Anomaly and Exotic Statistics in One Dimension

We study the influence of the anomaly on the physical quantum picture of the chiral Schwinger model (CSM) defined on $S^1$. We show that such phenomena as the total screening of charges and the dynamical mass generation characteristic for the standard Schwinger model do not take place here. Instead of them, the anomaly results in the background linearly rising electric field or, equivalently, in the exotic statistics of the physical matter field. We construct the algebra of the Poincare generators and show that it differs from the Poincare one. For the CSM on $R^1$, the anomaly influences only the mass generation mechanism.Comment: LATEX file, 38 page

Path-integral quantization of Galilean Fermi fields

The Galilei-covariant fermionic field theories are quantized by using the path-integral method and five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. Firstly, we review the five-dimensional approach to the Galilean Dirac equation, which leads to the Levy-Leblond equations, and define the Galilean generating functional and Green's functions for positive- and negative-energy/mass solutions. Then, as an example of interactions, we consider the quartic self-interacting potential ${\lambda} (\bar{\Psi} {\Psi})^2$, and we derive expressions for the 2- and 4-point Green's functions. Our results are compatible with those found in the literature on non-relativistic many-body systems. The extended manifold allows for compact expressions of the contributions in $(3+1)$ space-time. This is particularly apparent when we represent the results with diagrams in the extended $(4+1)$ manifold, since they usually encompass more diagrams in Galilean $(3+1)$ space-time.Comment: LATEX file, 27 pages, 8 figures; typos in the journal version are removed, equation (1) in Introduction is correcte

Relativistic two-body system in 1+1-dimensional QED. I. on the circle S"1

Consiglio Nazionale delle Ricerche (CNR). Biblioteca Centrale / CNR - Consiglio Nazionale delle RichercheSIGLEITItal