the Dirac-Maxwell electrodynamics). As the Dirac equation is one of the most fundamental equations, these results both belong in textbooks and can be used for development of new efficient methods and algorithms of quantum chemistry.
DIRAC - The Distributed MC Production and Analysis for LHCb
Tsaregorodtsev, A; Closier, J; Frank, M; Garonne, V; Witek, M; Romanovski, V; Egede, U; Vagnoni, V; Korolko, I; Blouw, J; Kuznetsov, G; Patrick, G; Gandelman, M; Graciani-Diaz, R; Bernet, R; Brook, N; Pickford, A; Tobin, M; Saroka, A; Stokes-Rees, I; Saborido-Silva, J; Sanchez-Garcia, M
2004-09-30
DIRAC is the LHCb distributed computing grid infrastructure for Monte Carlo (MC) production and analysis. Its architecture is based on a set of distributed collaborating services. The service decomposition broadly follows the CERN/ARDA-RTAG proposal, which should allow for the interchange of the EGEE/gLite and DIRAC components. In this paper we give an overview of the DIRAC architecture, as well as the main design choices in its implementation. The light nature and modular design of the DIRAC components allows its functionality to be easily extended to include new computing and storage elements or to handle new types of tasks. The DIRAC system already uses different types of computing resources - from single PC's to a variety of batch systems and to the Grid environment. In particular, the DIRAC interface to the LCG2 grid will be presented.
Deconstructing non-Dirac-Hermitian supersymmetric quantum systems
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Pijush K, E-mail: pijushkanti.ghosh@visva-bharati.ac.in [Department of Physics, Siksha-Bhavana, Visva-Bharati University, Santiniketan 731 235, West Bengal (India)
2011-05-27
A method to construct a non-Dirac-Hermitian supersymmetric quantum system that is isospectral with a Dirac-Hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving both bosonic and fermionic degrees of freedom in terms of non-Dirac-Hermitian operators which are Hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. A pseudo-Hermitian realization of the Clifford algebra for a pre-determined positive-definite metric is used to construct supersymmetric systems with one or many degrees of freedom. It is shown that exactly solvable non-Dirac-Hermitian supersymmetric quantum systems can be constructed corresponding to each exactly solvable Dirac-Hermitian system. Examples of non-Dirac-Hermitian (i) non-relativistic Pauli Hamiltonian, (ii) super-conformal quantum system, and (iii) supersymmetric Calogero-type models admitting entirely real spectra are presented.
A constant mean curvature surface and the Dirac operator
International Nuclear Information System (INIS)
The shape of a surface with constant mean curvature (CMC) has been studied in mathematics and physics related to nonlinear integrable theory and harmonic map (σ-model) theory. In the study a fictitious (linear) Dirac-type operator appears as a tool of the calculus (Konopelchenko B.G. and Taimanov I.A. 1996 J. Phys. A: Math. Gen. 29 1261-5). In this paper, I confine the Dirac field defined in R3 to a thin surface embedded in R3 and obtain a proper Dirac operator for the thin surface. Then it completely agrees with the Dirac-type operator used in the calculus of the CMC surface theory. In other words, the mathematical Dirac-type operator is realized by a physical Dirac particle. (author)
Moduli of weighted hyperplane arrangements
Lahoz, Martí; Macrí, Emanuele; Stellari, Paolo
2015-01-01
This book focuses on a large class of geometric objects in moduli theory and provides explicit computations to investigate their families. Concrete examples are developed that take advantage of the intricate interplay between Algebraic Geometry and Combinatorics. Compactifications of moduli spaces play a crucial role in Number Theory, String Theory, and Quantum Field Theory – to mention just a few. In particular, the notion of compactification of moduli spaces has been crucial for solving various open problems and long-standing conjectures. Further, the book reports on compactification techniques for moduli spaces in a large class where computations are possible, namely that of weighted stable hyperplane arrangements.
Arrangement for selectively irradiating webs
International Nuclear Information System (INIS)
The arrangement for selectively irradiating a web includes a perforated band of a radiation impermeable substance which is guided in an endless path via a pair of guide rollers and has two juxtaposed runs in this path. A take-up roller conveys a web of material past one of the runs at a side thereof remote from the other run, the direction of movement of the web being other than parallel to that of the band and, preferably, normal thereto. An electron accelerator is provided at the far side of the run remote from the web and is effective for directing a radiation beam at the web through the perforations
Dirac Neutrinos and Dark Matter Stability from Lepton Quarticity
Chuliá, Salvador Centelles; Ma, Ernest; Srivastava, Rahul; Valle, José W. F.
2016-01-01
We propose to relate dark matter stability to the possible Dirac nature of neutrinos. The idea is illustrated in a simple scheme where small Dirac neutrino masses arise from a type--I seesaw mechanism as a result of a $Z_4$ discrete lepton number symmetry. The latter implies the existence of a viable WIMP dark matter candidate, whose stability arises from the same symmetry which ensures the Diracness of neutrinos.
A new algorithm for multiplying two Dirac numbers
Cariow, Aleksandr; Cariowa, Galina
2015-01-01
In this work a rationalized algorithm for Dirac numbers multiplication is presented. This algorithm has a low computational complexity feature and is well suited to FPGA implementation. The computation of two Dirac numbers product using the na\\"ive method takes 256 real multiplications and 240 real additions, while the proposed algorithm can compute the same result in only 88 real multiplications and 256 real additions. During synthesis of the discussed algorithm we use the fact that Dirac nu...
Supersymmetrization of Quaternion Dirac Equation for Generalized Fields of Dyons
Rawat, A S; Li, Tianjun; Negi, O P S
2012-01-01
The quaternion Dirac equation in presence of generalized electromagnetic field has been discussed in terms of two gauge potentials of dyons. Accordingly, the supersymmetry has been established consistently and thereafter the one, two and component Dirac Spinors of generalized quaternion Dirac equation of dyons for various energy and spin values are obtained for different cases in order to understand the duality invariance between the electric and magnetic constituents of dyons.
Some Sharp L^2 Inequalities for Dirac Type Operators
Directory of Open Access Journals (Sweden)
Alexander Balinsky
2007-11-01
Full Text Available We use the spectra of Dirac type operators on the sphere $S^n$ to produce sharp $L^2$ inequalities on the sphere. These operators include the Dirac operator on $S^n$, the conformal Laplacian and Paenitz operator. We use the Cayley transform, or stereographic projection, to obtain similar inequalities for powers of the Dirac operator and their inverses in ${mathbb R}^n$.
The GridPP DIRAC project: Implementation of a multi-VO DIRAC service
Bauer, D.; Colling, D.; Currie, R.; Fayer, S.; Huffman, A.; Martyniak, J.; Rand, D.; Richards, A.
2015-12-01
The GridPP consortium provides computing support to many high energy physics projects in the UK. As part of this GridPP offers access to a large amount of highly distributed resources across the UK for multiple collaborations. The userbase supported by GridPP includes hundreds of users spanning multiple virtual organisations with many different computing requirements. In order to provide a common interface to these distributed a centralised DIRAC instance has been setup at Imperial College London. This paper describes the experiences learnt from deploying this DIRAC instance and the modifications that have made to support the GridPP use case.
The covariant quantum Green-Schwarz superstring
International Nuclear Information System (INIS)
First we present the covariantly quantized space-time supersymmetric superstring. The main ingredients are additional auxiliary variables and their corresponding auxiliary gauge symmetries. They allow a Lorentz covariant gauge fixed lagrangian path integral which has the form of a free 2-dimensional conformal field theory with a finite number of 2-dimensional world-sheet fields and ghosts. Next we show that the path integral is anomaly free in 10 space-time dimensions. Then, by a canonical (operator) quantization we obtain in the point-particle limit the covariant equations of motion of the D=10 super Yang-Mills (SYM) theory. (authors)
Dirac-mode expansion analysis for Polyakov loop
Iritani, Takumi; Gongyo, Shinya; Suganuma, Hideo
2012-01-01
To clarify the relation between chiral symmetry breaking and color confinement, we investigate the Polyakov loop in terms of the Dirac eigenmodes in SU(3) lattice QCD. We analyze the low-lying (IR) and UV Dirac-mode contribution to the Polyakov loop, respectively, using the Dirac-mode expansion method. In the confined phase, the Polyakov loop $$ remains almost zero and $Z_3$ center symmetry is thus unbroken, even after removing low-lying Dirac-modes, which are responsible to chiral sym...
Polyakov loop analysis with Dirac-mode expansion
Iritani, Takumi; Gongyo, Shinya; Suganuma, Hideo
2013-01-01
In order to investigate the direct relation between confinement and chiral symmetry breaking in QCD, we investigate the Polyakov loop in terms of the Dirac eigenmodes in both confined and deconfined phases. Using the Dirac-mode expansion method in SU(3) lattice QCD, we analyze the contribution of low-lying and higher Dirac-modes to the Polyakov loop, respectively.In the confined phase below T_c, after removing low-lying Dirac-modes, the chiral condensate $$ is largely reduced, how...
Computational Determination of the Dirac-Theory Adjunctator
Directory of Open Access Journals (Sweden)
M. Dima
2013-01-01
Full Text Available A number of particle properties stem from the use of γ0 as adjunctator (Bargmann-Pauli in the Dirac theory (spin alignment, Dirac current, etc.. The early motivations for accepting γ0 as adjunctator were representation-dependent, mildly bearing relation to the actual conditions forcing γ0 as adjunctator. Representation-independent approaches to the physical predictions of the Dirac equation are somewhat new, here presented as being the reasons for γ0 as adjunctator of the Dirac theory, together with the essential role of the latter in the physical aspects of the theory.
