Calculation of the regularized vacuum energy in cavity field theories

Abstract

A novel technique based on Schwinger's proper time method is applied to the Casimir problem of the M.I.T. bag model. Calculations of the regularized vacuum energies of massless scalar and Dirac spinor fields confined to a static and spherical cavity are presented in a consistent manner. While our results agree partly with previous calculations based on asymptotic methods, the main advantage of our technique is that the numerical errors are under control. Interpreting the bag constant as a vacuum expectation value,we investigate potential cancellations of boundary divergences between the canonical energy and its bag constant counterpart in the fermionic case. It is found that such cancellations do not occur.

The constant background bag model of the hadron

“…Equations ( 9) and ( 10) can be solved separetaly and the set of solutions (8) will consist of the solutions of ( 9) and (10). Let us consider equation (9). Acting on this equation by the operator − → P 2 we get the same equation for the function ξ…”

“…Thus, we can solve (12) instead of (9). Obviously, (12) keeps the rotational invariance property of equivalent equation ( 9) and so is easily solved in a spherical coordinate system using the separation ansatz [12]:…”

“…We have solved (9) and found the corresponding two branches of the energy spectrum. In the same manner we can solve (10) too.…”

“…The vacuum average values of the chromofield components E a E a and H a H a of the gluon condensate in the QCD vacuum were estimated in [5][6][7]. These estimations are used for the study of vacuum energy and structure of the bag models, which connected with the bag constant [8,9]. Here we aim to consider the gluon condensate as a color background field and take into account the coupling of the constituent quarks with it as an interaction with the external color filed.…”

Vacuum structure of a modified MIT bag

“…Our numerical method to compute the regularized canonical vacuum energy and the bag constant of the fermionic MIT bag was explained in Ref. [21]. The procedure is based on a mode sum representation of the cavity propagator.…”