Abstract
We propose a technique for regularizing the determinant of a non-invertible elliptic operator restricted to the complement of its nilpotent elements. We apply this approach to the study of chiral changes in the fermionic path-integral variables.
Similar content being viewed by others
References
Hawking, S.W.: Zeta function regularization of path integrals in curved spacetime. Commun. Math. Phys.55, 133–148 (1977)
Seeley, R.T.: Complex powers of an elliptic operator. Am. Math. Soc. Proc. Sym. Pure Math.10, 288–307 (1967)
Gamboa-Saraví, R.E., Muschietti, M.A., Solomin, J.E.: On perturbation theory for regularized determinants of differential operators. Commun. Math. Phys.89, 363–373 (1983)
Agmon, S.: Lectures on elliptic boundary value problems. New York: Van Nostrand Company, Inc. 1965
Calderón, A.P.: Lecture Notes on pseudo-differential operators and elliptic boundary value problems, I. Instituto Argentino de Matemática, (1976)
Fujikawa, K.: Path integral for gauge theories with fermions. Phys. Rev. D21, 2848 (1980)
Adler, S.: Axial-vector vertex in spinor electrodynamics, Phys. Rev.177, 2426 (1969);
Bell, J., Jackiw, R.: A PCAC Puzzle: π0→γγ in the σ-Model. Nuovo Cimento60 A, 47 (1969)
Berezin, F.: The method of second quantization. New York: Academic Press 1969
Gamboa-Saraví, R.E., Muschietti, M.A., Schaposnik, F.A., Solomin, J.E.: Chiral symmetry and functional integral. La Plata University preprint (1983). Ann. Phys. (in press)
Author information
Authors and Affiliations
Additional information
Communicated by H. Araki
Rights and permissions
About this article
Cite this article
Gamboa-Saraví, R.E., Muschietti, M.A. & Solomin, J.E. On the regularized determinant for non-invertible elliptic operators. Commun.Math. Phys. 93, 407–415 (1984). https://doi.org/10.1007/BF01258537
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01258537