On the disformal invariance of the Dirac equation
Bittencourt, Eduardo; Lobo, Iarley P.; Carvalho, Gabriel G.
2015-09-01
We analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field acting on the metric tensor. Using the Weyl-Cartan formalism, we construct a large class of disformal maps between different metric tensors, respecting the order of differentiability of the Dirac operator and satisfying the Clifford algebra in both metrics. We split the analysis in some cases according to the spinor mass and the norm of the Dirac current, exhibiting sufficient conditions to find classes of solutions which keep the Dirac operator invariant under the action of the disformal group.
On the disformal invariance of the Dirac equation
Bittencourt, Eduardo; Carvalho, Gabriel G
2015-01-01
In this paper we analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field. Using the Weyl-Cartan formalism, we construct a large class of disformal maps between different metric tensors, respecting the order of differentiability of the Dirac operator and satisfying the Clifford algebra in both metrics. Then, we have shown that there is a subclass of solutions of the Dirac equation, provided by Inomata's condition, which keeps the Dirac operator invariant under the action of the disformal group.
Comment on covariant Stora--Zumino chain terms
Adam, C.
1999-01-01
In a recent paper, Ekstrand proposed a simple expression from which covariant anomaly, covariant Schwinger term and higher covariant chain terms may be computed. We comment on the relation of his result to the earlier work of Tsutsui.
Maxwell-Dirac stress-energy tensor in terms of Fierz bilinear currents
Inglis, Shaun; Jarvis, Peter
2016-03-01
We analyse the stress-energy tensor for the self-coupled Maxwell-Dirac system in the bilinear current formalism, using two independent approaches. The first method used is that attributed to Belinfante: starting from the spinor form of the action, the well-known canonical stress-energy tensor is augmented, by extending the Noether symmetry current to include contributions from the Lorentz group, to a manifestly symmetric form. This form admits a transcription to bilinear current form. The second method used is the variational derivation based on the covariant coupling to general relativity. The starting point here at the outset is the transcription of the action using, as independent field variables, both the bilinear currents, together with a gauge invariant vector field (a proxy for the electromagnetic vector potential). A central feature of the two constructions is that they both involve the mapping of the Dirac contribution to the stress-energy from the spinor fields to the equivalent set of bilinear tensor currents, through the use of appropriate Fierz identities. Although this mapping is done at quite different stages, nonetheless we find that the two forms of the bilinear stress-energy tensor agree. Finally, as an application, we consider the reduction of the obtained stress-energy tensor in bilinear form, under the assumption of spherical symmetry.
Modular covariance, PCT, spin and statistics
Guido, D
1995-01-01
The notion of modular covariance is reviewed and the reconstruction of the Poincar\\'e group extended to the low-dimensional case. The relations with the PCT symmetry and the Spin and Statistics theorem are described.
The Covariant Picard Groupoid in Differential Geometry
Waldmann, Stefan
2005-01-01
In this article we discuss some general results on the covariant Picard groupoid in the context of differential geometry and interpret the problem of lifting Lie algebra actions to line bundles in the Picard groupoid approach.
Covariance data evaluation for experimental data
International Nuclear Information System (INIS)
Some methods and codes have been developed and utilized for covariance data evaluation of experimental data, including parameter analysis, physical analysis, Spline fitting etc.. These methods and codes can be used in many different cases
Forecasting Covariance Matrices: A Mixed Frequency Approach
DEFF Research Database (Denmark)
Halbleib, Roxana; Voev, Valeri
This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows for flexi......This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows...... for flexible dependence patterns for volatilities and correlations, and can be applied to covariance matrices of large dimensions. The separate modeling of volatility and correlation forecasts considerably reduces the estimation and measurement error implied by the joint estimation and modeling of covariance...
Characteristic Polynomials of Sample Covariance Matrices
Kösters, Holger
2009-01-01
We investigate the second-order correlation function of the characteristic polynomial of a sample covariance matrix. Starting from an explicit formula for the generating function, we re-obtain several well-known kernels from random matrix theory.
Covariance Spectroscopy for Fissile Material Detection
Energy Technology Data Exchange (ETDEWEB)
Rusty Trainham, Jim Tinsley, Paul Hurley, Ray Keegan
2009-06-02
Nuclear fission produces multiple prompt neutrons and gammas at each fission event. The resulting daughter nuclei continue to emit delayed radiation as neutrons boil off, beta decay occurs, etc. All of the radiations are causally connected, and therefore correlated. The correlations are generally positive, but when different decay channels compete, so that some radiations tend to exclude others, negative correlations could also be observed. A similar problem of reduced complexity is that of cascades radiation, whereby a simple radioactive decay produces two or more correlated gamma rays at each decay. Covariance is the usual means for measuring correlation, and techniques of covariance mapping may be useful to produce distinct signatures of special nuclear materials (SNM). A covariance measurement can also be used to filter data streams because uncorrelated signals are largely rejected. The technique is generally more effective than a coincidence measurement. In this poster, we concentrate on cascades and the covariance filtering problem.
Evaluation of covariance for fission neutron spectra
Energy Technology Data Exchange (ETDEWEB)
Kawano, Toshihiko; Nakashima, Hideki [Kyushu Univ., Fukuoka (Japan); Ohsawa, Takaaki; Shibata, Keiichi
1999-02-01
A covariance evaluation system for the evaluated nuclear data library JENDL-3.2 was established, and the covariance data for fission neutron spectra of {sup 233}U, {sup 235}U, {sup 238}U, {sup 239}Pu were evaluated. Two methods were employed to evaluate the covariance. One is based on the experimental data, and the other is based on a model calculation including some kinds of renormalizations. The latter technique was adopted for the covariance evaluation of the fission neutron spectra in JENDL-3.2. We performed an adjustment of the evaluated fission neutron spectrum of {sup 235}U using the spectrum averaged cross sections for the {sup 27}Al(n, p), {sup 46,47,48}Ti(n, p), {sup 54,56}Fe(n, p), {sup 58}Ni(n, p), {sup 90}Zr(n, 2n) reactions. The adjusted spectrum integrated over energy was found to be unity. (author)
Covariance Eigenvector Sparsity for Compression and Denoising
Schizas, Ioannis D
2012-01-01
Sparsity in the eigenvectors of signal covariance matrices is exploited in this paper for compression and denoising. Dimensionality reduction (DR) and quantization modules present in many practical compression schemes such as transform codecs, are designed to capitalize on this form of sparsity and achieve improved reconstruction performance compared to existing sparsity-agnostic codecs. Using training data that may be noisy a novel sparsity-aware linear DR scheme is developed to fully exploit sparsity in the covariance eigenvectors and form noise-resilient estimates of the principal covariance eigenbasis. Sparsity is effected via norm-one regularization, and the associated minimization problems are solved using computationally efficient coordinate descent iterations. The resulting eigenspace estimator is shown capable of identifying a subset of the unknown support of the eigenspace basis vectors even when the observation noise covariance matrix is unknown, as long as the noise power is sufficiently low. It i...
Attenuation caused by infrequently updated covariates in survival analysis
DEFF Research Database (Denmark)
Andersen, Per Kragh; Liestøl, Knut
Attenuation; Cox regression model; Measurement errors; Survival analysis; Time-dependent covariates......Attenuation; Cox regression model; Measurement errors; Survival analysis; Time-dependent covariates...
'Chrysanthemum petal' arrangements of silver nano wires.
Cui, Hui-Wang; Jiu, Jin-Ting; Sugahara, Tohru; Nagao, Shijo; Suganuma, Katsuaki; Uchida, Hiroshi
2014-12-01
Highly ordered 'Chrysanthemum petal' arrangements of silver nano wires were fabricated in a biodegradable polymer of polyvinyl alcohol using a simple one-step blending method without any template. The degree of the arrangement increased with the decreasing content of polyvinyl alcohol. The mechanism for the formation of these 'Chrysanthemum petal' arrangements was discussed specifically. These 'Chrysanthemum petal' arrangements will be helpful to increase the electrical conductivity of silver nano wires films. PMID:25397618
Hyperplane Arrangements with Large Average Diameter
Deza, Antoine; Xie, Feng
2007-01-01
The largest possible average diameter of a bounded cell of a simple hyperplane arrangement is conjectured to be not greater than the dimension. We prove that this conjecture holds in dimension 2, and is asymptotically tight in fixed dimension. We give the exact value of the largest possible average diameter for all simple arrangements in dimension 2, for arrangements having at most the dimension plus 2 hyperplanes, and for arrangements having 6 hyperplanes in dimension 3. In dimension 3, we g...
Face monoid actions and tropical hyperplane arrangements
Johnson, Marianne; Kambites, Mark
2016-01-01
We study the combinatorics of tropical hyperplane arrangements, and their relationship to (classical) hyperplane face monoids. We show that the refinement operation on the faces of a tropical hyperplane arrangement, introduced by Ardila and Develin in their definition of a tropical oriented matroid, induces an action of the hyperplane face monoid of the classical braid arrangement on the arrangement, and hence on a number of interesting related structures. Along the way, we introduce a new ch...
On covariant Poisson brackets in field theory
Sharapov, Alexey A.
2014-01-01
A general approach is proposed to constructing covariant Poisson brackets in the space of histories of a classical field-theoretical model. The approach is based on the concept of Lagrange anchor, which was originally developed as a tool for path-integral quantization of Lagrangian and non-Lagrangian dynamics. The proposed covariant Poisson brackets generalize the Peierls' bracket construction known in the Lagrangian field theory.
Time varying covariance structures in financial markets
Gerhard, Frank; Hess, Dieter E.
