New class of plane waves for κ-noncommutative Quantum Field Theory

In this work (arXiv:2211.11627) we discuss the construction of a free scalar quantum field theory on κ-Minkowski noncommutative spacetime. We do so in terms of κ-Poincaré-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 κ-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, κ-Poincaré-invariant, version of the bosonic oscillator algebra.