Spinor Effective Action in Curved Space

Details Spinor Effective Action in Curved Space Spinor Effective Action in Curved Space

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002nmgm.meet.1411z&link_type=abstract

"THE NINTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and R

Physics

Scientific paper

In this contribution, we would like to report recent results obtained in collaboration with E. Elizalde and G. Cognola [hep-th/9910038]. To begin with, we recall the motivations: The Euclidean one-loop effective action Γ for spinor operator A (first order operator.) are usually expressed by means the "folk theorem" Γ ≡ ln det √ {A^ + A} = (1)/(2) ln det A^ + A in which the second order differential operator L = A+A is the spinor Laplacian. Is that totally correct? Recall that the ultraviolet divergences of Γ due to the functional determinant may be cured by zeta-function regularization. As a result, the regularized functional determinat is finite and is given by log det L = - ζ '(0{{|}}L), where the zeta-function is given by ζ (s|L) = ∑ limits i λ i-s = (1)/({Γ (s))} ∫ 0∞ dt ts - 1} {Tr} e- tL} , Here no problems exist because L is a non negative operator ...

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