1996-01-01
Reliable estimates of variances and covariances are crucial for portfolio management and risk controlling. This paper investigates alternative methods to estimate time varying variance-covariance matrices: ordinary estimates and exponentially weighted moving averages in comparison to Markov switching models. Different criteria are used to assess the quality of estimators. Bootstrapped confidence intervals for variances and correlations allow to compare the reliability of these estimates. Most...
Covariate analysis of bivariate survival data
Energy Technology Data Exchange (ETDEWEB)
Bennett, L.E.
1992-01-01
The methods developed are used to analyze the effects of covariates on bivariate survival data when censoring and ties are present. The proposed method provides models for bivariate survival data that include differential covariate effects and censored observations. The proposed models are based on an extension of the univariate Buckley-James estimators which replace censored data points by their expected values, conditional on the censoring time and the covariates. For the bivariate situation, it is necessary to determine the expectation of the failure times for one component conditional on the failure or censoring time of the other component. Two different methods have been developed to estimate these expectations. In the semiparametric approach these expectations are determined from a modification of Burke's estimate of the bivariate empirical survival function. In the parametric approach censored data points are also replaced by their conditional expected values where the expected values are determined from a specified parametric distribution. The model estimation will be based on the revised data set, comprised of uncensored components and expected values for the censored components. The variance-covariance matrix for the estimated covariate parameters has also been derived for both the semiparametric and parametric methods. Data from the Demographic and Health Survey was analyzed by these methods. The two outcome variables are post-partum amenorrhea and breastfeeding; education and parity were used as the covariates. Both the covariate parameter estimates and the variance-covariance estimates for the semiparametric and parametric models will be compared. In addition, a multivariate test statistic was used in the semiparametric model to examine contrasts. The significance of the statistic was determined from a bootstrap distribution of the test statistic.
On the covariant relativistic separable kernel
Bondarenko, S G; Rogochaya, E P; Yanev, Y
2008-01-01
Two different methods of the covariant relativistic separable kernel construction in the Bethe-Salpeter approach are considered. One of them leads in the center-of-mass system of two particles to the quasipotential equation. The constructed 4-dimensional covariant functions are used to reproduce neutron-proton phase shifts for total angular momenta $J=0,1$. Obtained results are compared with other model calculations.
Optimal Non-Universally Covariant Cloning
D'Ariano, G. M.; Presti, P. Lo
2001-01-01
We consider non-universal cloning maps, namely cloning transformations which are covariant under a proper subgroup G of the universal unitary group U(d), where d is the dimension of the Hilbert space H of the system to be cloned. We give a general method for optimizing cloning for any cost-function. Examples of applications are given for the phase-covariant cloning (cloning of equatorial qubits) and for the Weyl-Heisenberg group (cloning of "continuous variables").
Functional CLT for sample covariance matrices
Bai, Zhidong; Zhou, Wang; 10.3150/10-BEJ250
2010-01-01
Using Bernstein polynomial approximations, we prove the central limit theorem for linear spectral statistics of sample covariance matrices, indexed by a set of functions with continuous fourth order derivatives on an open interval including $[(1-\\sqrt{y})^2,(1+\\sqrt{y})^2]$, the support of the Mar\\u{c}enko--Pastur law. We also derive the explicit expressions for asymptotic mean and covariance functions.
Covariant action for type IIB supergravity
Sen, Ashoke
2016-07-01
Taking clues from the recent construction of the covariant action for type II and heterotic string field theories, we construct a manifestly Lorentz covariant action for type IIB supergravity, and discuss its gauge fixing maintaining manifest Lorentz invariance. The action contains a (non-gravitating) free 4-form field besides the usual fields of type IIB supergravity. This free field, being completely decoupled from the interacting sector, has no physical consequence.
Solution of the Dirac-Coulomb problem by the second-order Dirac equation approach
International Nuclear Information System (INIS)
A complete solution of the relativistic Coulomb problem is presented on the basis of the second-order Dirac equation. A set of fundamental solutions of the linear and squared relativistic equation is investigated. The different forms of both the ordinary and the reduced relativistic Coulomb Green functions and the wavefunctions are discussed. (orig.)
29 CFR 779.229 - Other arrangements.
2010-07-01
..., Franchise and Other Business Arrangements § 779.229 Other arrangements. With respect to those arrangements...” establishment will be considered a part of the same “enterprise.” For example, whether a franchise, lease, or... the enterprise which grants the franchise, right, or concession. (S. Rept. 145, 87th Cong., 1st...
Sequential BART for imputation of missing covariates.
Xu, Dandan; Daniels, Michael J; Winterstein, Almut G
2016-07-01
To conduct comparative effectiveness research using electronic health records (EHR), many covariates are typically needed to adjust for selection and confounding biases. Unfortunately, it is typical to have missingness in these covariates. Just using cases with complete covariates will result in considerable efficiency losses and likely bias. Here, we consider the covariates missing at random with missing data mechanism either depending on the response or not. Standard methods for multiple imputation can either fail to capture nonlinear relationships or suffer from the incompatibility and uncongeniality issues. We explore a flexible Bayesian nonparametric approach to impute the missing covariates, which involves factoring the joint distribution of the covariates with missingness into a set of sequential conditionals and applying Bayesian additive regression trees to model each of these univariate conditionals. Using data augmentation, the posterior for each conditional can be sampled simultaneously. We provide details on the computational algorithm and make comparisons to other methods, including parametric sequential imputation and two versions of multiple imputation by chained equations. We illustrate the proposed approach on EHR data from an affiliated tertiary care institution to examine factors related to hyperglycemia. PMID:26980459
Diverse living arrangements of children.
1993-01-01
In the United States, over the past few decades, the prominence of the traditional two-parent family has gradually faded, with its place usually being taken by homes headed by a mother. Relatively few children are raised by single fathers. The pattern of this ongoing development varies considerably by major racial groups as well as by age of child. Current living arrangements for children by three classes of age, race and presence of parents were analyzed by four parental characteristics--age, educational attainment, labor force participation and existence of other siblings. Racial similarities and differences--some significant--are noted. For example, among white children, 36 percent of those under age six had a parent under age 30. Among black children, the proportion was 57 percent and among Hispanics, 46 percent. In all groups, educational attainment was higher in families with two parents. Parents' educational levels were parallel with their employment rates. PMID:8211668
MUSICAL ARRANGEMENT OF MEDIA ADS
Directory of Open Access Journals (Sweden)
Chernyshov Alexander V.
2015-01-01
Full Text Available The music-compositional principles of commercial and political advertising and also the self-promotion of electronic media (radio, television, Internet are considered in this mediatext: from the elementary beeps, symbolic functions, emblems/logos and musical brands to the sound engineering technology to underscore the product's name and the complex synthesis between music and intra movements and color-light design of frames. Simultaneously examines, how the musical arrangement of ethereal advertising is involved in creation the emotional drama or bravado which reach the level of explicit or associative counterpoint 'music with the advertised object or subject' and which extend to expression of cultural image of all the broadcast channel. The article explores the works of the next genres like infomercial, teleshopping, film-ad, and autonomous commercials that have been produced in European countries or USA.
International arrangements against nuclear terrorism
International Nuclear Information System (INIS)
International efforts to show the spread of nuclear weapons have created an international norm of nonproliferation, backed by a variety of enforcement mechanisms. Together they are often referred to as the nonproliferation regime. This regime is reviewed, starting with the 1963 Limited Test Ban Treaty. The centerpiece of the regime, the Non-Proliferation Treaty (NPT), signed in 1968, now has 135 parties, including most of the advanced industrial nuclear countries. Results of the 1985 NPT Review Conference are briefly discussed; the 86 NPT parties that attended reaffirmed the treaty's value, pledged continued support for the IAEA safeguards system, and called upon nonsigners to renounce nuclear weapons and accept IAEA safeguards. A section is devoted to the physical protection of nuclear materials, facilities, and weapons. Finally, recommendations are presented to improve international arrangements against nuclear terrorists
Dirac operator normality and chiral properties
International Nuclear Information System (INIS)
Normality and γ5-hermiticity are what gives rise to chiral properties and rules. The Ginsparg-Wilson (GW) relation is only one of the possible spectral constraints. The sum rule for chiral differences of real modes has important consequences. The alternative transformation of Luescher gives the same Ward identity as the usual chiral one (if zero modes are properly treated). Imposing normality on a general function of the hermitean Wilson-Dirac operator H leads at same time to the GW relation and to the Neuberger operator
Dirac Born Infeld (DBI) Cosmic Strings
Babichev, Eugeny; Brax, Philippe; Caprini, Chiara; Martin, Jerome; Steer, Daniele
2008-01-01
Motivated by brane physics, we consider the non-linear Dirac-Born-Infeld (DBI) extension of the Abelian-Higgs model and study the corresponding cosmic string configurations. The model is defined by a potential term, assumed to be of the mexican hat form, and a DBI action for the kinetic terms. We show that it is a continuous deformation of the Abelian-Higgs model, with a single deformation parameter depending on a dimensionless combination of the scalar coupling constant, the vacuum expectati...
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.
D-Instanton Generated Dirac Neutrino Masses
Cvetic, Mirjam
2008-01-01
We present a stringy mechanism to generate Dirac neutrino masses by D-instantons. Within Type IIA string theory with intersecting D6-branes, we spell out specific conditions for the emergence of such couplings and provide a class of explicit supersymmetric local SU(5) Grand Unified models, based on the Z_2 x Z'_2 orientifold compactification, where perturbatively absent neutrino masses can be generated by D2-brane instantons in the desired mass regime, thus providing an intriguing mechanism for the origin of small neutrino masses due to exponentially suppressed non-perturbative stringy effects.
