# 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 »

- 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}

}