Nonmetricity and torsion induced by dilaton gravity in two dimension

We develop a theory in which there are couplings amongst Dirac spinor, dilaton and non-Riemannian gravity and explore the nature of connection-induced dilaton couplings to gravity and Dirac spinor when the theory is reformulated in terms of the Levi-Civita connection. After presenting some exact solutions without spinors, we investigate the minimal spinor couplings to the model and in conclusion we cannot find any nontrivial dilaton couplings to spinor.     

A General Method for Obtaining Degenerate Solutions to the Dirac and Weyl Equations and a Discussion on the Experimental Detection of Degenerate States

In this work, a general method is described for obtaining degenerate solutions of the Dirac equation, corresponding to an infinite number of electromagnetic 4-potentials and fields, which are explicitly calculated. More specifically, using four arbitrary real functions, one can automatically construct a spinor that satisfies the Dirac equation for an infinite number of electromagnetic 4-potentials, defined by those functions. An interesting characteristic of these solutions is that, in the case of Dirac particles with nonzero mass, the degenerate spinors should be localized, both in space and time. The method is also extended to the cases of massless Dirac and Weyl particles, where the localization of the spinors is no longer required. Finally, two experimental methods are proposed for detecting the presence of degenerate states.     

Opening the Pandora’s box of quantum spinor fields

Lounesto’s classification of spinors is a comprehensive and exhaustive algorithm that, based on the bilinears covariants, discloses the possibility of a large variety of spinors, comprising regular and singular spinors and their unexpected applications in physics and including the cases of Dirac, Weyl, and Majorana as very particular spinor fields. In this paper we pose the problem of an analogous classification in the framework of second quantization. We first discuss in general the nature of the problem. Then we start the analysis of two basic bilinear covariants, the scalar and pseudoscalar, in the second quantized setup, with expressions applicable to the quantum field theory extended to all types of spinors. One can see that an ampler set of possibilities opens up with respect to the classical case. A quantum reconstruction algorithm is also proposed. The Feynman propagator is extended for spinors in all classes.     

Dirac and Maxwell equations in the Clifford and spin-Clifford bundles

We show how to write the Dirac and the generalized Maxwell equations (including monopoles) in the Clifford and spin-Clifford bundles (of differential forms) over space-time (either of signaturep=1,q=3 orp=3,q=1). In our approach Dirac and Maxwell fields are represented by objects of the same mathematical nature and the Dirac and Maxwell equations can then be directly compared. We show also that all presentations of the Maxwell equations in (matrix) Dirac-like spinor form appearing in the literature can be obtained by choosing particular global idempotents in the bundles referred to above. We investigate also the transformation laws under the action of the Lorentz group of Dirac and Maxwell fields (defined as algebraic spinor sections of the Clifford or spin-Clifford bundles), clearing up several misunderstandings and misconceptions found in the literature. Among the many new results, we exhibit a factorization of the Maxwell field into two-component spinor fields (Weyl spinors), which is important.     

Flag-dipole and flagpole spinor fluid flows in Kerr spacetimes

Flagpole and flag-dipole spinors are particular classes of spinor fields that has been recently used in different branches of theoretical physics. In this paper, we study the possibility and consequences of these spinor fields to induce an underlying fluid flow structure in the background of Kerr spacetimes. We show that flag-dipole spinor fields are solutions of the equations of motion in this context. To our knowledge, this is the second time that this class of spinor field appears as a physical solution, the first one occurring as a solution of the Dirac equation in ESK gravities.     

A Modified Theory of Gravity with Torsion and Its Applications to Cosmology and Particle Physics

In this paper we consider the most general least-order derivative theory of gravity in which not only curvature but also torsion is explicitly present in the Lagrangian, and where all independent fields have their own coupling constant: we will apply this theory to the case of ELKO fields, which is the acronym of the German Eigenspinoren des LadungsKonjugationsOperators designating eigenspinors of the charge conjugation operator, and thus they are a Majorana-like special type of spinors; and to the Dirac fields, the most general type of spinors. We shall see that because torsion has a coupling constant that is still undetermined, the ELKO and Dirac field equations are endowed with self-interactions whose coupling constant is undetermined: we discuss different applications according to the value of the coupling constants and the different properties that consequently follow. We highlight that in this approach, the ELKO and Dirac field’s self-interactions depend on the coupling constant as a parameter that may even make these non-linearities manifest at subatomic scales.     