An embedding scheme for the Dirac equation
Crampin, S
2004-01-01
An embedding scheme is developed for the Dirac Hamiltonian H. Dividing space into regions I and II separated by surface S, an expression is derived for the expectation value of H which makes explicit reference to a trial function defined in I alone, with all details of region II replaced by an effective potential acting on S and which is related to the Green function of region II. Stationary solutions provide approximations to the eigenstates of H within I. The Green function for the embedded...
Dirac gauginos, gauge mediation and unification
International Nuclear Information System (INIS)
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 Gluinos in the Pyramid Scheme
Banks, T
2013-01-01
I point out several terms in the low energy effective Lagrangian of the Pyramid Scheme, which were missed in a previous analysis of the phenomenological consequences of the model. They lead to a Dirac contribution to the gluino mass, much larger than the one loop Majorana mass. The gluino can thus be much heavier than in previous estimates, without introducing corresponding large loop corrections to squark masses. As pointed out by a number of authors, this ameliorates the tension between the predictions of the model, and LHC data. I also point out that the model has corrections to the Higgs potential, both at the tree and loop levels, which may ameliorate fine tuning.
Incomplete Dirac reduction of constrained Hamiltonian systems
International Nuclear Information System (INIS)
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
Covariance Modifications to Subspace Bases
Energy Technology Data Exchange (ETDEWEB)
Harris, D B
2008-11-19
Adaptive signal processing algorithms that rely upon representations of signal and noise subspaces often require updates to those representations when new data become available. Subspace representations frequently are estimated from available data with singular value (SVD) decompositions. Subspace updates require modifications to these decompositions. Updates can be performed inexpensively provided they are low-rank. A substantial literature on SVD updates exists, frequently focusing on rank-1 updates (see e.g. [Karasalo, 1986; Comon and Golub, 1990, Badeau, 2004]). In these methods, data matrices are modified by addition or deletion of a row or column, or data covariance matrices are modified by addition of the outer product of a new vector. A recent paper by Brand [2006] provides a general and efficient method for arbitrary rank updates to an SVD. The purpose of this note is to describe a closely-related method for applications where right singular vectors are not required. This note also describes the SVD updates to a particular scenario of interest in seismic array signal processing. The particular application involve updating the wideband subspace representation used in seismic subspace detectors [Harris, 2006]. These subspace detectors generalize waveform correlation algorithms to detect signals that lie in a subspace of waveforms of dimension d {ge} 1. They potentially are of interest because they extend the range of waveform variation over which these sensitive detectors apply. Subspace detectors operate by projecting waveform data from a detection window into a subspace specified by a collection of orthonormal waveform basis vectors (referred to as the template). Subspace templates are constructed from a suite of normalized, aligned master event waveforms that may be acquired by a single sensor, a three-component sensor, an array of such sensors or a sensor network. The template design process entails constructing a data matrix whose columns contain the
Dirac oscillator and nonrelativistic Snyder-de Sitter algebra
International Nuclear Information System (INIS)
Three dimensional Dirac oscillator was considered in space with deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations give rise to appearance of minimal uncertainties in position as well as in momentum. To derive energy spectrum and wavefunctions of the Dirac oscillator, supersymmetric quantum mechanics and shape invariance technique were applied
Neutrino masses from a pseudo-Dirac Bino
Coloma, Pilar
2016-01-01
We show that, in $U(1)_R$-symmetric supersymmetric models, the bino and its Dirac partner (the singlino) can play the role of right-handed neutrinos and generate the neutrino masses and mixing, without the need for bilinear or trilinear R-parity violating operators. The two particles form a pseudo-Dirac pair, the `bi$\
NEW KINDS OF DIRAC ENERGY LEVELS AND THEIR CROSSING REGIONS
Institute of Scientific and Technical Information of China (English)
杨树政; 林理彬
2001-01-01
In the space-time of a non-Kerr-Newman black hole, the Dirac energy levels and their crossing regions are inves-tigated. Near the event horizon of the black hole there are crossing Dirac energy levels, which lead to the occurrence of non-thermal radiation.
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.
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.…
Dirac's principle in multimode interference of independent sources
Sancho, Pedro
2005-01-01
The extended Dirac's principle describes the interference between different particles as an effect of the multiparticle system with itself. In this paper we present a novel example, based on the detection of particles emitted in multimode states by independent sources, which illustrates in a simple way the necessity of extending the original Dirac's criterion.
Fractional Dirac operators and deformed field theory on Clifford algebra
International Nuclear Information System (INIS)
Fractional Dirac equations are constructed and fractional Dirac operators on Clifford algebra in four dimensional are introduced within the framework of the fractional calculus of variations recently introduced by the author. Many interesting consequences are revealed and discussed in some details.
Tools for analysis of Dirac structures on banach spaces
Iftime, Orest V.; Sandovici, Adrian; Golo, Goran
2005-01-01
Power-conserving and Dirac structures are known as an approach to mathematical modeling of physical engineering systems. In this paper connections between Dirac structures and well known tools from standard functional analysis are presented. The analysis can be seen as a possible starting framework
Optical analogue of relativistic Dirac solitons in binary waveguide arrays
International Nuclear Information System (INIS)
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
The Clifford algebra of physical space and Dirac theory
Vaz, Jayme, Jr.
2016-09-01
The claim found in many textbooks that the Dirac equation cannot be written solely in terms of Pauli matrices is shown to not be completely true. It is only true as long as the term β \\psi in the usual Dirac factorization of the Klein–Gordon equation is assumed to be the product of a square matrix β and a column matrix ψ. In this paper we show that there is another possibility besides this matrix product, in fact a possibility involving a matrix operation, and show that it leads to another possible expression for the Dirac equation. We show that, behind this other possible factorization is the formalism of the Clifford algebra of physical space. We exploit this fact, and discuss several different aspects of Dirac theory using this formalism. In particular, we show that there are four different possible sets of definitions for the parity, time reversal, and charge conjugation operations for the Dirac equation.
Dirac particle, gravity, and inertial effects
Huang, Justin C.
Dirac's equation with gravity for a noninertial observer is derived using local coordinate methods. Calculations for the equation are carried out to second order in the local coordinates. For easy application to interference experiments, the Schrödinger form of the Dirac equation with a well defined Hamiltonian in the local coordinates is presented. The presence of gravitational weighting factors in the scalar product lead to hermitian and antihermitian sectors for the Hamiltonian. The antihermitian part depends directly on the curvature and vanishes for zero curvature. The hermitian part which is important for the determination of phases is studied in detail and the nonrelativistic case is obtained by the application of three successive Foldy-Wouthuysen transformations. The results also give local currents and interactions which have pure inertial, pure gravity and mixed sectors. The pure inertial terms are the ones obtained by Hehl and Ni. The pure gravity and mixed sectors have contributions which are electric, magnetic and double magnetic in character. The focus is on the curvature contributions. Some are well within reach of the anticipated accuracy of atomic interferometers currently under consideration and other terms may follow if improvements can be made.
Topological insulators. Dirac equation in condensed matters
International Nuclear Information System (INIS)
Describes the hot newly discovered materials. Presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A starting point to enter the new research field-topological insulators. 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 polyacetylene, 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 insulators and related areas.
DIRAC File Replica and Metadata Catalog
International Nuclear Information System (INIS)
File replica and metadata catalogs are essential parts of any distributed data management system, which are largely determining its functionality and performance. A new File Catalog (DFC) was developed in the framework of the DIRAC Project that combines both replica and metadata catalog functionality. The DFC design is based on the practical experience with the data management system of the LHCb Collaboration. It is optimized for the most common patterns of the catalog usage in order to achieve maximum performance from the user perspective. The DFC supports bulk operations for replica queries and allows quick analysis of the storage usage globally and for each Storage Element separately. It supports flexible ACL rules with plug-ins for various policies that can be adopted by a particular community. The DFC catalog allows to store various types of metadata associated with files and directories and to perform efficient queries for the data based on complex metadata combinations. Definition of file ancestor-descendent relation chains is also possible. The DFC catalog is implemented in the general DIRAC distributed computing framework following the standard grid security architecture. In this paper we describe the design of the DFC and its implementation details. The performance measurements are compared with other grid file catalog implementations. The experience of the DFC Catalog usage in the CLIC detector project are discussed.
Option of Three Pseudo-Dirac Neutrinos
International Nuclear Information System (INIS)
As an alternative for popular see-saw mechanism, the option of three pseudo-Dirac neutrinos is discussed, where 1/2(m(L)+m(R)) (D) for their Majorana and Dirac masses. The actual neutrino mass matrix is assumed in the form of tensor product M(ν) x matrix(2x2 with elements akl where a11=λ(L), a12=1, a21=λ(R) and a22=1) where M(ν) is a neutrino family mass matrix (M(ν)† M(ν) and λ(L,R)≡ m(L,R)/m(D) with m(L), m(R) and m(D) being taken as universal for three neutrino families. It is shown that three neutrino effects (deficits of solar νe's and atmospheric νμ's as well as the possible LSND excess of νe's in accelerator νμ beam) can be nicely described by the corresponding neutrino oscillations, though the LSND effect may, alternatively, be eliminated (by a parameter choice). Atmospheric νμ's oscillate dominantly into ντ's, while solar νe's - into (existing here automatically) Majorana sterile counterparts of νe's. A phenomenological texture for neutrinos, compatible with the proposed description, is briefly presented. (author)
Particle creation and Dirac's large numbers hypothesis
International Nuclear Information System (INIS)
Reference is made to cosmologies based on Dirac's large numbers hypothesis (Nature 139:323 (1937) and Proc. Roy. Soc. A333:403 (1973)). Dirac suggested that continuous creation of matter is required. Two modes of particle creation have been proposed and cosmological models corresponding to each mode have been studied. It is here shown that, within the context of the large numbers hypothesis, the number of particles in the Universe varies as expected (N proportional to t2) so that particle creation is unnecessary. Some undesirable features of cosmologies based on the large numbers hypothesis are also discussed. In order to appreciate fully the results presented for cosmologies based on the large numbers hypothesis a review is made of the corresponding relationship in conventional cosmologies in which the gravitational constant G does not vary with time. It is found, amongst other things that there is no nucleosynthesis in cosmologies based on the large numbers hypothesis, making the large and uniform abundance of He inexplicable. Another undesirable finding with the large numbers hypothesis is the extremely steep decline in the number of particles in the Universe with increasing temperature. Yet another undesirable finding concerns the scattering of photons by electrons in the early Universe; there is no way to establish thermodynamic equilibrium between the photons and electrons, and the black body spectrum of the background radiation is without explanation. (U.K.)
