1997/12/05 by S. Deser, Luca Griguolo, L. Griguolo +2 · 5 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum Electrodynamics and Casimir Effect #cond-mat.supr-con #hep-th
paper · pdf · doi:10.1103/physrevd.57.7444
published as Phys.Rev.D57:7444-7459,1998 · 36 pages, RevTeX, no figures
arxiv created 1997/12/05 · openalex publication_date 1998/06/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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 \ensuremathζ-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.