Wave functions and energy for the vacuum and heavy quarks from the WKB Schroedinger equation for massive gauge theories with instantons

Journal Article · Mon Jan 15 00:00:00 EST 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.19.604· OSTI ID:6445275

de Vega, H J; Gervais, J L; Sakita, B

The physics of vacuum tunneling for gauge field theories is studied following methods developed in a series of earlier papers by explicitly constructing the eigenstates of the Hamiltonian which correspond to the ground state in the presence of an arbitrary external static charge distribution. This is achieved in the A/sub 0/ = 0 canonical formalism where this charge distribution was shown before to be a cyclic degree of freedom. The corresponding wave functionals represent the theta vacuum and very-heavy-quark states. We work in the Schroedinger picture where the field configurations are functions only of the space coordinates. Hence we have one less space dimension than the usual Euclidean approach, and instantons are paths in configuration space which connect different classical vacuums through classically forbidden regions. There we solve the Schroedinger equation exactly to the first two orders in h using the one-instanton solution. The resulting wave functionals are concentrated around the instanton paths which are the locus of maximum tunneling probability. Around classical vacuums the wave functional is shown to possess, besides the usual perturbative Gaussian, a part which is an exponentially increasing function of the fluctuation. The energy and eigenfunctional are determined by matching this wave functional to the WKB expression in an overlap region where both are valid. Special care must be taken concerning the continuous symmetries of the problem since the instantons and the classical vacuum break different subgroups of the symmetry group. Although the formalism applies to any field theory with instantons, the present discussion of matching strictly holds if there are no massless particles. It has thus the same limitations as the dilute-gas approximation (DGA) in the Euclidean approach, the results of which are comprised in the outcome of the present discussion.

• Research Organization: Laboratoire de Physique Theorique et Hautes Energies Universite Pierre et Marie Curie
• OSTI ID: 6445275
• Journal Information: Phys. Rev., D; (United States), Vol. 19:2
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
GAUGE INVARIANCE
INSTANTONS
QUARKS
WAVE FUNCTIONS
BOUNDARY CONDITIONS
CHARGE DISTRIBUTION
EIGENSTATES
FEYNMAN PATH INTEGRAL
HAMILTONIANS
QUANTUM FIELD THEORY
SCHROEDINGER EQUATION
TUNNEL EFFECT
VACUUM STATES
WKB APPROXIMATION
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
FIELD THEORIES
FUNCTIONS
INTEGRALS
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
POSTULATED PARTICLES
QUANTUM OPERATORS
QUASI PARTICLES
WAVE EQUATIONS
645201* - High Energy Physics- Particle Interactions & Properties-Theoretical- General & Scattering Theory
645400 - High Energy Physics- Field Theory