A Note on Quantum Compactons

TL;DR

This paper demonstrates that quantum theories of compactons, which are localized solutions with singular fluctuation operators, are well-defined, and it calculates the one-loop mass shift for a specific scalar field model.

Contribution

It shows that despite singularities in fluctuation operators, the quantum theory of compactons remains well-defined and provides a concrete calculation of the one-loop mass shift.

Findings

Quantum fluctuations around compactons can be well-defined despite singular operators.

The one-loop mass shift for a scalar field compacton is explicitly calculated.

Quantum stability of compactons is supported by the analysis.

Abstract

Compactons are solutions of the equations of motion that behave trivially outside a compact region. In general, the operators describing quantum fluctuations above compactons have singularities. However, we show that despite these singularities the quantum theory is well defined. As an example, we calculate the one-loop mass shift of a compacton in a model described by a single real scalar field.