# Equivalence of four-dimensional self duality equations and the continuum analog of the principal chiral field problem

## Abstract

A connection is established between the self-dual equations of four-dimensional space and the principal chiral field problem in a space of n dimensions. It is shown that any solution of the equations of the principal chiral field in n-dimensional space with arbitrary two-dimensional functions of definite linear combinations of the four variables, y, y, z, z, as independent arguments satisfies the system of self-dual equations of four-dimensional space. The general solution of the self-dual equations, depending on the necessary number of functions of three independent arguments, is identical to the general solution to the principal chiral field problem when the dimension of the space tends to infinity.

- Authors:

- Publication Date:

- Research Org.:
- Institute of High Energy Physics, Serpukhov (USSR)

- OSTI Identifier:
- 5974023

- Resource Type:
- Journal Article

- Journal Name:
- Theor. Math. Phys.; (United States)

- Additional Journal Information:
- Journal Volume: 73:2; Other Information: Translated from Teor. Mat. Fiz.; 73: No. 2, 302-307(Nov 1987)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ELEMENTARY PARTICLES; CHIRAL SYMMETRY; PARTICLE MODELS; FOUR-DIMENSIONAL CALCULATIONS; EIGENVALUES; FIELD EQUATIONS; FUNCTIONS; QUANTUM FIELD THEORY; SOLITONS; TWO-DIMENSIONAL CALCULATIONS; EQUATIONS; FIELD THEORIES; MATHEMATICAL MODELS; QUASI PARTICLES; SYMMETRY; 645300* - High Energy Physics- Particle Invariance Principles & Symmetries; 645400 - High Energy Physics- Field Theory

### Citation Formats

```
Leznov, A N.
```*Equivalence of four-dimensional self duality equations and the continuum analog of the principal chiral field problem*. United States: N. p., 1988.
Web.

```
Leznov, A N.
```*Equivalence of four-dimensional self duality equations and the continuum analog of the principal chiral field problem*. United States.

```
Leznov, A N. 1988.
"Equivalence of four-dimensional self duality equations and the continuum analog of the principal chiral field problem". United States.
```

```
@article{osti_5974023,
```

title = {Equivalence of four-dimensional self duality equations and the continuum analog of the principal chiral field problem},

author = {Leznov, A N},

abstractNote = {A connection is established between the self-dual equations of four-dimensional space and the principal chiral field problem in a space of n dimensions. It is shown that any solution of the equations of the principal chiral field in n-dimensional space with arbitrary two-dimensional functions of definite linear combinations of the four variables, y, y, z, z, as independent arguments satisfies the system of self-dual equations of four-dimensional space. The general solution of the self-dual equations, depending on the necessary number of functions of three independent arguments, is identical to the general solution to the principal chiral field problem when the dimension of the space tends to infinity.},

doi = {},

url = {https://www.osti.gov/biblio/5974023},
journal = {Theor. Math. Phys.; (United States)},

number = ,

volume = 73:2,

place = {United States},

year = {1988},

month = {5}

}

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