Abstract
The Sommerfield model with a massive vector field coupled to a massless fermion in 1+1 dimensions is an exactly solvable analog of a Bank-Zaks model. The “physics” of the model comprises a massive boson and an unparticle sector that survives at low energy as a conformal field theory (Thirring model). I discuss the “Schwinger point” of the Sommerfield model in which the vector boson mass goes to zero. The limit is singular but gauge invariant quantities should be well-defined. I give a number of examples, both (trivially) with local operators and with nonlocal products connected by Wilson lines (the primary technical accomplishment in this note is the explicit and very pedestrian calculation of correlators involving straight Wilson lines). I hope that this may give some insight into the nature of bosonization in the Schwinger model and its connection with unparticle physics which in this simple case may be thought of as “incomplete bosonization.”
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Georgi and Y. Kats, Unparticle self-interactions, JHEP 02 (2010) 065 [arXiv:0904.1962] [INSPIRE].
C.M. Sommerfield, On the definition of currents and the action principle in field theories of one spatial dimension, Annals Phys. 26 (1964) 1.
L.S. Brown, Gauge invariance and mass in a two-dimensional model, Nuovo Cim. 29 (1963) 617.
W.E. Thirring and J.E. Wess, Solution of a field theoretical model in one space-one time dimension, Annals Phys. 27 (1964) 331.
D.A. Dubin and J. Tarski, Interactions of massless spinors in two dimensions, Annals Phys. 43 (1967) 263.
C.R. Hagen, Current definition and mass renormalization in a model field theory, Nuovo Cim. A 51 (1967) 1033.
H. Georgi and Y. Kats, An Unparticle Example in 2D, Phys. Rev. Lett. 101 (2008) 131603 [arXiv:0805.3953] [INSPIRE].
R. Roskies and F. Schaposnik, Comment on Fujikawa’s Analysis Applied to the Schwinger Model, Phys. Rev. D 23 (1981) 558 [INSPIRE].
H. Georgi and J.M. Rawls, Anomalies of the axial-vector current in two dimensions, Phys. Rev. D 3 (1971) 874 [INSPIRE].
J.S. Schwinger, Gauge Invariance and Mass. 2., Phys. Rev. 128 (1962) 2425 [INSPIRE].
K.G. Wilson, Confinement of Quarks, Phys. Rev. D 10 (1974) 2445 [INSPIRE].
S.R. Coleman, The Quantum sine-Gordon Equation as the Massive Thirring Model, Phys. Rev. D 11 (1975) 2088 [INSPIRE].
A.V. Smilga, On the fermion condensate in Schwinger model, Phys. Lett. B 278 (1992) 371 [INSPIRE].
C. Jayewardena, Schwinger model on S2 , Helv. Phys. Acta 61 (1988) 636 [INSPIRE].
J.E. Hetrick and Y. Hosotani, QED on a circle, Phys. Rev. D 38 (1988) 2621 [INSPIRE].
H. Georgi and B. Warner, Generalizations of the Sommerfield and Schwinger models, arXiv:1907.12705 [INSPIRE].
H.A. Falomir, R.E. Gamboa Saravi and F.A. Schaposnik, Wilson Loop Dependence on the Contour Shape, Phys. Rev. D 25 (1982) 547 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1905.09632
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Georgi, H. The Schwinger point. J. High Energ. Phys. 2019, 57 (2019). https://doi.org/10.1007/JHEP11(2019)057
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2019)057