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Orthogonal transforms and lattice field theories

Journal Article · · Phys. Rev., D; (United States)
;
In a previous paper we showed that a class of real-space renormalization-group calculations could be reinterpreted as an orthogonal transformation of coordinates followed by an approximate (variational) evaluation of the resulting Hamiltonian. Here we shall discuss the orthogonal-transform method and concentrate on analytic rather than numerical results. The transform method may ultimately be more accurate because even though similar approximations are made in coupling the lattice oscillators, at no time is the system split into noninteracting finite-sized blocks. Approximate variational solutions to a phi/sup 4/ lattice field theory in 2, 3, and 4 space-time dimensions are constructed using an anharmonic-oscillator basis. The solutions exhibit an ordered and a disordered phase. Analytic expressions are obtained for certain critical surfaces of these theories in regions of parameter space where a spin approximation would be invalid. The continuum limit of our solutions is discussed. The resultant perturbation expansion is also discussed and a method for its evaluation is described.
Research Organization:
Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305
DOE Contract Number:
AC03-76SF00515
OSTI ID:
5388725
Journal Information:
Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 21:10; ISSN PRVDA
Country of Publication:
United States
Language:
English

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Related Subjects

645201 -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
ANHARMONIC OSCILLATORS
FIELD THEORIES
FUNCTIONS
HAMILTONIANS
LATTICE FIELD THEORY
MATHEMATICAL OPERATORS
ORTHOGONAL TRANSFORMATIONS
PARTICLE PROPERTIES
PERTURBATION THEORY
PHI4-FIELD THEORY
QUANTUM FIELD THEORY
QUANTUM OPERATORS
RENORMALIZATION
SPACE-TIME
SPIN
TRANSFORMATIONS
VARIATIONAL METHODS
WAVE FUNCTIONS