Hamiltonians, path integrals, and a new renormalization group

Journal Article · Tue Jun 15 00:00:00 EDT 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.47.5499· OSTI ID:6583828

Weinstein, M ^[1]

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1. Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 (United States)

New nonperturbative methods for dealing with Hamiltonian systems are introduced. The derivation of these methods requires identities for rewriting exponentials of sums of operators which are different from the usual Campbell-Hausdorff formula. These identities allow one to derive approximations to [ital e][sup [minus][delta][ital H]] which are correct to higher order in [delta] and which contain fewer terms than the Campbell-Hausdorff formula. This allows one to generate path-integral actions which are more accurate for finite-size steps in time and which can be exploited to improve the rate of convergence of Monte Carlo calculations. To show that these methods allow one to include effects which show up in the stationary-phase approximation to the path integral, e.g., instantons, solitons, etc., I not only derive the connection between the Hamiltonian and path-integral formalism but the relationship between a specific stationary-phase approximation and the corresponding Hamiltonian calculation. My focus, however, is the direct application of these new identities to the study of nonperturbative Hamiltonian dynamics. I show that these methods are easier to apply and give better results than those based upon the naive [ital t]-expansion, block mean-field, or real-space renormalization ideas. Comparison of these older methods with the computational tools introduced in this paper are discussed in the context of simple examples. It is shown that the new methods allow one to extrapolate answers to finite [ital t] without the use of Pade approximants.

• DOE Contract Number: AC03-76SF00515
• OSTI ID: 6583828
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 47:12; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM MECHANICS
FEYNMAN PATH INTEGRAL
HAMILTONIANS
INSTANTONS
ISING MODEL
LATTICE FIELD THEORY
MEAN-FIELD THEORY
SOLITONS
CRYSTAL MODELS
FIELD THEORIES
INTEGRALS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
QUASI PARTICLES
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)