Abstract
The purpose of this paper is to show that P(ϕ) 2 Euclidean quantum field theories satisfy axioms of the type advocated by Graeme Segal.
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Bogachev, V.: Gaussian Measures. Mathematical Surveys and Monographs 62, Providence, RI: Amer. Math. Soc. 1998
Bourbaki, N.: Elements of Mathematique. Fasc. XXXV, Livre VI: Integration, Ch IX, Actualites Sci. Indust., No. 1343, Paris: Hermann, 1969
Burghelea, D., Friedlander, L., Kappeler, T.: Mayer-Vietoris type formulas for determinants of elliptic operators. J. Funct. Anal. 107, 34–65 (1992)
Colella, P., Lanford, O.E.: Sample field behavior for the free Markov random field. In: Constructive Quantum Field Theory, edited by G. Velo and A. Wightman, Lecture Notes in physics, 25, Berlin:Springer-Verlag, 1973, pp. 44–70
Dimock, J.: Transition amplitudes and sewing properties for bosons on the Riemann sphere. J. Math. Phys. 48 (5) (2007)
Dixmier, J.: Les algebres d’operateurs dans l’espace Hilbertien. Paris:Gauthier Villars, 1969
Folland, G.: Introduction to Partial Differential Equations. Mathematical Notes, Princeton, NJ: Princeton University Press, 1976
Friedlander, L.: PhD thesis, Dept. Math., MIT, 1989
Glimm, J., Jaffe, A.: Quantum Physics, a Functional Integral Point of View. Berlin-Heidelberg- New York:Springer-Verlag, 1981
Guillemin, V., Sternberg, S.: Geometric Asymptotics. Math. Surveys. no. 14, Providence, RI: Amer. Math. Soc., 1977
Howe, R.: The oscillator semigroup. In: The Mathematical Heritage of Hermann Weyl. edited by R. Wells, Proceedings of Symposia in Pure Mathematics, Vol. 48, Providence, RI: Amer. Math. Soc., 1989, pp. 61–132
Kontsevich, M., Vishik, S.: Geometry of determinants of elliptic operators. In: Functional analysis on the eve of the 21st century, Vol. 1 (New Brunswich, NJ, 1993) Progr. Math. 131, Boston, MA: Birkhä user, 1995, pp. 173–197
Segal, G.: The definition of conformal field theory, In: Geometry and Quantum Field Theory, edited by U. Tillmann, Oxford: Oxford Univ. Press, 2004, pp. 423–577
Segal, G.: Lectures at Stanford University, 1996 and 2006, unpublished
Simon, B.: The P(ϕ)2 Euclidean (Quantum) Field Theory. Princeton Series in Physics, Princeton, NJ: Princeton Univ. Press, 1974
Weinstein, A.: Symplectic geometry. Bull. Amer. Math. Soc. 5(1), 1–13 (1981)
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Pickrell, D. P(ϕ) 2 Quantum Field Theories and Segal’s Axioms. Commun. Math. Phys. 280, 403–425 (2008). https://doi.org/10.1007/s00220-008-0467-8
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DOI: https://doi.org/10.1007/s00220-008-0467-8