The divergence of Van Hove's model and its consequences

TL;DR

This paper examines a regularized Van Hove model and finds that a key orthogonality property from the original theory does not hold in the regularized version, impacting its foundational implications.

Contribution

It introduces a regularized Van Hove model and demonstrates the loss of a fundamental orthogonality property, challenging previous assumptions in quantum field theory.

Findings

Orthogonality between state spaces disappears in the regularized model.

Implications question the foundational relevance of Van Hove's original results.

Highlights the importance of model regularization in quantum field theory.

Abstract

We study a regularized version of Van Hove's 1952 model, in which a quantum field interacts linearly with sources of finite width lying at fixed positions. We show that the central result of Van Hove's 1952 paper on the foundations of Quantum Field Theory, the orthogonality between the spaces of state vectors which correspond to different values of the parameters of the theory, disappears when a well-defined model is considered. We comment on the implications of our results for the contemporary relevance of Van Hove's article.