Renormalization Group Approach to Scalar Theory

TL;DR

This paper applies the exact renormalization group method to scalar $bb^4$ theory, revealing limitations of the one-loop approximation at large coupling constants through numerical analysis.

Contribution

It introduces a comprehensive renormalization group approach that incorporates higher loop effects, improving upon traditional one-loop calculations for scalar theories.

Findings

Naive one-loop results break down at large couplings

Higher loop effects are significant in scalar $bb^4$ theory

Numerical calculations demonstrate the importance of including multiple loop contributions

Abstract

Effective potential for scalar $\lambda\phi^4$ theory is obtained using the exact renormalization group method which includes both the usual one-loop contribution as well as the dominant higher loop effects. Our numerical calculation indicates a breakdown of naive one-loop result for sufficiently large renormalized coupling constant.