Linked-cluster Tamm-Dancoff Field Theory

TL;DR

This paper extends a non-perturbative relativistic bound-state approach combining coupled cluster and Wilsonian renormalization, demonstrating its effectiveness through two-loop renormalized phi^4 theory calculations.

Contribution

It introduces a linked-cluster Tamm-Dancoff field theory that integrates coupled cluster and Wilsonian renormalization, providing a practical loop expansion method for relativistic bound states.

Findings

Successful two-loop renormalization of phi^4 theory.

The non-unitary formalism remains hermitian and computationally efficient.

Supports the method's applicability to complex quantum field theories.

Abstract

To solve the relativistic bound-state problem one needs to systematically and simultaneously decouple the high-energy from the low-energy modes and the many-body from the few-particle states using a consistent renormalization scheme. In a recent paper we have shown that one such approach can be a combination of the coupled cluster method as used in many-body theory and the Wilsonian exact renormalization group. Even though the method is intrinsically non-perturbative, one can easily implement a loop expansion within it. In this letter we provide further support for this aspect of our formalism by obtaining results for the two-loop renormalized $\phi^{4}$ theory. We show that the non-unitary representation inherent in our method leads to an economic computation and does not produce any non-hermiticity in the relevant terms.