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Title: Schroedinger equation in the theory of massless non-Abelian fields

Abstract

The Schroedinger equation is analyzed for state vectors in the gauge theory of massless non-Abelian fields. The energy operator H takes its simplest form when expressed in terms of the three-dimensional potentials A/sub j//sup a/ (j=1, 2, 3 is the spatial index, and a is the group index) which are generally not transverse. The state spectrum of an operator H of this type, however, is broader than the spectrum of physical states. It is shown that all states of the operator H can be classified on the basis of representations of a group Y, whose generators are the covariant divergences of the electric field. The physical-state vectors form a unit representation of the Y group and depend on only the fields B/sub j//sup a/, which are transverse in the three-dimensional sense. These fields are related to A/sub j//sup a/ by a gauge transformation. The operator H/sub r/, which represents the energy of the physical states, is found from the operator H through a transformation from the potentials A/sub j//sup a/ to the potentials B/sub j//sup a/. The equation derived for H/sub r/ differs from that found earlier by Schwinger (Phys. Rev. 127, 324 (1962)). Schwinger's result is shown to bemore » incorrect. The operator H/sub r/ is singular on a surface in the space of the fields B/sub j//sup a/ where the Faddeev-Popov determinant Z vanishes. Near the Z=0 surface, this operator can be interpreted as an energy operator with a singular repulsive potential. The boundary condition at Z=0 is discussed.« less

Authors:
Publication Date:
Research Org.:
Leningrad Institute of Nuclear Physics, Academy of Sciences of the USSR
OSTI Identifier:
5876725
Alternate Identifier(s):
OSTI ID: 5876725
Resource Type:
Journal Article
Journal Name:
Sov. J. Nucl. Phys. (Engl. Transl.); (United States)
Additional Journal Information:
Journal Volume: 29:2
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM FIELD THEORY; HAMILTONIANS; SCHROEDINGER EQUATION; BOUNDARY CONDITIONS; QUANTUM OPERATORS; DIFFERENTIAL EQUATIONS; EQUATIONS; FIELD THEORIES; MATHEMATICAL OPERATORS; WAVE EQUATIONS 645400* -- High Energy Physics-- Field Theory

Citation Formats

Danilov, G.S. Schroedinger equation in the theory of massless non-Abelian fields. United States: N. p., 1979. Web.
Danilov, G.S. Schroedinger equation in the theory of massless non-Abelian fields. United States.
Danilov, G.S. Thu . "Schroedinger equation in the theory of massless non-Abelian fields". United States.
@article{osti_5876725,
title = {Schroedinger equation in the theory of massless non-Abelian fields},
author = {Danilov, G.S.},
abstractNote = {The Schroedinger equation is analyzed for state vectors in the gauge theory of massless non-Abelian fields. The energy operator H takes its simplest form when expressed in terms of the three-dimensional potentials A/sub j//sup a/ (j=1, 2, 3 is the spatial index, and a is the group index) which are generally not transverse. The state spectrum of an operator H of this type, however, is broader than the spectrum of physical states. It is shown that all states of the operator H can be classified on the basis of representations of a group Y, whose generators are the covariant divergences of the electric field. The physical-state vectors form a unit representation of the Y group and depend on only the fields B/sub j//sup a/, which are transverse in the three-dimensional sense. These fields are related to A/sub j//sup a/ by a gauge transformation. The operator H/sub r/, which represents the energy of the physical states, is found from the operator H through a transformation from the potentials A/sub j//sup a/ to the potentials B/sub j//sup a/. The equation derived for H/sub r/ differs from that found earlier by Schwinger (Phys. Rev. 127, 324 (1962)). Schwinger's result is shown to be incorrect. The operator H/sub r/ is singular on a surface in the space of the fields B/sub j//sup a/ where the Faddeev-Popov determinant Z vanishes. Near the Z=0 surface, this operator can be interpreted as an energy operator with a singular repulsive potential. The boundary condition at Z=0 is discussed.},
doi = {},
journal = {Sov. J. Nucl. Phys. (Engl. Transl.); (United States)},
number = ,
volume = 29:2,
place = {United States},
year = {1979},
month = {2}
}