UV-Regularization of Field Discontinuities

Abstract

A nonperturbative regularization of UV-divergencies, caused by finite discontinuities in the field configuration, is discussed in the context of 1+1-dimensional kink models. The relationship between this procedure and the appearance of "quantum copies" of classical kink solutions is studied in detail and confirmed by conventional methods of soliton quantization.

Chiral hybrid bag model with the boson field inside the bag

“…First, let us note, that the initial formulation of the model is a local field theory, and in spite of the variety of classical solutions one needs to deal with, the covariance is broken only spontaneously, and so can be restored by means of the methods of refs. [23] using the covariant group center-of-mass variables for a localized quantum-field system. Besides this, the positive points of this approach are: the more correct derivation of chiral boundary conditions, by which any term in the initial Lagrangian has exact physical meaning; the presence of an intermediate phase describing quasifree massive "constituent" quarks; physically acceptable behavior of the total energy of the bag as a function of it's geometry.…”

“…One can obviously construct the Lagrangian containing as many fields θ(x) as needed with appropriate self-interaction, which will determine (almost) rectangular division of space into regions corresponding to different phases, while the Lorentz-covariance will be broken only spontaneously, namely on the level of solutions of equations of motion. The latter circumstance allows one to use the framework of covariant group variables [23] in order to restore the covariance. Assuming further that subsidiary fields θ(x) have already formed the required bag configuration, let us start with the following Lagrangian:…”

“…Actually, the most subtle point in the HCM is the Cheshire Cat Principle (CCP) which is basic for parting space into regions with different phases inside of them [17]. The essence of CCP is the hypothesis [18] that the fermion theory inside of bag and the boson theory outside are actually equivalent and can be transformed into each other via the bosonization procedure.…”