Evidence for Expanding Quantum Field Theory

TL;DR

This paper discusses limitations of canonical quantization in quantum field theory and presents evidence that affine quantization can lead to genuinely interacting theories, suggesting a broader framework for QFT.

Contribution

It provides evidence that affine quantization can produce interacting quantum field theories where canonical quantization fails, proposing an expanded approach to QFT.

Findings

Affine quantization yields truly interacting theories.

Canonical quantization treats some interacting models as free.

Evidence suggests combining quantization methods broadens QFT.

Abstract

Present day quantum field theory (QFT) is founded on canonical quantization, which has served quite well, but also has led to several issues. The free field describing a free particle (with no interaction term) can suddenly become nonrenormalizable the instant a suitable interaction term appears. For example, using canonical quantization, $\varphi^4_4$, has been deemed a ``free" theory with no difference from a truly free field [1], [2], [3]. Using the same model, affine quantization has led to a truly interacting theory [4]. This fact alone asserts that canonical and affine tools of quantization deserve to be open to their procedures together as a significant enlargement of QFT.