Quantum statistical correlations in thermal field theories: boundary effective theory

• Autor(a) principal: Moreira, André Bessa
• Data de Publicação: 2010
• Outros Autores: Brandt, Fernando Tadeu Caldeira, Carvalho Filho, Carlos Alberto Aragão de, Fraga, Eduardo Souza
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFRN
• Texto Completo: https://repositorio.ufrn.br/jspui/handle/123456789/29790
• topic: Quantum statistical correlations; Thermal field theories; Boundary effective theory

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field ϕc, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schrödinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field ϕc, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example