Perfect 3-Dimensional Lattice Actions for 4-Dimensional Quantum Field Theories at Finite Temperature

Abstract

We propose a two-step procedure to study the order of phase transitions at finite temperature in electroweak theory and in simplified models thereof. In a first step a coarse grained free energy is computed by perturbative methods. It is obtained in the form of a 3-dimensional perfect lattice action by a block spin transformation. It has finite temperature dependent coefficients. In this way the UV-problem and the infrared problem is separated in a clean way. In the second step the effective 3-dimensional lattice theory is treated in a nonperturbative way, either by the Feynman-Bogoliubov method (solution of a gap equation), by real space renormalization group methods, or by computer simulations. In this paper we outline the principles for ${\phi }^4$-theory and scalar electrodynamics. The Bałaban-Jaffe block spin transformation for the gauge field is used. It is known how to extend this transformation to the nonabelian case, but this will not be discussed here.

path to figures (in added uu-file) revised, no other changes 33 pages, 3 figures, latex

References in corpus (9)

• The Effective Potential and First-Order Phase Transitions: Beyond Leading Order
• Perfect lattice action for asymptotically free theories
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• Some Two-Loop Corrections to the Finite Temperature Effective Potential in the Electroweak Theory
• Electroweak Baryogenesis in the Adiabatic Limit
• Finite Temperature Effective Potential for the Abelian Higgs Model to the Order $e^4,{\lambda }^2$
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• A Self Consistent Study of the Phase Transition in the Scalar Electroweak Theory at Finite Temperature

Cited by in corpus (11)

• Nonperturbative Evolution Equation for Quantum Gravity
• On the non-perturbative gluon mass and heavy quark physics
• Fixed point action for the massless lattice Schwinger model
• Finite T Electroweak Phase Transition on the Lattice
• Partial Path Integration of Quantum Fields: Two-Loop Analysis of the SU(2) Gauge-Higgs Model at Finite Temperature
• Non-perturbative singularity structure of gluon and quark propagators
• Static correlation lengths in QCD at high temperature and finite density
• Thermal variational principle and gauge fields
• 1-Loop improved lattice action for the nonlinear sigma-model
• Blockspin transformation for finite temperature field theories with gauge fields
• Analytic calculation of the 1-loop effective action for the O(N+1)-symmetric 2-dimensional nonlinear sigma-model