How (not) to teach Lorentz covariance of the Dirac equation
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
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
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
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
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
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
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
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.
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
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
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
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
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
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.
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
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
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
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.
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
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
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?
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...
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
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
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.
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...
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.
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.
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
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...
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
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
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
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
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
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
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.
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...
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
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
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 [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
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
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
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.
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.
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
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
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)
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
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...
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
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.
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
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
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
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
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
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
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
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
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...
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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...
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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 ...