Finite-dimensional approximation of time evolution operators: A nonperturbative approach to quantum field theories

Journal Article · Sun Dec 15 00:00:00 EST 1985 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.32.3221· OSTI ID:6387365

Kroeger, H; Smailagic, A; Girard, R

We suggest a time-dependent, finite-dimensional approximation scheme for time evolution operators and the S matrix in relativistic quantum field theories. It can be solved by diagonalization of finite-dimensional Hermitian matrices. The method is presented for a phi/sup 4/-field theory. In the weak-coupling regime, where perturbation theory is applicable, our method tends to the results of perturbation theory in all orders, when the approximation parameters tend to infinity. Renormalization is achieved by introducing counterterms in the Lagrangian in the usual way. This method does not involve vertices and propagators and is a nonperturbative scheme. It is applicable to arbitrary coupling constants.

• Research Organization: Departement de Physique, Universite Laval, Quebec, Canada, P.Q.XK 7P4
• OSTI ID: 6387365
• Journal Information: Phys. Rev. D; (United States), Vol. 32:12
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM FIELD THEORY
S MATRIX
TIME DEPENDENCE
BOUND STATE
BOUNDARY CONDITIONS
COUPLING CONSTANTS
HAMILTONIANS
LAGRANGIAN FUNCTION
PERTURBATION THEORY
PHI4-FIELD THEORY
PROPAGATOR
RELATIVITY THEORY
RENORMALIZATION
WEAK-COUPLING MODEL
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATRICES
NUCLEAR MODELS
QUANTUM OPERATORS
645400* - High Energy Physics- Field Theory