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Scientific paper
Jun 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003aipc..668..154s&link_type=abstract
COSMOLOGY AND GRAVITATION: Xth Brazilian School of Cosmology and Gravitation; 25th Anniversary (1977-2002). AIP Conference Proc
Other
Mathematical And Relativistic Aspects Of Cosmology, Singularities And Cosmic Censorship, Quantum Electrodynamics
Scientific paper
We discuss the strong-coupling expansion in the (λΦ4)d theory, quantum electrodynamics and also in different scalar models in a d-dimensional Euclidean space, and the singularities of this perturbative expansion assuming the ultra-local approximation. We analyse the analytic structure of the zero-dimensional generating functions in the complex coupling constant plane for the case of (λ J4)d and also quantum electrodynamics. We find a superposition between a branch point and essential singularity at g0 = 0 in the scalar model and also in quantum electrodynamics. Further, still using the strong-coupling expansion as a formal representation for the generating functional of complete Schwinger functions given by Z(h), we present an interacting field theory model that we call the Sinh-Gordon model (V(g1, g2; J) = g1(cosh(g2 J) - 1)) where the ultra-local generating functional given by Q0(h) coincides with the generating functional of complete Schwinger functions. In other words, the ultra-local approximation is exact, i.e. Z(h) ≡ Q0(h). As a consequence, it is possible to calculate the vacuum energy per unit-volume. From the distribution of the the zeros of the modified Bessel function of third kind it is possible to show that the model has a finite vacuum energy per unit-volume. Finally we sketch how it is possible to obtain a renormalized generating functional for all Schwinger functions, going beyond the ultra-local approximation.
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