Nuclear data covariances in the Indian context
International Nuclear Information System (INIS)
The topic of covariances is recognized as an important part of several ongoing nuclear data science activities, since 2007, in the Nuclear Data Physics Centre of India (NDPCI). A Phase-1 project in collaboration with the Statistics department in Manipal University, Karnataka (Prof. K.M. Prasad and Prof. S. Nair) on nuclear data covariances was executed successfully during 2007-2011 period. In Phase-I, the NDPCI has conducted three national Theme meetings sponsored by the DAE-BRNS in 2008, 2010 and 2013 on nuclear data covariances. In Phase-1, the emphasis was on a thorough basic understanding of the concept of covariances including assigning uncertainties to experimental data in terms of partial errors and micro correlations, through a study and a detailed discussion of open literature. Towards the end of Phase-1, measurements and a first time covariance analysis of cross-sections for 58Ni (n, p) 58Co reaction measured in Mumbai Pelletron accelerator using 7Li (p,n) reactions as neutron source in the MeV energy region were performed under a PhD programme on nuclear data covariances in which enrolled are two students, Shri B.S. Shivashankar and Ms. Shanti Sheela. India is also successfully evolving a team of young researchers to code nuclear data of uncertainties, with the perspectives on covariances, in the IAEA-EXFOR format. A Phase-II DAE-BRNS-NDPCI proposal of project at Manipal has been submitted and the proposal is undergoing a peer-review at this time. In Phase-2, modern nuclear data evaluation techniques that including covariances will be further studied as a research and development effort, as a first time effort. These efforts include the use of techniques such as that of the Kalman filter. Presently, a 48 hours lecture series on treatment of errors and their propagation is being formulated under auspices of the Homi Bhabha National Institute. The talk describes the progress achieved thus far in the learning curve of the above-mentioned and exciting
Activities on covariance estimation in Japanese Nuclear Data Committee
Energy Technology Data Exchange (ETDEWEB)
Shibata, Keiichi [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1997-03-01
Described are activities on covariance estimation in the Japanese Nuclear Data Committee. Covariances are obtained from measurements by using the least-squares methods. A simultaneous evaluation was performed to deduce covariances of fission cross sections of U and Pu isotopes. A code system, KALMAN, is used to estimate covariances of nuclear model calculations from uncertainties in model parameters. (author)
Linearly arranged polytypic CZTSSe nanocrystals
Fan, Feng-Jia; Wu, Liang; Gong, Ming; Chen, Shi You; Liu, Guang Yao; Yao, Hong-Bin; Liang, Hai-Wei; Wang, Yi-Xiu; Yu, Shu-Hong
2012-01-01
Even colloidal polytypic nanostructures show promising future in band-gap tuning and alignment, researches on them have been much less reported than the standard nano-heterostructures because of the difficulties involved in synthesis. Up to now, controlled synthesis of colloidal polytypic nanocrsytals has been only realized in II-VI tetrapod and octopod nanocrystals with branched configurations. Herein, we report a colloidal approach for synthesizing non-branched but linearly arranged polytypic I2-II-IV-VI4 nanocrystals, with a focus on polytypic non-stoichiometric Cu2ZnSnSxSe4−x nanocrystals. Each synthesized polytypic non-stoichiometric Cu2ZnSnSxSe4−x nanocrystal is consisted of two zinc blende-derived ends and one wurtzite-derived center part. The formation mechanism has been studied and the phase composition can be tuned through adjusting the reaction temperature, which brings a new band-gap tuning approach to Cu2ZnSnSxSe4-x nanocrystals. PMID:23233871
Schroedinger covariance states in anisotropic waveguides
International Nuclear Information System (INIS)
In this paper Squeezed and Covariance States based on Schroedinger inequality and their connection with other nonclassical states are considered for particular case of anisotropic waveguide in LiNiO3. Here, the problem of photon creation and generation of squeezed and Schroedinger covariance states in optical waveguides is solved in two steps: 1. Quantization of electromagnetic field is provided in the presence of dielectric waveguide using normal-mode expansion. The photon creation and annihilation operators are introduced, expanding the solution A-vector(r-vector,t) in a series in terms of the Sturm - Liouville mode-functions. 2. In terms of these operators the Hamiltonian of the field in a nonlinear waveguide is derived. For such Hamiltonian we construct the covariance states as stable (with nonzero covariance), which minimize the Schroedinger uncertainty relation. The evolutions of the three second momenta of q-circumflexj and p-circumflexj are calculated. For this Hamiltonian all three momenta are expressed in terms of one real parameters s only. It is found out how covariance, via this parameter s, depends on the waveguide profile n(x,y), on the mode-distributions u-vectorj(x,y), and on the waveguide phase mismatching Δβ. (author). 37 refs
Cross-covariance functions for multivariate geostatistics
Genton, Marc G.
2015-05-01
Continuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years, scientists developed models that aimed at capturing the spatial behavior for an individual process; only within the last few decades has it become commonplace to model multiple processes jointly. The key difficulty is in specifying the cross-covariance function, that is, the function responsible for the relationship between distinct variables. Indeed, these cross-covariance functions must be chosen to be consistent with marginal covariance functions in such a way that the second-order structure always yields a nonnegative definite covariance matrix. We review the main approaches to building cross-covariance models, including the linear model of coregionalization, convolution methods, the multivariate Matérn and nonstationary and space-time extensions of these among others. We additionally cover specialized constructions, including those designed for asymmetry, compact support and spherical domains, with a review of physics-constrained models. We illustrate select models on a bivariate regional climate model output example for temperature and pressure, along with a bivariate minimum and maximum temperature observational dataset; we compare models by likelihood value as well as via cross-validation co-kriging studies. The article closes with a discussion of unsolved problems. © Institute of Mathematical Statistics, 2015.
Accurate covariance estimation of galaxy-galaxy weak lensing: limitations of jackknife covariance
Shirasaki, Masato; Miyatake, Hironao; Takahashi, Ryuichi; Hamana, Takashi; Nishimichi, Takahiro; Murata, Ryoma
2016-01-01
We develop a method to simulate galaxy-galaxy weak lensing by utilizing all-sky, light-cone simulations. We populate a real catalog of source galaxies into a light-cone simulation realization, simulate the lensing effect on each galaxy, and then identify lensing halos that are considered to host galaxies or clusters of interest. We use the mock catalog to study the error covariance matrix of galaxy-galaxy weak lensing and find that the super-sample covariance (SSC), which arises from density fluctuations with length scales comparable with or greater than a size of survey area, gives a dominant source of the sample variance. We then compare the full covariance with the jackknife (JK) covariance, the method that estimates the covariance from the resamples of the data itself. We show that, although the JK method gives an unbiased estimator of the covariance in the shot noise or Gaussian regime, it always over-estimates the true covariance in the sample variance regime, because the JK covariance turns out to be a...
Progress on Nuclear Data Covariances: AFCI-1.2 Covariance Library
Energy Technology Data Exchange (ETDEWEB)
Oblozinsky,P.; Oblozinsky,P.; Mattoon,C.M.; Herman,M.; Mughabghab,S.F.; Pigni,M.T.; Talou,P.; Hale,G.M.; Kahler,A.C.; Kawano,T.; Little,R.C.; Young,P.G
2009-09-28
Improved neutron cross section covariances were produced for 110 materials including 12 light nuclei (coolants and moderators), 78 structural materials and fission products, and 20 actinides. Improved covariances were organized into AFCI-1.2 covariance library in 33-energy groups, from 10{sup -5} eV to 19.6 MeV. BNL contributed improved covariance data for the following materials: {sup 23}Na and {sup 55}Mn where more detailed evaluation was done; improvements in major structural materials {sup 52}Cr, {sup 56}Fe and {sup 58}Ni; improved estimates for remaining structural materials and fission products; improved covariances for 14 minor actinides, and estimates of mubar covariances for {sup 23}Na and {sup 56}Fe. LANL contributed improved covariance data for {sup 235}U and {sup 239}Pu including prompt neutron fission spectra and completely new evaluation for {sup 240}Pu. New R-matrix evaluation for {sup 16}O including mubar covariances is under completion. BNL assembled the library and performed basic testing using improved procedures including inspection of uncertainty and correlation plots for each material. The AFCI-1.2 library was released to ANL and INL in August 2009.
