Effective Action for Self-Interacting Scalar Field in 3-dimensional Ball

TL;DR

This paper calculates the renormalized one-loop effective action for a massless self-interacting scalar field within a 3D ball, applying heat kernel methods and bag model renormalization.

Contribution

It introduces a detailed calculation of the effective action for scalar fields with boundary conditions in three dimensions using heat kernel expansion and renormalization techniques.

Findings

Divergent parts of the effective action are explicitly calculated.

Renormalized effective action is obtained for the scalar field in a 3D ball.

Methodology can be applied to similar boundary value problems.

Abstract

In this paper we have considered the renormalized one-loop effective action for massless self-interacting scalar field in the 3-dimensional ball. The scalar field satisfies Dirichlet boundary condition on the ball. Using heat kernel expansion method we calculate the divergent part of effective action, then by bag model renormalization procedure we obtain the renormalized one-loop effective action.