Tadpoles and vacuum bubbles in light-front quantization

TL;DR

This paper introduces a method to include vacuum transitions, such as tadpoles and bubbles, in light-front quantization calculations, addressing a key limitation of standard approaches and enabling more accurate nonperturbative analyses.

Contribution

The authors develop a novel regularization and subtraction scheme to incorporate vacuum bubble effects into light-front calculations, enhancing the treatment of symmetry-breaking phenomena.

Findings

Successfully applied to free scalar theory, quenched scalar Yukawa theory, and truncated $4$ theory.

Enables inclusion of tadpole contributions in nonperturbative light-front calculations.

Provides a practical method for handling vacuum bubbles and energy subtractions.

Abstract

We develop a method by which vacuum transitions may be included in light-front calculations. This allows tadpole contributions which are important for symmetry-breaking effects and yet are missing from standard light-front calculations. These transitions also dictate a nontrivial vacuum and contributions from vacuum bubbles to physical states. In nonperturbative calculations these separate classes of contributions (tadpoles and bubbles) cannot be filtered; instead, we regulate the bubbles and subtract the vacuum energy from the eigenenergy of physical states. The key is replacement of momentum-conserving delta functions with model functions of finite width; the width becomes the regulator and is removed after subtractions. The approach is illustrated in free scalar theory, quenched scalar Yukawa theory, and in a limited Fock-space truncation of $\phi^4$ theory.