# Solving two-dimensional [phi][sup 4] field (complex scalar) theory by discretized light-front quantization

## Abstract

The discretized light-front quantization method is applied to [phi][sup 4] field (complex scalar) theory in 1+1 dimensions. The interaction Hamiltonian is constructed in its normal-ordered form, and calculations are performed with and without finite-mass renormalization in the charge-0 sector of the field. It is found that, like real scalar theory, finite-mass renormalization prevents the phase transition by restricting the theory to the weak-coupling region. A comparison of the results with and without mass renormalization demonstrates the same estimate of the critical coupling for which the mass gap vanishes. The invariant mass of various states is calculated as a function of bare coupling. In the weak-coupling region where extrapolation to the continuum limit is easily found, there is evidence for scattering, but there is no two-particle bound state in agreement with the well-known result established for constructive quantum field theory. Also, no multiparticle bound states are found. The essential outcome is that the results valid for real-scalar theories are found to be valid for complex scalar theory also.

- Authors:

- (Department of Materials Science, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700032 (India))

- Publication Date:

- OSTI Identifier:
- 6991095

- Alternate Identifier(s):
- OSTI ID: 6991095

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review, D (Particles Fields); (United States)

- Additional Journal Information:
- Journal Volume: 46:12; Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; PHI4-FIELD THEORY; MASS RENORMALIZATION; BOUND STATE; HAMILTONIANS; PHASE TRANSFORMATIONS; QUANTIZATION; QUANTUM FIELD THEORY; SCALAR FIELDS; TWO-DIMENSIONAL CALCULATIONS; WEAK-COUPLING MODEL; FIELD THEORIES; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NUCLEAR MODELS; QUANTUM OPERATORS; RENORMALIZATION 662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)

### Citation Formats

```
Ghosh, S.N.
```*Solving two-dimensional [phi][sup 4] field (complex scalar) theory by discretized light-front quantization*. United States: N. p., 1992.
Web. doi:10.1103/PhysRevD.46.5497.

```
Ghosh, S.N.
```*Solving two-dimensional [phi][sup 4] field (complex scalar) theory by discretized light-front quantization*. United States. doi:10.1103/PhysRevD.46.5497.

```
Ghosh, S.N. Tue .
"Solving two-dimensional [phi][sup 4] field (complex scalar) theory by discretized light-front quantization". United States. doi:10.1103/PhysRevD.46.5497.
```

```
@article{osti_6991095,
```

title = {Solving two-dimensional [phi][sup 4] field (complex scalar) theory by discretized light-front quantization},

author = {Ghosh, S.N.},

abstractNote = {The discretized light-front quantization method is applied to [phi][sup 4] field (complex scalar) theory in 1+1 dimensions. The interaction Hamiltonian is constructed in its normal-ordered form, and calculations are performed with and without finite-mass renormalization in the charge-0 sector of the field. It is found that, like real scalar theory, finite-mass renormalization prevents the phase transition by restricting the theory to the weak-coupling region. A comparison of the results with and without mass renormalization demonstrates the same estimate of the critical coupling for which the mass gap vanishes. The invariant mass of various states is calculated as a function of bare coupling. In the weak-coupling region where extrapolation to the continuum limit is easily found, there is evidence for scattering, but there is no two-particle bound state in agreement with the well-known result established for constructive quantum field theory. Also, no multiparticle bound states are found. The essential outcome is that the results valid for real-scalar theories are found to be valid for complex scalar theory also.},

doi = {10.1103/PhysRevD.46.5497},

journal = {Physical Review, D (Particles Fields); (United States)},

issn = {0556-2821},

number = ,

volume = 46:12,

place = {United States},

year = {1992},

month = {12}

}