# $\mathcal{PT}$-symmetric quantum field theory on the noncommutative spacetime

## TL;DR

This paper develops a $ ext{PT}$-symmetric quantum field theory framework on noncommutative spacetime, revealing new interactions and demonstrating symmetry preservation in scattering amplitudes at leading order.

## Contribution

It introduces a pseudo-Hermitian interpretation of $ ext{PT}$-symmetric QFT on noncommutative spacetime with angular twist, identifying new interactions and analyzing symmetry properties.

## Key findings

- New $ ext{PT}$-symmetric interactions specific to noncommutative spacetime.
- Leading order $T$-matrix formula matches commutative case results.
- Scattering amplitudes preserve noncommutative symmetries if unbroken in the non-Hermitian formulation.

## Abstract

We consider the $\mathcal{PT}$-symmetric quantum field theory on the noncommutative spacetime with angular twist and construct its pseudo-Hermitian interpretation. We explore the differences between internal and spatial parities in the context of the angular twist and for the latter we find new $\mathcal{PT}$-symmetric interactions that are nontrivial only for the noncommutative spacetime. We reproduce the same formula for the leading order $T$-matrix of the equivalent Hermitian model as the one obtained earlier for the quantum field theory on the commutative spacetime. This formula implies that the leading order scattering amplitude preserves the symmetries of the noncommutative geometry if they are not broken in the non-Hermitian formulation.