New class of plane waves for $\kappa$-noncommutative Quantum Field Theory

TL;DR

This paper develops a covariant scalar quantum field theory on $kappa$-Minkowski noncommutative spacetime, introducing new Fourier modes to preserve Lorentz invariance and constructing a consistent, deformed oscillator algebra.

Contribution

It presents a novel approach to constructing a fully covariant quantum field theory on $kappa$-Minkowski spacetime by extending momentum space and defining a consistent Pauli-Jordan function.

Findings

Successfully extended momentum space with new Fourier modes

Defined a deformed, $kappa$-Poincaré-invariant Pauli-Jordan function

Derived a consistent deformed bosonic oscillator algebra

Abstract

We discuss the construction of a free scalar quantum field theory on $\kappa$-Minkowski noncommutative spacetime. We do so in terms of $\kappa$-Poincar\'e-invariant $N$-point functions, i.e. multilocal functions which respect the deformed symmetries of the spacetime. As shown in a previous paper by some of us, this is only possible for a lightlike version of the commutation relations, which allow the construction of a covariant algebra of $N$ points that generalizes the $\kappa$-Minkowski commutation relations. We solve the main shortcoming of our previous approach, which prevented the development of a fully covariant quantum field theory: the emergence of a non-Lorentz-invariant boundary of momentum space. To solve this issue, we propose to ``extend" momentum space by introducing a class of new Fourier modes and we prove that this approach leads to a consistent definition of the Pauli-Jordan function, which turns out to be undeformed with respect to the commutative case. We finally address the quantization of our scalar field and obtain a deformed, $\kappa$-Poincar\'e-invariant, version of the bosonic oscillator algebra.