EFFECTIVE QED ACTIONS - REPRESENTATIONS, GAUGE-INVARIANCE, ANOMALIES,AND MASS EXPANSIONS

We analyze and give explicit representations for the effective Abelian vector gauge field actions generated by charged fermions with particu lar attention to the thermal regime in odd dimensions, where spectral asymmetry can be present. We show, through zeta-function regularizatio n, that both small and large gauge invariances are preserved at any te mperature and for any number of fermions at the usual price of anomali es: helicity (parity) invariance will be lost in even (odd) dimensions , and in the latter even at zero mass. Gauge invariance dictates a ver y general ''Fourier'' representation of the action in terms of the hol onomies that carry the novel, large gauge-invariant, information. We s how that large (unlike small) transformations and hence their Ward ide ntities are not perturbative order-preserving, and clarify the role of (properly redefined) Chern-Simons terms in this context. From a power ful representation of the action in terms of massless heat kernels, we so able to obtain rigorous gauge-invariant expansions, for both small and large fermion masses, of its separate parity even and odd parts i n arbitrary dimension. The representation also displays both the nonpe rturbative origin of a finite renormalization ambiguity and its physic al resolution by requiring decoupling at infinite mass. Finally, we il lustrate these general results by explicit computation of the effectiv e action for some physical examples of field configurations in the thr ee-dimensional case, where our conclusions on finite temperature effec ts may have physical relevance. Non-Abelian results will be presented separately.