On the chiral anomaly in non-Riemannian spacetimes

Obukhov, Yuri N.; Mielke, Eckehard W.; Budczies, J.; Hehl, Friedrich W.

doi:10.1007/bf02551525

Cited by 60 publications

(70 citation statements)

References 18 publications

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“…In this paper, however, the explicit result has not been achieved because of the cumbersome way of calculation. Let us indicate only some of the subsequent calculations [116,142,135,193,52,51,65] and other papers devoted to the closely related issues like index theorems, topological structures and Wess-Zumino [189] conditions [143,46,128,192,151]. We shall not go into details of these works but only present the most important and simple expression for the anomaly and give a brief review of other results.…”

Section: Chiral Anomaly In the Spaces With Torsion Cancellation Of Amentioning

confidence: 99%

Physical aspects of the space–time torsion

2002

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Abstract. We review many quantum aspects of torsion theory and discuss the possibility of the space-time torsion to exist and to be detected. The paper starts, in Chapter 2, with a pedagogical introduction to the classical gravity with torsion, that includes also interaction of torsion with matter fields. Special attention is paid to the conformal properties of the theory. In Chapter 3, the renormalization of quantum theory of matter fields and related topics, like renormalization group, effective potential and anomalies, are considered. Chapter 4 is devoted to the action of spinning and spinless particles in a space-time with torsion, and to the discussion of possible physical effects generated by the background torsion. In particular, we review the upper bounds for the magnitude of the background torsion which are known from the literature. In Chapter 5, the comprehensive study of the possibility of a theory for the propagating completely antisymmetric torsion field is presented. It is supposed that the propagating field should be quantized, and that its quantum effects must be described by, at least, some effective low-energy quantum field theory. We show, that the propagating torsion may be consistent with the principles of quantum theory only in the case when the torsion mass is much greater than the mass of the heaviest fermion coupled to torsion. Then, universality of the fermion-torsion interaction implies that torsion itself has a huge mass, and can not be observed in realistic experiments. Thus, the theory of quantum matter fields on the classical torsion background can be formulated in a consistent way, while the theory of dynamical torsion meets serious obstacles. In Chapter 6, we briefly discuss the string-induced torsion and the possibility to induce torsion action and torsion itself through the quantum effects of matter fields.

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Section: Chiral Anomaly In the Spaces With Torsion Cancellation Of Amentioning

confidence: 99%

Physical aspects of the space–time torsion

2002

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“…This Lagrangian was studied extensively in the framework of various approaches to gravity on the basis of the de Sitter group, see [55][56][57][58], for example. The same action was also used in [22,23] for the derivation of the conserved current associated with a vector field.…”

Section: B Regularization Via Relocalizationmentioning

confidence: 99%

Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry

2006

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We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in many covariant and noncovariant(ly looking) ways. An interesting mathematical fact underlies such a diversity: there is a certain ambiguity in a definition of the (Lorentz-) covariant generalization of the usual Lie derivative. Using this freedom, we develop a general approach to the construction of invariant conserved currents generated by an arbitrary vector field on the spacetime. This is done in any dimension, for any Lagrangian of the gravitational field and of a (minimally or nonminimally) coupled matter field. A development of the ''regularization via relocalization'' scheme is used to obtain finite conserved quantities for asymptotically nonflat solutions. We illustrate how our formalism works by some explicit examples.

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“…Mielke et al have questioned the contribution of the NY term to the chiral anomaly as well as its non triviality after renormalization [36,37,38]. Contribution of the NY term to chiral anomaly has been confirmed by Obukhov et al [39] and in an independent analysis [40], computing the index of the Dirac operator on a four dimensional compact manifold, it has been shown that the integral of the NY term is necessarily an integer, it is the difference of two Chern classes SO(5) and SO(4) and therefore being topological N is non-renormalizable. In our present analysis this bears an important implication as we see from (43) that topological N globally defines the gravitational constant, at least in the case where the cosmological constant is the only source of gravity, by the equation…”

Section: Euler-lagrange Equations and Gravitational Constantmentioning

confidence: 99%

de Sitter group and Einstein-Hilbert Lagrangian

Mahato¹

2004

Phys. Rev. D

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Axial vector torsion in the Einstein-Cartan space U 4 is considered here. By picking a particular term from the SO(4, 1) Pontryagin density and then modifying it in a SO(3, 1) invariant way, we get a Lagrangian density with Lagrange multipliers. Then considering torsion and torsion-less connection as independent fields, it has been found that κ and λ of Einstein-Hilbert Lagrangian, appear as integration constants in such a way that κ has been found to be linked with the topological Nieh-Yan density of U 4 space.

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On the chiral anomaly in non-Riemannian spacetimes

Cited by 60 publications

References 18 publications

Physical aspects of the space–time torsion

Physical aspects of the space–time torsion

Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry

de Sitter group and Einstein-Hilbert Lagrangian

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