Gauge-invariant variational methods for Hamiltonian lattice gauge theories

Journal Article · Tue Jun 15 04:00:00 EDT 1982 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.25.3331· OSTI ID:5230414

Horn, D; Weinstein, M

This paper develops variational methods for calculating the ground-state and excited-state spectrum of Hamiltonian lattice gauge theories defined in the A/sub 0/ = 0 gauge. The scheme introduced in this paper has the advantage of allowing one to convert more familiar tools such as mean-field, Hartree-Fock, and real-space renormalization-group approximation, which are by their very nature gauge-noninvariant methods, into fully gauge-invariant techniques. We show that these methods apply in the same way to both Abelian and non-Abelian theories, and that they are at least powerful enough to describe correctly the physics of periodic quantum electrodynamics (PQED) in (2+1) and (3+1) space-time dimensions. This paper formulates the problem for both Abelian and non-Abelian theories and shows how to reduce the Rayleigh-Ritz problem to that of computing the partition function of a classical spin system. We discuss the evaluation of the effective spin problem which one derives the PQED and then discuss ways of carrying out the evaluation of the partition function for the system equivalent to a non-Abelian theory. The explicit form of the effective partition function for the non-Abelian theory is derived, but because the evaluation of this function is considerably more complicated than the one derived in the Abelian theory no explicit evaluation of this function is presented. However, by comparing the gauge-projected Hartree-Fock wave function for PQED with that of the pure SU(2) gauge theory, we are able to show that extremely interesting differences emerge between these theories even at this simple level. We close with a discussion of fermions and a discussion of how one can extend these ideas to allow the computation of the glueball and hadron spectrum.

• Research Organization: Tel Aviv University, Ramat Aviv, Israel
• DOE Contract Number: AC03-76SF00515
• OSTI ID: 5230414
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 25:12; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
ELECTRODYNAMICS
ENERGY LEVELS
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
HAMILTONIANS
HARTREE-FOCK METHOD
INVARIANCE PRINCIPLES
LATTICE FIELD THEORY
MATHEMATICAL OPERATORS
PARTICLE PROPERTIES
PARTITION FUNCTIONS
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
RENORMALIZATION
SPIN
VARIATIONAL METHODS