Manifest Covariant Hamiltonian Theory of General Relativity
Cremaschini, Claudio
2016-01-01
The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called "DeDonder-Weyl" formalism to the treatment of classical fields in curved space-time. The theory is based on a synchronous variational principle for the Einstein equation, formulated in terms of superabundant variables. The technique permits one to determine the continuum covariant Hamiltonian structure associated with the Einstein equation. The corresponding continuum Poisson bracket representation is also determined. The theory relies on first-principles, in the sense that the conclusions are reached in the framework of a non-perturbative covariant approach, which allows one to preserve both the 4-scalar nature of Lagrangian and Hamiltonian densities as well as the gauge invariance property of the theory.
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.
Parametric number covariance in quantum chaotic spectra.
Vinayak; Kumar, Sandeep; Pandey, Akhilesh
2016-03-01
We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated. PMID:27078354
Notes on Cosmic Censorship Conjecture revisited: Covariantly
Hamid, Aymen I M; Maharaj, Sunil D
2016-01-01
In this paper we study the dynamics of the trapped region using a frame independent semi-tetrad covariant formalism for general Locally Rotationally Symmetric (LRS) class II spacetimes. We covariantly prove some important geometrical results for the apparent horizon, and state the necessary and sufficient conditions for a singularity to be locally naked. These conditions bring out, for the first time in a quantitative and transparent manner, the importance of the Weyl curvature in deforming and delaying the trapped region during continual gravitational collapse, making the central singularity locally visible.
Canonical quantization of generally covariant systems
International Nuclear Information System (INIS)
Kretschmann (1917) argued that general relativity does not satisfy any relativity principle and that it is actually a theory of absolute space-time. The issues raised by Kretschmann, that of Hamiltonian dynamics and of canonical quantization of generally covariant systems, are discussed. The questions raised are: what is the role of space-time diffeomorphisms in Hamiltonian dynamics of generally covariant systems, what is the role of isometries in Hamiltonian dynamics of such systems and what happens to both problems in canonical quantization. (author)
Modular invariance and covariant loop calculus
International Nuclear Information System (INIS)
The covariant loop calculus provides and efficient technique for computing explicit expressions for the density on moduli space corresponding to arbitrary (bosonic string) loop diagrams. Since modular invariance is not manifest, however, we carry out a detailed comparison with known explicit 2- and 3- loop results derived using analytic geometry (1 loop is known to be ok). We establish identity to 'high' order in some moduli and exactly in others. Agreement is found as a result of various non-trivial cancellations, in part related to number theory. We feel our results provide very strong support for the correctness of the covariant loop calculus approach. (orig.)
On covariant quantization of massive superparticle
International Nuclear Information System (INIS)
We have obtained, by dimensional reduction of the Green-Schwarz superstring, the action of a D=9 massive superparticle. Because of the presence of a Wess-Zumino term the action has Siegel symmetry. Harmonic variables realizing the coset space (SO(1,8))/SO(8) have been introduced to separate covariantly the fermionic constraints into irreducible first and second class constraints. Lorentz covariant gauge fixing conditions are imposed and the resulting BRST charge is of rank one and very simple in structure. (author). 21 refs
A violation of the covariant entropy bound?
Masoumi, Ali
2014-01-01
Several arguments suggest that the entropy density at high energy density $\\rho$ should be given by the expression $s=K\\sqrt{\\rho/G}$, where $K$ is a constant of order unity. On the other hand the covariant entropy bound requires that the entropy on a light sheet be bounded by $A/4G$, where $A$ is the area of the boundary of the sheet. We find that in a suitably chosen cosmological geometry, the above expression for $s$ violates the covariant entropy bound. We consider different possible explanations for this fact; in particular the possibility that entropy bounds should be defined in terms of volumes of regions rather than areas of surfaces.
Exchange rate arrangements from extreme to normal
Emilija Beker
2006-01-01
The paper studies theoretical and empirical location dispersion of exchange rate arrangements - rigid-intermediate-flexible regimes, in the context of extreme arrangements of a currency board, dollarization and monetary union, moderate characteristics of intermediate arrangements (adjustable pegs, crawling pegs and target zones) and imperative-process normalization in the form of a managed or clean floating system. It is established that de iure and de facto classifications generate fear of f...
Exchange rate arrangements from extreme to normal
Beker Emilija
2006-01-01
The paper studies theoretical and empirical location dispersion of exchange rate arrangements - rigid-intermediate-flexible regimes, in the context of extreme arrangements of a currency board, dollarization and monetary union moderate characteristics of intermediate arrangements (adjustable pegs crawling pegs and target zones) and imperative-process "normalization" in the form of a managed or clean floating system. It is established that de iure and de facto classifications generate "fear of ...
Flexible Working Time Arrangements in Bulgaria
Beleva, Iskra
2009-01-01
The objective of this paper is to analyze the flexible working time arrangements in Bulgaria, using a life-course perspective. Two important features have to be outlined, namely: underdeveloped flexible forms of employment in the country, including working time arrangement, and lack of previous analysis on flexible working time arrangements from the angle of life-course perspective. The author describes the regulatory framework, collective agreements at national and company level as a frame w...
Axial anomaly and index theorem for Dirac-Kaehler fermions
International Nuclear Information System (INIS)
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.)
Strain-Engineering the Gauge Potential of Dirac fermions in PECVD-grown Graphene
Hsu, Chen-Chih; Teague, Marcus; Wang, Jaiqing; Yeh, Nai-Chang
Non-trivial strain can induce pseudo-magnetic fields in graphene so that the electronic properties of Dirac fermions can be tuned by controlling the strain on graphene. Here we employ nearly strain-free single-domain PECVD-graphene1 to induce controlled strain by placing graphene on nanostructured substrates. Strain-induced gauge potentials and pseudo-magnetic fields can be manifested by the local tunneling conductance peaks at quantized energies.2,3 Additionally, pseudo-magnetic field-induced local spontaneous time-reversal symmetry breaking can be revealed by spatially alternating presence and absence of the zero mode in the tunneling conductance spectra.2,3 We also employ molecular dynamics simulations to determine the spatial distribution of the pseudo-magnetic field for a given nanostructure. We find that a tetrahedron-like nanostructure can be an effective ``valley splitter'' to separate the trajectories of Dirac fermions of opposite pseudo-spins. Proper design and arrangement of several valley filters can function as a ``valley propagator'' to guide valley-polarized currents. We plan to verify the valley Hall effect associated with a valley splitter and to assess the feasibility of realistic valleytronic applications.
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 ...
Massive mesons in Weyl-Dirac theory
Mirabotalebi, S.; Ahmadi, F.; Salehi, H.
2008-01-01
In order to study the mass generation of the vector fields in the framework of a conformal invariant gravitational model, the Weyl-Dirac theory is considered. The mass of the Weyl’s meson fields plays a principal role in this theory, it connects basically the conformal and gauge symmetries. We estimate this mass by using the large-scale characteristics of the observed universe. To do this we firstly specify a preferred conformal frame as a cosmological frame, then in this frame, we introduce an exact possible solution of the theory. We also study the dynamical effect of the massive vector meson fields on the trajectories of an elementary particle. We show that a local change of the cosmological frame leads to a Hamilton-Jacobi equation describing a particle with an adjustable mass. The dynamical effect of the massive vector meson field presents itself in the form of a correction term for the mass of the particle.
New formulation of Dirac's constraint theory
International Nuclear Information System (INIS)
Dirac's method of obtaining a Hamiltonian H(q1 ... qsub(N), p1 ... psub(N),t) corresponding to a Lagrangian L(q1 ... qsub(N),q1 ... qsub(N),t) for which the usual expression Σpsub(i)q - L does not allow one to find the solutions of the Euler-Lagrange equations via Hamiltons canonical equations is formulated in a more explicit way by making extensive use of the eigenvectors to the matrix theta2L/thetaqsub(i)thetaqsub(k). The question of secondary and so on and first and seond-class constraints is well separated from the basic problem of finding a Hamiltonian and is also discussed in terms of certain eigenvectors. It is also shown that different but equivalent forms of the Hamiltonians exist. (orig.)
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...
Chaos, Dirac observables and constraint quantization
Dittrich, Bianca; Koslowski, Tim A; Nelson, Mike I
2015-01-01
There is good evidence that full general relativity is non-integrable or even chaotic. We point out the severe repercussions: differentiable Dirac observables and a reduced phase space do not exist in non-integrable constrained systems and are thus unlikely to occur in a generic general relativistic context. Instead, gauge invariant quantities generally become discontinuous, thus not admitting Poisson-algebraic structures and posing serious challenges to a quantization. Non-integrability also renders the paradigm of relational dynamics cumbersome, thereby straining common interpretations of the dynamics. We illustrate these conceptual and technical challenges with simple toy models. In particular, we exhibit reparametrization invariant models which fail to be integrable and, as a consequence, can either not be quantized with standard methods or lead to sick quantum theories without a semiclassical limit. These troubles are qualitatively distinct from semiclassical subtleties in unconstrained quantum chaos and...
From "Dirac combs" to Fourier-positivity
Giraud, Bertrand G
2015-01-01
Motivated by various problems in physics and applied mathematics, we look for constraints and properties of real Fourier-positive functions, i.e. with positive Fourier transforms. Properties of the "Dirac comb" distribution and of its tensor products in higher dimensions lead to Poisson resummation, allowing for a useful approximation formula of a Fourier transform in terms of a limited number of terms. A connection with the Bochner theorem on positive definiteness of Fourier-positive functions is discussed. As a practical application, we find simple and rapid analytic algorithms for checking Fourier-positivity in 1- and (radial) 2-dimensions among a large variety of real positive functions. This may provide a step towards a classification of positive positive-definite functions.
