Lessons of spin and torsion: Reply to “Consistent coupling to Dirac fields in teleparallelism”

Yu. N. Obukhov; J. G. Pereira

doi:10.1103/PhysRevD.69.128502

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Lessons of spin and torsion: Reply to “Consistent coupling to Dirac fields in teleparallelism”

Yu. N. Obukhov^*

J. G. Pereira

Institute for Theoretical Physics, University of Cologne, 50923 Köln, Germany

Instituto de Física Teórica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900 São Paulo SP, Brazil

^*On leave from Department of Theoretical Physics, Moscow State University, 117234 Moscow, Russia.

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Phys. Rev. D 69, 128502 – Published 2 June, 2004

DOI: https://doi.org/10.1103/PhysRevD.69.128502

Abstract

In reply to the criticism made by Mielke in the preceding Comment on our recent paper, we once again explicitly demonstrate the inconsistency of the coupling of a Dirac field to gravitation in the teleparallel equivalent of general relativity. Moreover, we stress that the mentioned inconsistency is generic for all sources with spin and is by no means restricted to the Dirac field. In this sense the $SL (4, R)$ -covariant generalization of the spinor fields in the teleparallel gravity theory is irrelevant to the inconsistency problem.

Original Article

Metric-affine approach to teleparallel gravity

Yu. N. Obukhov and J. G. Pereira

Phys. Rev. D 67, 044016 (2003)

References (10)

K. Hayashi and T. Shirafuji, Phys. Rev. D 19, 3524 (1979).
V.C. de Andrade and J.G. Pereira, Phys. Rev. D 56, 4689 (1997).
V.C. de Andrade, L.C.T. Guillen, and J.G. Pereira, Phys. Rev. Lett. 84, 4533 (2000).
V.C. de Andrade, L.C.T. Guillen, and J.G. Pereira, Phys. Rev. D 64, 027502 (2001).
Yu.N. Obukhov and J.G. Pereira, Phys. Rev. D 67, 044016 (2003).
E.W. Mielke, preceding Comment, Phys. Rev. D 69, 128501 (2004).
Our notation and conventions are as in [5][8]. In particular, the Greek indices $α, β, \dots$ label the anholonomic frame components (e.g., $ϑ^{α}),$ and the Latin indices $i, j, \dots$ label the local spacetime coordinates (e.g., $x^{i}$ and ${dx}^{i}) .$
F.W. Hehl, J.D. McCrea, E.W. Mielke, and Y. Ne’eman, Phys. Rep. 258, 1 (1995).
J.W. Maluf, Phys. Rev. D 67, 108501 (2003).
Yu.N. Obukhov, E.J. Vlachynsky, W. Esser, and F.W. Hehl, Phys. Rev. D 56, 7769 (1997).

[c1] K. Hayashi and T. Shirafuji, Phys. Rev. D 19, 3524 (1979).

[c2] V.C. de Andrade and J.G. Pereira, Phys. Rev. D 56, 4689 (1997).

[c3] V.C. de Andrade, L.C.T. Guillen, and J.G. Pereira, Phys. Rev. Lett. 84, 4533 (2000).

[c4] V.C. de Andrade, L.C.T. Guillen, and J.G. Pereira, Phys. Rev. D 64, 027502 (2001).

[c5] Yu.N. Obukhov and J.G. Pereira, Phys. Rev. D 67, 044016 (2003).

[c6] E.W. Mielke, preceding Comment, Phys. Rev. D 69, 128501 (2004).

[c7] Our notation and conventions are as in [5][8]. In particular, the Greek indices $α, β, \dots$ label the anholonomic frame components (e.g., $ϑ^{α}),$ and the Latin indices $i, j, \dots$ label the local spacetime coordinates (e.g., $x^{i}$ and ${dx}^{i}) .$

[c8] F.W. Hehl, J.D. McCrea, E.W. Mielke, and Y. Ne’eman, Phys. Rep. 258, 1 (1995).

[c9] J.W. Maluf, Phys. Rev. D 67, 108501 (2003).

[c10] Yu.N. Obukhov, E.J. Vlachynsky, W. Esser, and F.W. Hehl, Phys. Rev. D 56, 7769 (1997).

Physical Review D

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Lessons of spin and torsion: Reply to “Consistent coupling to Dirac fields in teleparallelism”

Abstract

Comments & Replies

Dirac spinor fields in the teleparallel gravity: Comment on “Metric-affine approach to teleparallel gravity”

Consistent coupling to Dirac fields in teleparallelism: Comment on “Metric-affine approach to teleparallel gravity”

Comment on “Metric-affine approach to teleparallel gravity”

Original Article

Metric-affine approach to teleparallel gravity

References (10)

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