Structure of (real-time) P(⌽)2 Green’s Functions
By Green’s functions in the P(⌽)2 model we shall mean vacuum expectation values of time-ordered products of field operators. The central role played by such objects in any many-body quantum mechanical problem is well-established. Here we discuss three general structural questions for Green’s functions: first, how to compute derivatives with respect to coupling constants; second, how to take them apart by a kind of pull-through formula; and finally as an application of the first two, we sketch a proof that the perturbation series is asymptotic to all orders.
KeywordsPerturbation Series Path Integral Representation Real Time Version Quantum Field Model Real Time Theory
Unable to display preview. Download preview PDF.
- [D2]J. Dimock, The P ( ⌽ )2 Green’s Functions: Smoothness in the Coupling Constant, to appear in J. Func. Anal.Google Scholar
- [D3]J. Dimock, The P(⌽)2 Green’s Functions: Asymptotic Perturbation Expansion, to appear in Helv. Phys. Acta.Google Scholar
- [EEF]J.-P. Eckmann, H. Epstein, J. Fröhlich, Asymptotic Perturbation Expansion for the S-matrix and the Definition of Time Ordered Functions in Relativistic Quantum Field Models, preprint.Google Scholar
- [GJ]J. Glimm, A. Jaffe, Two and Three Body equations in Quantum Field Models, to appear Commun. Math. Phys.Google Scholar
- [OS]K. Osterwalder, R. Seneor, The Scattering Matrix is Nontrivial for Weakly Coupled P(⌽)2 Models, preprint.Google Scholar