Renormalization in a classical lattice field theory

Journal Article · Mon Jan 15 04:00:00 EST 1990 · Physical Review, A (General Physics); (USA)

DOI:https://doi.org/10.1103/PhysRevA.41.598· OSTI ID:6902344

Bartels, J ^[1]; Chang, S ^[2]

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1. Institute for Nonlinear Science, University of California at San Diego, La Jolla, California 92093 (USA) II. Institut fur Theoretische Physik, Universitaet Hamburg, (West Germany)
2. Institute for Nonlinear Science, University of California at San Diego, La Jolla, California 92093 La Jolla Institute, La Jolla, California 92037 Physics Department, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (USA)

We formulate and describe a renormalization-group transformation for classical {lambda}{phi}{sup 4}-field theory on a lattice. The main idea is to divide the angle variables of the oscillators into the fast ones (large momenta) and the slow ones (low momenta) and to average over the fast ones. This results in an effective Hamiltonian for the remaining slow modes, which can be compared with the starting Hamiltonian. We derive fixed-point conditions and obtain a scaling law for those classical solutions for which the renormalization step can be iterated. There is a striking resemblence between our classical treatment and the analogous procedure in quantum field theory, which we discuss in some detail.

• OSTI ID: 6902344
• Journal Information: Physical Review, A (General Physics); (USA), Journal Name: Physical Review, A (General Physics); (USA) Vol. 41:2; ISSN PLRAA; ISSN 0556-2791
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COUPLING
DEGREES OF FREEDOM
ELECTRONIC EQUIPMENT
EQUIPMENT
FIELD THEORIES
HARMONIC OSCILLATORS
LATTICE FIELD THEORY
OSCILLATORS
PHASE TRANSFORMATIONS
PHI4-FIELD THEORY
QUANTUM FIELD THEORY
RENORMALIZATION