Absorbing layers for the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Pinaud, Olivier, E-mail: pinaud@math.colostate.edu
2015-05-15
This work is devoted to the construction of perfectly matched layers (PML) for the Dirac equation, that not only arises in relativistic quantum mechanics but also in the dynamics of electrons in graphene or in topological insulators. While the resulting equations are stable at the continuous level, some care is necessary in order to obtain a stable scheme at the discrete level. This is related to the so-called fermion doubling problem. For this matter, we consider the numerical scheme introduced by Hammer et al. [19], and combine it with the discretized PML equations. We state some arguments for the stability of the resulting scheme, and perform simulations in two dimensions. The perfectly matched layers are shown to exhibit, in various configurations, superior absorption than the absorbing potential method and the so-called transport-like boundary conditions.
Massive photons and Dirac monopoles: electric condensate and magnetic confinement
International Nuclear Information System (INIS)
Full text: The main objective of this presentation is to discuss how to generalize the Dirac prescription for the introduction of monopoles when the vector bosons are massive, helping to clarify some misunderstandings found in the literature like the claims that Dirac monopoles and massive photons cannot coexist, that the unphysical Dirac strings would become observable and, consequently, that it would be impossible to consistently derive the Dirac charge quantization condition when the vector bosons are massive. One of the main points involved in this issue regards the fact that the Dirac theory of monopoles was indeed developed in the context of massless vector bosons and its extension to the case of massive photons is not immediate. Another key point refers to the very general observation that a massive photon generates a Meissner effect, which confines magnetic probe sources. Aside with these observations, one must also keep in mind that being unphysical artifacts of a particular formalism, there are no physical processes that could turn the Dirac strings (or more generally, Dirac branes) into observables, since it would violate Elitzur's theorem. This point is in fact a consistency condition that must be always satisfied in order to the formalism be consistent. These basic observations can be gathered together through the use of the so-called Julia-Toulouse approach for condensation of charges and defects Here, the Julia-Toulouse approach is used to argue that massive photons can coexist consistently with Dirac monopoles. The Proca theory is obtained via the Julia-Toulouse approach as a hydrodynamic effective theory describing an electric condensate and the mass of the vector boson is responsible for generating a Meissner effect which confines the magnetic defects in pairs of monopoles-antimonopoles connected by physical open magnetic vortices instead of unphysical Dirac branes. These open vortices are brane invariants corresponding to the physical confining
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
New Dirac equation from the view point of particle
International Nuclear Information System (INIS)
According to the classical approach, especially the Lorentz Invariant Dirac Equation, when particles are bound to each other, the interaction term appears as a quantity belonging to the “field”. In this work, as a totally new approach, we propose to alter the rest masses of the particles due to their interaction, as much as their respective contributions to the static binding energy. Thus we re-write and solve the Dirac Equation for the hydrogen atom, and amazingly, obtain practically the same numerical results for the ground states, as those obtained from the Dirac Equation.
ENDF-6 File 30: Data covariances obtained from parameter covariances and sensitivities
International Nuclear Information System (INIS)
File 30 is provided as a means of describing the covariances of tabulated cross sections, multiplicities, and energy-angle distributions that result from propagating the covariances of a set of underlying parameters (for example, the input parameters of a nuclear-model code), using an evaluator-supplied set of parameter covariances and sensitivities. Whenever nuclear data are evaluated primarily through the application of nuclear models, the covariances of the resulting data can be described very adequately, and compactly, by specifying the covariance matrix for the underlying nuclear parameters, along with a set of sensitivity coefficients giving the rate of change of each nuclear datum of interest with respect to each of the model parameters. Although motivated primarily by these applications of nuclear theory, use of File 30 is not restricted to any one particular evaluation methodology. It can be used to describe data covariances of any origin, so long as they can be formally separated into a set of parameters with specified covariances and a set of data sensitivities
Red'kov, V M
2011-01-01
Tetrad based equation for Dirac-K\\"{a}hler particle is solved in spherical coordinates in the flat Minkocski space-time. Spherical solutions of boson type (J =0,1,2,...) are constructed. After performing a special transformation over spherical boson solutions of the Dirac-K\\"{a}hler equation, 4 \\times 4-matrices U(x) \\Longrightarrow V(x), simple linear expansions of the four rows of new representativeof the Dirac--K\\"{a}hler field V(x) in terms of spherical fermion solutions \\Psi_{i}(x) of the four ordinary Dirac equations have been derived. However, this fact cannot be interpreted as the possibility not to distinguish between the Dirac-K\\"{a}hler field and the system four Dirac fermions. The main formal argument is that the special transformation (I \\otimes S(x)) involved does not belong to the group of tetrad local gauge transformation for Dirac-K\\"{a}hler field, 2-rank bispinor under the Lorentz group. Therefore, the linear expansions between boson and fermion functions are not gauge invariant under the gr...
Covariant derivative expansion of the heat kernel
International Nuclear Information System (INIS)
Using the technique of labeled operators, compact explicit expressions are given for all traced heat kernel coefficients containing zero, two, four and six covariant derivatives, and for diagonal coefficients with zero, two and four derivatives. The results apply to boundaryless flat space-times and arbitrary non-Abelian scalar and gauge background fields. (orig.)
Covariates of Sesame Street Viewing by Preschoolers.
Spaner, Steven D.
A study was made of nine covariates as to their discriminating power between preschoolers who watch Sesame Street regularly and preschoolers who do not watch Sesame Street, Surveyed were 372 3-4 year old children on 9 variables. The nine variables were: race, socioeconomic status, number of siblings, child's birth order, maternal age, maternal…
Optimal covariate designs theory and applications
Das, Premadhis; Mandal, Nripes Kumar; Sinha, Bikas Kumar
2015-01-01
This book primarily addresses the optimality aspects of covariate designs. A covariate model is a combination of ANOVA and regression models. Optimal estimation of the parameters of the model using a suitable choice of designs is of great importance; as such choices allow experimenters to extract maximum information for the unknown model parameters. The main emphasis of this monograph is to start with an assumed covariate model in combination with some standard ANOVA set-ups such as CRD, RBD, BIBD, GDD, BTIBD, BPEBD, cross-over, multi-factor, split-plot and strip-plot designs, treatment control designs, etc. and discuss the nature and availability of optimal covariate designs. In some situations, optimal estimations of both ANOVA and the regression parameters are provided. Global optimality and D-optimality criteria are mainly used in selecting the design. The standard optimality results of both discrete and continuous set-ups have been adapted, and several novel combinatorial techniques have been applied for...
Economical Phase-Covariant Cloning of Qudits
Buscemi, Francesco; D'Ariano, Giacomo Mauro; Macchiavello, Chiara
2004-01-01
We derive the optimal N to M phase-covariant quantum cloning for equatorial states in dimension d with M=kd+N, k integer. The cloning maps are optimal for both global and single-qudit fidelity. The map is achieved by an ``economical'' cloning machine, which works without ancilla.
Modern applications of covariant density functional theory
International Nuclear Information System (INIS)
Modern applications of Covariant Density Functional Theory (CDFT) are discussed. First we show a systematic investigation of fission barriers in actinide nuclei within constraint relativistic mean field theory allowing for triaxial deformations. In the second part we discuss a microscopic theory of quantum phase transitions (QPT) based on the relativistic generator coordinate method. (author)
Linear transformations of variance/covariance matrices
Parois, P.J.A.; Lutz, M.
2011-01-01
Many applications in crystallography require the use of linear transformations on parameters and their standard uncertainties. While the transformation of the parameters is textbook knowledge, the transformation of the standard uncertainties is more complicated and needs the full variance/covariance
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Shephard, N.
2004-01-01
This paper analyses multivariate high frequency financial data using realized covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis, and covariance. It will be based on a fixed interval of time (e.g., a day or week), allowing the...... number of high frequency returns during this period to go to infinity. Our analysis allows us to study how high frequency correlations, regressions, and covariances change through time. In particular we provide confidence intervals for each of these quantities....
Deformed Hamilton-Jacobi Method in Covariant Quantum Gravity Effective Models
Benrong, Mu; Yang, Haitang
2014-01-01
We first briefly revisit the original Hamilton-Jacobi method and show that the Hamilton-Jacobi equation for the action $I$ of tunnelings of a fermionic particle from a charged black hole can be written in the same form as that of a scalar particle. For the low energy quantum gravity effective models which respect covariance of the curved spacetime, we derive the deformed model-independent KG/Dirac and Hamilton-Jacobi equations using the methods of effective field theory. We then find that, to all orders of the effective theories, the deformed Hamilton-Jacobi equations can be obtained from the original ones by simply replacing the mass of emitted particles $m$ with a parameter $m_{eff}$ that includes all the quantum gravity corrections. Therefore, in this scenario, there will be no corrections to the Hawking temperature of a black hole from the quantum gravity effects if its original Hawking temperature is independent of the mass of emitted particles. As a consequence, our results show that breaking covariance...
Simulik, V M
2015-01-01
The investigation of arXiv 1409.2766v2 [quant-ph] has been continued by the general form of the numerous equations with partial values of arbitrary spin, which were considered in above mentioned preprint. The general forms of quantum-mechanical and covariant equations for arbitrary spin together with the general description of the arbitrary spin field formalism are presented. The corresponding relativistic quantum mechanics of arbitrary spin is given as the system of axioms. Previously ignored partial example of the spin s=(0,0) particle-antiparticle doublet is considered. The partial example of spin s=(3/2,3/2) particle-antiparticle doublet is highlighted. The new 64 dimensional Clifford--Dirac algebra over the field of real numbers is suggested. The general operator, which transformed the relativistic canonical quantum mechanics of arbitrary spin into the locally covariant field theory, has been introduced. Moreover, the study of the place of the results given in arXiv 1409.2766v2 [quant-ph] among the resul...