Gauge Formalism for General Relativity and Fermionic Matter

A new formulation for General Relativity is developed; it is a canonical, global and geometrically well posed formalism in which gravity is described using only variables related to spin structures. It does not require any background metric fixing and it applies to quite general manifolds, i.e. it does not need particular symmetries requirement or global frames. A global Lagrangian framework for Dirac spinors is also provided; conserved quantities and superpotentials are given. The interaction between gravity and spinors is described in a minimal coupling fashion with respect to the new variables and the Hilbert stress tensor of spinor fields is computed, providing the gravitational field generated by spinors. Finally differences and analogies between this formalism and gauge theories are discussed.     

On the interaction of the Dirac oscillator with the Aharonov–Casher system in topological defect backgrounds

In this paper, we study the influence of the Aharonov–Casher effect [Y. Aharonov, A. Casher, Phys. Rev. Lett. 53 (1984) 319] on the Dirac oscillator in three different scenarios of general relativity: the Minkowski spacetime, the cosmic string spacetime and the cosmic dislocation spacetime. In this way, we solve the Dirac equation and obtain the energy levels for bound states and the Dirac spinors for positive-energy solutions. We show that the relativistic energy levels depend on the Aharonov–Casher geometric phase. We also discuss the influence of curvature and torsion on the relativistic energy levels and the Dirac spinors due to the topology of the cosmic string and cosmic dislocation spacetimes.     

Spineurs,opérateurs de dirac et variations de métriques

In this article a geometric process to compare spinors for different metrics is constructed. It makes possible the extension to spinor fields of a variant of the Lie derivative (called the metric Lie derivative), giving a geometric approach to a construction originally due to Yvette Kosmann. The comparison of spinor fields for two different Riemannian metrics makes the study of the variation of Dirac operators feasible. For this it is crucial to take into account the fact that the bundle in which the sections acted upon by the Dirac operators take their values is changing. We also give the formulas for the change in the eigenvalues of the Dirac operator. We conclude by giving a few cases in which an eigenvalue is stationary.

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Recherche soutenue par le programme européen C.E.E. G.A.D.G.E.T. SC1-0105-C     

Triality and Quantization of Singularities in Massive Fermion

It is proved that fermions can acquire the mass through the additional non-integrable exponential factor. For this propose the special vector potential associated with the spinor field was introduced. Such a vector potential has closk relation with the. triality property in Dirac spinors and plays crucial role in the construction of massive term. It is shown that the change in phase of a wavefunction round any closed curve with the possibility of there being singularities in our vector potential will lead to the law of quantization of physical constants including the mass. The triality properties of Dirac's spinors are studied and it leads to a double covering vector representation of Dirac spinor field. It is proved that massive Dirac equation in the bosonic representation is self-dual.     

Boson-Fermion Duality in A2 Toda Field Theory

In this paper, we consider a two-dimensional integrable and conformal invariant field theory with two Dirac spinors and two scalar fields. This model has chiral symmetry and CP-like symmetry. Moreover, this model also has a Neother current depending only on the matter field. At last, we bosonize the spinor fields.     

Interacting Gravitational and Dirac Fields with Torsion

A general interaction scheme is formulated in a general space–time with torsion from the action principle by considering the gravitational, the Dirac, and the torsion field as independent fields. Some components of the torsion field come out to be automatically zero. Both the resulting Einstein-like and the Dirac-like fields equations contain nonlinear terms given by a self-interaction of the Dirac spinor and originally produced by torsion. The theory is specialized to the Robertson–Walker space–time without torsion. To solve he corresponding equations, that still have a complex structure, the spin coefficients have to be calculated explicitly from the tetrad employed. A solution, even if simple and elementary, is then determined.     

