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Maxwell-Dirac stress-energy tensor in terms of Fierz bilinear currents


Inglis, S and Jarvis, P, Maxwell-Dirac stress-energy tensor in terms of Fierz bilinear currents, Annals of Physics, 366 pp. 57-75. ISSN 0003-4916 (2016) [Refereed Article]

Copyright Statement

Copyright 2016 Elsevier Inc.

DOI: doi:10.1016/j.aop.2016.01.007


We analyse the stress-energy tensor for the self-coupled Maxwell-Dirac system in the bilinear current formalism, using two independent approaches. The first method used is that attributed to Belinfante: starting from the spinor form of the action, the well-known canonical stress-energy tensor is augmented, by extending the Noether symmetry current to include contributions from the Lorentz group, to a manifestly symmetric form. This form admits a transcription to bilinear current form. The second method used is the variational derivation based on the covariant coupling to general relativity. The starting point here at the outset is the transcription of the action using, as independent field variables, both the bilinear currents, together with a gauge invariant vector field (a proxy for the electromagnetic vector potential). A central feature of the two constructions is that they both involve the mapping of the Dirac contribution to the stress-energy from the spinor fields to the equivalent set of bilinear tensor currents, through the use of appropriate Fierz identities. Although this mapping is done at quite different stages, nonetheless we find that the two forms of the bilinear stress-energy tensor agree. Finally, as an application, we consider the reduction of the obtained stress-energy tensor in bilinear form, under the assumption of spherical symmetry.

Item Details

Item Type:Refereed Article
Keywords:stress-energy tensor, Dirac field, Maxwell-Dirac equations, Fierz identities, symmetry reduction
Research Division:Mathematical Sciences
Research Group:Mathematical physics
Research Field:Algebraic structures in mathematical physics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the physical sciences
UTAS Author:Inglis, S (Mr Shaun Inglis)
UTAS Author:Jarvis, P (Dr Peter Jarvis)
ID Code:115123
Year Published:2016
Web of Science® Times Cited:2
Deposited By:Mathematics and Physics
Deposited On:2017-03-08
Last Modified:2017-11-01

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