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Effective QED actions: Representations, gauge invariance, anomalies, and mass expansions

Deser, S. and Griguolo, L. and Seminara, D. (1998) Effective QED actions: Representations, gauge invariance, anomalies, and mass expansions. Physical Review D, 57 (12). pp. 7444-7459. ISSN 2470-0010. doi:10.1103/PhysRevD.57.7444.

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We analyze and give explicit representations for the effective Abelian vector gauge field actions generated by charged fermions with particular attention to the thermal regime in odd dimensions, where spectral asymmetry can be present. We show, through ζ-function regularization, that both small and large gauge invariances are preserved at any temperature and for any number of fermions at the usual price of anomalies: helicity (parity) invariance will be lost in even (odd) dimensions, and in the latter even at zero mass. Gauge invariance dictates a very general “Fourier” representation of the action in terms of the holonomies that carry the novel, large gauge-invariant, information. We show that large (unlike small) transformations and hence their Ward identities are not perturbative order-preserving, and clarify the role of (properly redefined) Chern-Simons terms in this context. From a powerful representation of the action in terms of massless heat kernels, we are able to obtain rigorous gauge-invariant expansions, for both small and large fermion masses, of its separate parity even and odd parts in arbitrary dimension. The representation also displays both the nonperturbative origin of a finite renormalization ambiguity and its physical resolution by requiring decoupling at infinite mass. Finally, we illustrate these general results by explicit computation of the effective action for some physical examples of field configurations in the three-dimensional case, where our conclusions on finite temperature effects may have physical relevance. Non-Abelian results will be presented separately.

Item Type:Article
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URLURL TypeDescription Paper
Deser, S.0000-0001-9285-9434
Additional Information:© 1998 American Physical Society. (Received 8 December 1997; published 15 May 1998) This work is supported by NSF Grant No. PHY-9315811, in part by funds provided by the U.S. DOE under Cooperative Agreement No. DE-FC02-94ER40818 and by INFN, Frascati, Italy.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FC02-94ER40818
Istituto Nazionale di Fisica Nucleare (INFN)UNSPECIFIED
Issue or Number:12
Classification Code:PACS number(s): 11.10.Wx, 11.15.Bt, 11.30.Er, 11.30.Rd
Record Number:CaltechAUTHORS:20170110-124101919
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Official Citation:Effective QED actions: Representations, gauge invariance, anomalies, and mass expansions S. Deser, L. Griguolo, and D. Seminara Phys. Rev. D 57, 7444
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73380
Deposited By: George Porter
Deposited On:10 Jan 2017 21:34
Last Modified:11 Nov 2021 05:15

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