Covariant momentum projection of the soliton bag: recoil corrections to the hadronic masses
International Nuclear Information System (INIS)
A central problem in calculations based on relativistic bags is that of projection onto an eigenstate of zero momentum and the subsequent covariant boosting of that state to a non-zero momentum eigenstate. We are here particularly concerned with relativistic bag models. The prototype of such models is the MIT bag model. Along with a number of derivative models, it shares the common feature of a surface boundary condition to confine the quarks. The Lagrangian contains coordinates which describe the surface, but the time derivatives of these coordinates do not appear. This complicates quantization which can, however, be accomplished through the techniques of Dirac constraints. It is important to work in a fully quantum mechanical framework. A model which fulfills that requirement, is covariant, and is tractable is the soliton bag model of Freidberg and Lee. This is a model for the low energy properties of QCD in which hadrons appear as solitons in a scalar field with quarks trapped inside the structures. The soliton model, for the present discussion, contains (massless) quarks interacting with a nonlinear scalar field sigma; the momentum operator conjugate to sigma is π = sigma, and the two satisfy the usual canonical equal-time commutation reltions. 12 references
Encoding and Decoding Procedures for Arrangements
Directory of Open Access Journals (Sweden)
Alexander A. Babaev
2012-05-01
Full Text Available This article discusses an algorithm based on the encoding procedure for representing a set of arrangement elements as a single number. Also the author provides the procedure for the inverse transformation of the code into arrangement elements. In addition the Article includes recommendations on the use of the above procedures in combinatorial algorithms of optimization.
The fundamental group of complex hyperplanes arrangements
International Nuclear Information System (INIS)
In this paper we suggest a new method to compute the fundamental group of the complemented of any complex hyperplanes arrangements. Our computation is based on a construction called labyrinth of an arrangement of complex lines. The method can be generalized for the case of an arbitrary affine curve. (author). 9 refs, 3 figs
The making of local hospital discharge arrangements
DEFF Research Database (Denmark)
Burau, Viola; Bro, Flemming
2015-01-01
with doctors, nurses and secretaries conducted at two different stages in the process of the making of the local discharge arrangements. Results From the analysis, two distinct local models of discharge arrangements that connect more or less directly to existing professional practice emerge: an ‘add...
Governance Arrangements for State Owned Enterprises
Vagliasindi, Maria
2008-01-01
The aim of this paper is to shed new light on key challenges in governance arrangements for state owned enterprises in infrastructure sectors. The paper provides guidelines on how to classify the fuzzy and sometimes conflicting development goals of infrastructure and the governance arrangements needed to reach such goals. Three policy recommendations emerge. First, some of the structures i...
Unravelling Lorentz Covariance and the Spacetime Formalism
Directory of Open Access Journals (Sweden)
Cahill R. T.
2008-10-01
Full Text Available We report the discovery of an exact mapping from Galilean time and space coordinates to Minkowski spacetime coordinates, showing that Lorentz covariance and the space- time construct are consistent with the existence of a dynamical 3-space, and “absolute motion”. We illustrate this mapping first with the standard theory of sound, as vibra- tions of a medium, which itself may be undergoing fluid motion, and which is covari- ant under Galilean coordinate transformations. By introducing a different non-physical class of space and time coordinates it may be cast into a form that is covariant under “Lorentz transformations” wherein the speed of sound is now the “invariant speed”. If this latter formalism were taken as fundamental and complete we would be lead to the introduction of a pseudo-Riemannian “spacetime” description of sound, with a metric characterised by an “invariant speed of sound”. This analysis is an allegory for the development of 20th century physics, but where the Lorentz covariant Maxwell equa- tions were constructed first, and the Galilean form was later constructed by Hertz, but ignored. It is shown that the Lorentz covariance of the Maxwell equations only occurs because of the use of non-physical space and time coordinates. The use of this class of coordinates has confounded 20th century physics, and resulted in the existence of a “flowing” dynamical 3-space being overlooked. The discovery of the dynamics of this 3-space has lead to the derivation of an extended gravity theory as a quantum effect, and confirmed by numerous experiments and observations
Spin dynamics in the relativistic Kapitza-Dirac effect
Energy Technology Data Exchange (ETDEWEB)
Ahrens, Sven; Bauke, Heiko; Keitel, Christoph H. [Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, Heidelberg (Germany); Mueller, Carsten [Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, Heidelberg (Germany); Institut fuer Theoretische Physik I, Heinrich-Heine-Universitaet Duesseldorf, Universitaetsstrasse 1, 40225 Duesseldorf (Germany)
2013-07-01
The Kapitza-Dirac effect, which is the diffraction of electrons at a standing wave of light, has been observed experimentally in the last decade. The availability of novel high intensity X-ray laser sources calls for a relativistic description of this electron scattering process. We discuss the quantum dynamics of the electron diffraction by solving the Dirac equation in momentum space. We demonstrate that generalized 3-photon Kapitza-Dirac scattering of the electron with the laser beam occurs if the energy and the momentum of corresponding classical kinematics are conserved. This 3-photon Kapitza-Dirac effect features a tunable electron spin-flip probability. We emphasize the significance of the electron's spin-degree of freedom by a comparison with corresponding quantum dynamics of the Klein-Gordon equation.
Higher-order Dirac solitons in binary waveguide arrays
International Nuclear Information System (INIS)
We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range. - Highlights: • Higher-order Dirac solitons in nonlinear binary waveguide arrays are numerically demonstrated. • Amplitude profiles of higher-order Dirac solitons are periodic during propagation. • The period of higher-order Dirac solitons decreases when the soliton order increases
Dirac Branes, Characteristic Currents and Anomaly Cancellations in 5-Branes
Lechner, K; Lechner, Kurt; Marchetti, Pieralberto
2001-01-01
The aim of this note is to discuss, in a somewhat informal language, the cancellation of anomalies (in topologically trivial space-time) for 5-branes using as "building blocks": i) a generalization to p-branes of the Dirac strings of monopoles (Dirac branes) and a refinement of this idea involving a geometric regularization of Dirac branes, leading to the formalism of "characteristic currents" ii) the PST formalism . As an example of the potentiality of the developed framework we discuss in some detail the anomaly cancellation in the D=10 effective theory of heterotic string and 5-brane coupled to supergravity, where the anomaly inflow is automatically generated. Some remarks are also made on a similar approach to the problem of anomaly cancellation in the effective theory of M5-brane coupled to D=11 supergravity, developed in collaboration with M.Tonin, where however still as open problem remains a Dirac anomaly.
Higher-order 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); Duong, Dũng C. [Department of Physics, Le Quy Don University, 236 Hoang Quoc Viet str., 10000 Hanoi (Viet Nam)
2015-10-15
We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range. - Highlights: • Higher-order Dirac solitons in nonlinear binary waveguide arrays are numerically demonstrated. • Amplitude profiles of higher-order Dirac solitons are periodic during propagation. • The period of higher-order Dirac solitons decreases when the soliton order increases.
Dirac mass dynamics in a multidimensional nonlocal parabolic equation
Lorz, Alexander; Perthame, Benoit
2010-01-01
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 co-exist? 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 structure of gradient flow. 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.
Semiclassical dynamics of Dirac and Weyl particles in rotating coordinates
Dayi, O F; Yunt, E
2016-01-01
Semiclassical kinetic theory of Dirac particles in the presence of external electromagnetic fields and global rotation is established. To provide the Hamiltonian formulation of Dirac particles a symplectic two-form which is a matrix in spin indices is proposed. The particle number and current densities for the Dirac particles are acquired in the helicity basis. Following a similar procedure, semiclassical kinetic theory of the Weyl particles is accomplished. It is shown that phase space dynamics of the Weyl and Dirac particles are directly linked and their continuity equations with source terms are derived. The anomalies and anomalous chiral effects due to the external electromagnetic fields and angular velocity of the frame are calculated.
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.
Dirac-Point Solitons in Nonlinear Optical Lattices
Xie, Kang; Boardman, Allan D; Guo, Qi; Shi, Zhiwei; Jiang, Haiming; Hu, Zhijia; Zhang, Wei; Mao, Qiuping; Hu, Lei; Yang, Tianyu; Wen, Fei; Wang, Erlei
2015-01-01
The discovery of a new type of solitons occuring in periodic systems without photonic bandgaps is reported. Solitons are nonlinear self-trapped wave packets. They have been extensively studied in many branches of physics. Solitons in periodic systems, which have become the mainstream of soliton research in the past decade, are localized states supported by photonic bandgaps. In this Letter, we report the discovery of a new type of solitons located at the Dirac point beyond photonic bandgaps. The Dirac point is a conical singularity of a photonic band structure where wave motion obeys the famous Dirac equation. These new solitons are sustained by the Dirac point rather than photonic bandgaps, thus provides a sort of advance in conceptual understanding over the traditional gap solitons. Apart from their theoretical impact within soliton theory, they have many potential uses because such solitons have dramatic stability characteristics and are possible in both Kerr material and photorefractive crystals that poss...
Dirac brackets for the chiral Schwinger model with chiral constraint
International Nuclear Information System (INIS)
Dirac brackets for the chiral Schwinger model with chiral constraint are derived perturbatively from the correlation function by the BJL limit method. The results show that the Poissons brackets are not consistent in this theory. (author)
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).
All you need to know about the Dirac equation
Weinberger, Peter
2008-01-01
Abstract A very brief introduction is given to all that is needed to appreciate the formal structure of the Dirac equation and why -- without destroying this structure -- it cannot be reduced to a Paul-Schrodinger type equation.