# Intersoliton forces in weak-coupling quantum field theories

## Abstract

We offer a procedure for evaluating the forces exerted by solitons of weak-coupling field theories on one another. We illustrate the procedure for the kink and the antikink of the two-dimensional phi/sup 4/ theory. To do this, we construct analytically a static solution of the theory which can be interpreted as a kink and an antikink held a distance R apart. This leads to a definition of the potential energy U (R) for the pair, which is seen to have all the expected features. A corresponding evaluation is also done for U (R) between a soliton and an antisoliton of the sine-Gordon theory. When this U (R) is inserted into a nonrelativistic two-body problem for the pair, it yields a set of bound states and phase shifts. These are found to agree with exact results known for the sine-Gordon field theory in those regions where U (R) is expected to be significant, i.e., when R is large compared to the soliton size. We take this agreement as support that our procedure for defining U (R) yields the correct description of the dynamics of well-separated soliton pairs. An important feature of U (R) is that it seems to give strong intersolitonmore »

- Authors:

- Publication Date:

- Research Org.:
- Centre for Theoretical Studies, Indian Institute of Science, Bangalore 560 012, India

- OSTI Identifier:
- 7259057

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev., D; (United States)

- Additional Journal Information:
- Journal Volume: 15:10

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM FIELD THEORY; SOLITONS; WEAK-COUPLING MODEL; COUPLING CONSTANTS; GAUGE INVARIANCE; HADRON-HADRON INTERACTIONS; MONOPOLES; SCALAR FIELDS; SINE-GORDON EQUATION; THIRRING MODEL; EQUATIONS; FIELD EQUATIONS; FIELD THEORIES; INTERACTIONS; INVARIANCE PRINCIPLES; MATHEMATICAL MODELS; NUCLEAR MODELS; PARTICLE INTERACTIONS; QUASI PARTICLES; 645400* - High Energy Physics- Field Theory; 645204 - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions & Properties

### Citation Formats

```
Rajaraman, R.
```*Intersoliton forces in weak-coupling quantum field theories*. United States: N. p., 1977.
Web. doi:10.1103/PhysRevD.15.2866.

```
Rajaraman, R.
```*Intersoliton forces in weak-coupling quantum field theories*. United States. https://doi.org/10.1103/PhysRevD.15.2866

```
Rajaraman, R. Sun .
"Intersoliton forces in weak-coupling quantum field theories". United States. https://doi.org/10.1103/PhysRevD.15.2866.
```

```
@article{osti_7259057,
```

title = {Intersoliton forces in weak-coupling quantum field theories},

author = {Rajaraman, R},

abstractNote = {We offer a procedure for evaluating the forces exerted by solitons of weak-coupling field theories on one another. We illustrate the procedure for the kink and the antikink of the two-dimensional phi/sup 4/ theory. To do this, we construct analytically a static solution of the theory which can be interpreted as a kink and an antikink held a distance R apart. This leads to a definition of the potential energy U (R) for the pair, which is seen to have all the expected features. A corresponding evaluation is also done for U (R) between a soliton and an antisoliton of the sine-Gordon theory. When this U (R) is inserted into a nonrelativistic two-body problem for the pair, it yields a set of bound states and phase shifts. These are found to agree with exact results known for the sine-Gordon field theory in those regions where U (R) is expected to be significant, i.e., when R is large compared to the soliton size. We take this agreement as support that our procedure for defining U (R) yields the correct description of the dynamics of well-separated soliton pairs. An important feature of U (R) is that it seems to give strong intersoliton forces when the coupling constant is small, as distinct from the forces between the ordinary quanta of the theory. We suggest that this is a general feature of a class of theories, and emphasize the possible relevance of this feature to real strongly interacting hadrons.},

doi = {10.1103/PhysRevD.15.2866},

url = {https://www.osti.gov/biblio/7259057},
journal = {Phys. Rev., D; (United States)},

number = ,

volume = 15:10,

place = {United States},

year = {1977},

month = {5}

}