Relativistic force and the anisotropy of mass

Abstract

The quantization of nonrelativistic electromagnetic interaction of anyons when higher derivative terms are included in the Lagrangian is discussed. The gauge model U(1) U(1) under consideration, contains the statistical U(1) Chern-Simons field and the electromagnetic field, both coupled to a fractional spin matter field. A higher derivative term preserving gauge invariance is added and the new model obtained is studied in the framework of the generalized constrained Hamiltonian systems. Next, by extending the Faddeev±Senjanovic method to higher derivative systems, the path-integral quantization is developed and the diagrammatic and Feynman rules in the framework of the perturbative theory, are discussed. In this context, only a mixed bosonic propagator can be defined. As happens in other more simple models, and in this case, the addition of higher derivative terms improves the ultraviolet behaviour of some diagrams, rendering this renormalizable model less divergent. Finally, a possible way of solving the unitary problem due to the presence of higher derivative terms is proposed.