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Title: Path Integral Solubility of Two-Dimensional Models

Abstract

We apply the technique of Fujikawa to solve for simple two-dimensional models by looking at the nontrivial transformation properties of the fermion measure in the path-integral formalism. We obtain the most general solution for the massless Thirring model and point out how the one-parameter solution reduces to that of Johnson and Sommerfield in a particular limit. We present the most general solution for the massive vector model indicating how it reduces to the solutions of Brown and Sommerfield for different values of the parameter. The solution of a gradient-coupling model is also discussed.

Authors:
 [1];  [2]
  1. Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Univ. of Rochester, New York (United States)
  2. Univ. of Rochester, NY (United States)
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1155510
Report Number(s):
FERMILAB-PUB-85-105-T
Journal ID: ISSN 0556-2821; PRVDAQ
DOE Contract Number:  
AC02-07CH11359
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 33; Journal Issue: 2; Journal ID: ISSN 0556-2821
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Das, Ashok K., and Mathur, Vishnu S. Path Integral Solubility of Two-Dimensional Models. United States: N. p., 1985. Web. doi:10.1103/PhysRevD.33.489.
Das, Ashok K., & Mathur, Vishnu S. Path Integral Solubility of Two-Dimensional Models. United States. https://doi.org/10.1103/PhysRevD.33.489
Das, Ashok K., and Mathur, Vishnu S. 1985. "Path Integral Solubility of Two-Dimensional Models". United States. https://doi.org/10.1103/PhysRevD.33.489. https://www.osti.gov/servlets/purl/1155510.
@article{osti_1155510,
title = {Path Integral Solubility of Two-Dimensional Models},
author = {Das, Ashok K. and Mathur, Vishnu S.},
abstractNote = {We apply the technique of Fujikawa to solve for simple two-dimensional models by looking at the nontrivial transformation properties of the fermion measure in the path-integral formalism. We obtain the most general solution for the massless Thirring model and point out how the one-parameter solution reduces to that of Johnson and Sommerfield in a particular limit. We present the most general solution for the massive vector model indicating how it reduces to the solutions of Brown and Sommerfield for different values of the parameter. The solution of a gradient-coupling model is also discussed.},
doi = {10.1103/PhysRevD.33.489},
url = {https://www.osti.gov/biblio/1155510}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 2,
volume = 33,
place = {United States},
year = {Mon Jul 01 00:00:00 EDT 1985},
month = {Mon Jul 01 00:00:00 EDT 1985}
}