Pauli-Jordan Function and Scalar Field Quantization in $\kappa$-Minkowski Noncommutative Spacetime

TL;DR

This paper develops a covariant second quantization framework for scalar fields in $ppa$-Minkowski spacetime using a generalized Pauli-Jordan function, revealing insights into light cone structure and superluminal signals.

Contribution

It introduces a noncommutative covariant approach to scalar field quantization without relying on canonical methods, utilizing a generalized Pauli-Jordan function.

Findings

Constructed a covariant algebra of creation and annihilation operators.

Generalized the Pauli-Jordan function for $ppa$-Minkowski spacetime.

Analyzed the light cone structure and superluminal propagation implications.

Abstract

We study a complex free scalar field theory on a noncommutative background spacetime called $\kappa$-Minkowski. In particular we address the problem of second quantization. We obtain the algebra of creation and annihilation operators in an explicitly covariant way. Our procedure does not use canonical/Hamiltonian formulations, which turn out to be ill-defined in our context. Instead we work in a spacetime covariant way by introducing a noncommutative Pauli-Jordan function. This function is obtained as a generalization of the ordinary, commutative, one by taking into account the constraints imposed by the symmetries of our noncommutative spacetime. The Pauli-Jordan function is later employed to study the structure of the light cone in $\kappa$-Minkowski spacetime, and to draw conclusions on the superluminal propagation of signals.