A Non-Perturbative Solution of the Zero-Dimensional <math>λϕ4</math> Field Theory

Nota de FísicaPublicado

A Non-Perturbative Solution of the Zero-Dimensional $<math>\lambda\varphi^{4}</math>$ Field Theory

A.P.C. Malbouisson; R. Portugal; N.F. Svaiter

1999

Autores: A.P.C. Malbouisson; R. Portugal; N.F. Svaiter
Tipo: Nota de Física
Status: Publicado
Data de publicação: 1999
Descrição: We have done a study of the zero-dimensional <math>\lambda\varphi^{4}\,\!</math> model. Firstly, we exhibit the partition function as a simple exact expression in terms of the Macdonald's function for <math>Re(\lambda)>0 \,\!</math> . Secondly, an analytic continuation of the partition function for <math>Re(\lambda)<0 \,\!</math> is performed, and we obtain an expression defined in the complex coupling constant plane <math> \lambda\,\!</math>, for <math>|arg\,\lambda|<\pi\,\!</math> . Consequently, the partition function understood as an analytic continuation is defined for all values of <math>\lambda\,\!</math> , except for a branch cut along the real negative<math> \lambda\,\!</math> axis. We also evaluate the partition function on perturbative grounds, using the Borel summation technique and we found that in the common domain of validity for <math>Re(\lambda)>0\,\!</math> , it coincides precisely with the exact expression.
Ano: 1999
Número: CBPF-NF-049/99
Vínculo com tese: Não
Vínculo com bolsa: Não