# Topological charge in 1+1 dimensional lattice {phi}{sup 4} theory

## Abstract

We investigate the topological charge in 1+1 dimensional {phi}{sup 4} theory on a lattice with antiperiodic boundary condition (APBC) in the spatial direction. We propose a simple order parameter for the lattice theory with APBC and we demonstrate its effectiveness. Our study suggests that kink condensation is a possible mechanism for the order-disorder phase transition in the 1+1 dimensional {phi}{sup 4} theory. With renormalizations performed on the lattice with periodic boundary condition (PBC), the topological charge in the renormalized theory is given as the ratio of the order parameters in the lattices with APBC and PBC. We present a comparison of topological charges in the bare and the renormalized theory and demonstrate invariance of the charge of the renormalized theory in the broken symmetry phase.

- Authors:

- Theory Group, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064 (India)

- Publication Date:

- OSTI Identifier:
- 20713852

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 9; Other Information: DOI: 10.1103/PhysRevD.72.094504; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUNDARY CONDITIONS; COMPARATIVE EVALUATIONS; LATTICE FIELD THEORY; ONE-DIMENSIONAL CALCULATIONS; ORDER PARAMETERS; PERIODICITY; PHASE TRANSFORMATIONS; PHI4-FIELD THEORY; RENORMALIZATION; SYMMETRY BREAKING; TOPOLOGY

### Citation Formats

```
De, Asit K., Harindranath, A., Maiti, Jyotirmoy, and Sinha, Tilak.
```*Topological charge in 1+1 dimensional lattice {phi}{sup 4} theory*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevD.72.094504.

```
De, Asit K., Harindranath, A., Maiti, Jyotirmoy, & Sinha, Tilak.
```*Topological charge in 1+1 dimensional lattice {phi}{sup 4} theory*. United States. doi:10.1103/PhysRevD.72.094504.

```
De, Asit K., Harindranath, A., Maiti, Jyotirmoy, and Sinha, Tilak. Tue .
"Topological charge in 1+1 dimensional lattice {phi}{sup 4} theory". United States.
doi:10.1103/PhysRevD.72.094504.
```

```
@article{osti_20713852,
```

title = {Topological charge in 1+1 dimensional lattice {phi}{sup 4} theory},

author = {De, Asit K. and Harindranath, A. and Maiti, Jyotirmoy and Sinha, Tilak},

abstractNote = {We investigate the topological charge in 1+1 dimensional {phi}{sup 4} theory on a lattice with antiperiodic boundary condition (APBC) in the spatial direction. We propose a simple order parameter for the lattice theory with APBC and we demonstrate its effectiveness. Our study suggests that kink condensation is a possible mechanism for the order-disorder phase transition in the 1+1 dimensional {phi}{sup 4} theory. With renormalizations performed on the lattice with periodic boundary condition (PBC), the topological charge in the renormalized theory is given as the ratio of the order parameters in the lattices with APBC and PBC. We present a comparison of topological charges in the bare and the renormalized theory and demonstrate invariance of the charge of the renormalized theory in the broken symmetry phase.},

doi = {10.1103/PhysRevD.72.094504},

journal = {Physical Review. D, Particles Fields},

number = 9,

volume = 72,

place = {United States},

year = {Tue Nov 01 00:00:00 EST 2005},

month = {Tue Nov 01 00:00:00 EST 2005}

}