Quantum statistical correlations in thermal field theories: Boundary effective theory

Journal Article · Wed Sep 15 04:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.065010· OSTI ID:21421193

Bessa, A ^[1]; Brandt, F T ^[2]; Fraga, E S ^[3]

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1. Escola de Ciencias e Tecnologia, Universidade Federal do Rio Grande do Norte, Caixa Postal 1524, 59072-970, Natal, RN (Brazil)
2. Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP (Brazil)
3. Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972, Rio de Janeiro, RJ (Brazil)

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 {phi}{sub c}, 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 Schroedinger 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 {phi}{sub c}, 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.

• OSTI ID: 21421193
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 6 Vol. 82; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
CALCULATION METHODS
CORRELATIONS
DENSITY MATRIX
EIGENSTATES
EXPANSION
FIELD THEORIES
FUNCTIONS
INTERACTIONS
MATRICES
PARTITION FUNCTIONS
PHYSICAL PROPERTIES
PROPAGATOR
SCALAR FIELDS
SEMICLASSICAL APPROXIMATION
THERMODYNAMIC PROPERTIES