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arXiv · 2211.11627

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

Maria Grazia Di Luca·Flavio Mercati
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Abstract

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.

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Maria Grazia Di Luca, Flavio Mercati. 2022-11-21. New class of plane waves for $κ$-noncommutative Quantum Field Theory. https://arxiv.org/abs/2211.11627

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