Couplings of a collection of BF models to matter theories

The couplings of a collection of BF models to matter theories are addressed in the framework of the antifield-BRST deformation procedure. The general theory is exemplified in the case where the matter fields are a set of Dirac spinors and respectively a collection of real scalar fields.Received: 7 September 2004, Revised: 21 March 2005, Published online: 18 May 2005PACS: 11.10.Ef     

Hamiltonian formulation of the theory of interacting gravitational and electron fields

The action which describes the interaction of gravitational and electron fields is expressed in canonical form. In addition to general covariance, it exhibits the local Lorentz invariance associated with four-dimensional rotations of the local orthonormal frames. The corresponding Hamiltonian constraints are derived and their (Dirac) bracket relations given. The derivative coupling of the gravitational tetrad and spinor fields is not present in the Hamiltonian, but rather in the unusual bracket relations of the field variables in the theory. If the timelike leg of the tetrad field is fixed to be normal to the x^o = constant hyper-surfaces (“time gauge”) the derivative coupling drops from the theory in the sense that the relation between the gravitational velocities and momenta is the same as when the spinor fields are absent.     

Algebraic spinors and directed random walks in the McKane-Parisi-Sourlas theorem

We present the Dirac propagator as a random walk on anS ^D–1 sphere for Majorana spinors, even spinor space, Dirac spinors, and Chevalley-Crumeyrolle spinors built from Minkowski space. We propose the Dirac propagator constructed from Chevalley-Crumeyrolle spinors as the generators of a Markov process such that McKane-Parisi-Sourlas theorem can be applied to calculate the expectation values for functions of local times.     

The Einstein–Cartan–Elko system

The present paper analyses the Einstein‐Cartan theory of gravitation with Elko spinors as sources of curvature and torsion. After minimally coupling the Elko spinors to torsion, the spin angular momentum tensor is derived and its structure is discussed. It shows a much richer structure than the Dirac analogue and hence it is demonstrated that spin one half particles do not necessarily yield only an axial vector torsion component. Moreover, it is argued that the presence of Elko spinors partially solves the problem of minimally coupling Maxwell fields to Einstein‐Cartan theory.     

Dirac-Hestenes spinor fields on Riemann-Cartan manifolds

In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the RCST), thereby being certain particular sections of a new bundle named the spin-Clifford bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to Geroch's theorem concerning the existence of spinor structures in a Lorentzian spacetime. We introduce also the covariant and algebraic Dirac spinor fields and compare these with DHSF, showing that all three kinds of spinor fields contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-Kähler spinor fields are of this type), showing that they cannot be used to describe fermionic fields. We develop a rigorous theory for the covariant derivatives of Clifford fields (sections of the Clifford bundle, CB) and of Dirac-Hestenes spinor fields. We show how to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian field theory in the Clifford bundle.     

7-Dimensional compact Riemannian manifolds with Killing spinors

Using a link between Einstein-Sasakian structures and Killing spinors we prove a general construction principle of odd-dimensional Riemannian manifolds with real Killing spinors. In dimensionn=7 we classify all compact Riemannian manifolds with two or three Killing spinors. Finally we classify nonflat 7-dimensional Riemannian manifolds with parallel spinor fields.     

Spinors in the Lorentz group and their implications for quantum mechanics

We investigate what the precise meaning is of a spinor in the rotation and Lorentz groups. We find that spinors correspond to a special coding of a group element. This is achieved by coding the whole reference frame into a special isotropic or “zero-length” vector. The precise form of that special vector in the Lorentz group is lacking in the literature, and this leads to some confusion, as the point that the coding can be complete has been missed. We then apply these ideas to quantum mechanics and find that the Dirac equation can be derived by just trying to describe a rotating electron. PACS 02.20.-a; 03.65.-w; 03.65.Fd     

Constraints on torsion from bounds on lorentz violation

Exceptional sensitivity to space-time torsion can be achieved by searching for its couplings to fermions. Recent experimental searches for Lorentz violation are exploited to extract new constraints involving 19 of the 24 independent torsion components down to levels of order 10(-31) GeV.