Calculation of ground state energy for confined fermion fields

Abstract

A method for renormalization of the Casimir energy of confined fermion fields in (1 + 1)D is proposed. It is based on the extraction of singularities which appear as poles at the point of physical value of the regularization parameter, and subsequent compensation of them by means of redefinition of the "bare" constants. A finite ground state energy of the two-phase hybrid fermion bag model with chiral boson-fermion interaction is calculated as the function of the bag's size.

Casimir Energy of Confined Fields: A Role of the Rg-Invariance

“…Here we will be interesting only in the small mass m limit, so we drop out all terms of the order m 4 and higher 5 . Then the eigenvalues uj n can be written as 77?…”

“…where γ E = 0.5772... is the Euler constant. It's interesting to note, that the regularization by the exponential cutoff gives the equivalent result 5 . The divergent part of (17) can be extracted in the form:…”