--- title: "The Strong-Coupling Expansion and the Ultra-local Approximation in Scalar Theories • CBPF Index" description: "CBPF INDEX es el sistema de seguimiento de la producción científica y tecnológica del CBPF. En él se puede obtener la lista de publicaciones de artículos, libros, informes técnicos, etc. de toda la comunidad del CBPF." canonical_url: "https://index.cbpf.br/es/publicacoes/6ad2a767639f62b11adbaf7d" locale: es meta: "og:description": "CBPF INDEX es el sistema de seguimiento de la producción científica y tecnológica del CBPF. En él se puede obtener la lista de publicaciones de artículos, libros, informes técnicos, etc. de toda la comunidad del CBPF." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_The%2BStrong-Coupling%2BExpansion%2Band%2Bthe%2BUltra-local%2BApproximation%2Bin%2BScalar%2BTheories%2Ctipo_~Tm90YSBkZSBGw61zaWNh%2Ccor_~I2E4MmMwMA%2Cautores_N.F.%2BSvaiter%2Cdetalhe_2003%2Csecao_Publicaciones%2Cp_Ii9lcy9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmFmN2Qi%2Cs_lEpMa622kfzPuxGW.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "The Strong-Coupling Expansion and the Ultra-local Approximation in Scalar Theories • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_The%2BStrong-Coupling%2BExpansion%2Band%2Bthe%2BUltra-local%2BApproximation%2Bin%2BScalar%2BTheories%2Ctipo_~Tm90YSBkZSBGw61zaWNh%2Ccor_~I2E4MmMwMA%2Cautores_N.F.%2BSvaiter%2Cdetalhe_2003%2Csecao_Publicaciones%2Cp_Ii9lcy9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmFmN2Qi%2Cs_lEpMa622kfzPuxGW.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Nota de Física****Publicado** # **The Strong-Coupling Expansion and the Ultra-local Approximation in Scalar Theories** **N.F. Svaiter** 2003 [**Descargar PDF **0,5 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbaf7d/pdf) [**Contactar al responsable**](mailto:apub@cbpf.br?subject=The%20Strong-Coupling%20Expansion%20and%20the%20Ultra-local%20Approximation%20in%20Scalar%20Theories) ## **Datos de la publicación**
Autores
N.F. Svaiter
Tipo
Nota de Física
Estado
Publicado
Fecha de publicación
2003
Descripción
We discuss the strong-coupling expansion in Euclidean field theory. In a formal representation for the Schwinger functional, we treat the off-diagonal terms of the Gaussian factor as a perturbation about the remaining terms of the functional integral. Consequently, we are developing the perturbative expansion around the ultra-local model, where fields defined in different points of the Euclidean space are decoupled. We first study the strong-coupling expansion in the $(\lambda\varphi^{4})_{d}$ theory. Assuming the ultra-local approximation, we study the singularities of this perturbative expansion, analysing the analytic structure of the zero-dimensional generating function in the complex coupling constant plane. Second, we discuss the ultra-local generating functional in two idealized field theory models defined by the following interaction Lagrangians: ${\cal{L}_{II}} (g_{1},g_{2};\varphi)=g_{1}\varphi^{\,p}(x)+g_{2}\varphi^{-p}(x)$, and the sinh-Gordon model, i.e., ${\cal{L}_{III}}(g_{3},g_{4};\,\varphi)= g_{3}\left(\cosh (g_{4}\,\varphi(x))-1\right)$. To control the divergences of the strong-coupling perturbative expansion two different steps are used through the paper. First we introduce a lattice structure only to give a meaning to the ultra-local generating functional. On the other hand, the resulting perturbative expansion is an expansion for the continuum and not for the lattice approximation. Thus, using an analytic regularization procedure we discuss briefly how it is possible to obtain a renormalized Schwinger functional associated with these models, going beyond the ultra-local approximation withouth using a lattice regularization procedure.
Año
2003
Número
CBPF-NF-014/03
Vínculo con tesis
No
Vínculo con beca
No
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