Anharmonic analysis of lattice field theories

Journal Article · Sat Sep 15 04:00:00 EDT 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.20.1351· OSTI ID:5883968

Richardson, J; Blankenbecler, R

A new calculational procedure for polynomial lattice field theories is discussed that utilizes an anharmonic basis and a general orthogonal transformation of coordinates. The standard blocking procedure is shown to correspond to a discrete Haar transform of the field coordinates. Some generalizations of the Haar transform are given which allow one to block an arbitrary number of sites. This is applied to both the energy density and to the correlation functions. In this paper only an ''unperturbed'' problem will be discussed, but the unperturbed Hamiltonian will be chosen using a variational principle: it includes couplings and nonharmonic effects in a very nontrivial way. Numerical results will be given for certain critical indices for a phi/sup 4/ theory in one space dimension.

• Research Organization: Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305
• OSTI ID: 5883968
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 20:6; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CALCULATION METHODS
CORRELATION FUNCTIONS
EIGENFUNCTIONS
EIGENVALUES
FIELD THEORIES
FUNCTIONS
HAMILTONIANS
LATTICE FIELD THEORY
MATHEMATICAL OPERATORS
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
PERTURBATION THEORY
PHI4-FIELD THEORY
QUANTUM FIELD THEORY
QUANTUM OPERATORS
VARIATIONAL METHODS
VIRIAL THEOREM