TL;DR
This paper explores how the Cholesky decomposition can be employed to determine the stability of vacuum configurations in scalar field theories, providing a practical method for stability analysis.
Contribution
It introduces a novel application of the Cholesky decomposition for assessing vacuum stability in field theories, including deriving explicit stability conditions.
Findings
Cholesky decomposition effectively identifies stable vacua.
Derived explicit stability criteria for a specific scalar potential.
Demonstrated the method's utility in a concrete example.
Abstract
We discuss how the Cholesky decomposition may be used to ascertain whether a critical point of the field theory scalar potential provides a stable vacuum configuration. We then use this method to derive the stability conditions in a specific example.
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