Renormalizable and unitary nonlocal quantum field theory with CPT violation and its implication

TL;DR

This paper presents a nonlocal Lorentz invariant quantum field theory that violates CPT symmetry but remains renormalizable, unitary, and causal, offering new insights into fundamental physics and cosmology.

Contribution

It introduces the first known nonlocal QFT that is both renormalizable and unitary despite CPT violation, with potential implications for the Standard Model and baryogenesis.

Findings

The nonlocal QFT is both renormalizable and unitary.

The theory satisfies causality despite CPT violation.

Potential to incorporate gauge theories and explain baryon asymmetry.

Abstract

It is a common belief that any relativistic nonlocal quantum field theory encounters either the problem of renormalizability or unitarity or both of them. It is also known that any local relativistic quantum field theory (QFT) possesses the CPT symmetry. In this Letter we show that a previously proposed nonlocal Lorentz invariant QFT, which violates the CPT theorem, is both renormalizable and unitary, thus being a first presented example in the literature of such a nonlocal theory. The theory satisfies the requirement of causality as well. A further generalization of such a nonlocal QFT to include the gauge theories is also envisaged. In particular, dressing such a Standard Model with a CP violating phase, will make the theory satisfying most of the necessary criteria to finally explain the baryon asymmetry of the universe by a viable QFT. As for the necessity of baryon number violation, there are hopefully several possibilities such as by GUT and electroweak baryogenesis, leptogenesis or sphalerons.