arXiv subjects

Tadeusz Adach

Publications and source records attributed to Tadeusz Adach.

3 recordsLinked to original sources

arXiv2025

\kappa-deformed spin-1/2 field

In this paper, we investigate the Poincar\'e and discrete symmetries of a $\kappa$-deformed spin-$\tfrac12$ field, extending recent results obtained for scalar fields. We construct an action that is Poincar\'e invariant and analyze its consequences within the deformed framework. Our results confirm the findings of our recent analysis of the $\kappa$-deformed scalar field, where we established that there is no action invariant under both Poincar\'e symmetry and charge conjugation in the $\kappa$-deformed case, while $\mathcal{CPT}$-symmetry can be restored through a natural deformation of time reversal. Furthermore, we present an explicit calculation of the Noether charges associated with Poincar\'e symmetry and show that their algebra closes, demonstrating the internal consistency of the theory.

hep-th↗

arXiv2025

Asymmetry in momentum space: restoring ${\cal C}{\cal P}{\cal T}$ invariance of $\kappa$-field theory

The positive and negative energy modes of a field theory in $\kappa$-Minkowski/$\kappa$-Poincar\'e noncommutative spacetime have very different symmetry properties. This can be understood geometrically by considering that they span two distinct sectors of a curved momentum space. By performing an explicit direct computation of the relativistic Noether charges and their algebra within the canonical formalism, we identify a striking consequence of this asymmetry in momentum space: charge conjugation and Poincar\'e invariance are incompatible. We then notice how the structure of momentum space suggests that time reversal could be deformed so that the overall ${\cal C}{\cal P}{\cal T}$-invariance is restored. We prove that this new proposal works by studying the transformation properties under deformed discrete symmetries of the new relativistic charges.

hep-th↗

arXiv2025

Complex scalar field in κ-Minkowski noncommutative spacetime

We present a comparison between translation charges for several Lagrangians for the $κ$-deformed complex scalar field using the canonical method. The Lagrangians are shown to be related by charge conjugation and twisted cyclicity, and these relationships are reflected in their conserved charges. The Lagrangian corresponding to the results obtained in arXiv:2011.09188 and arXiv:2201.10191 is identified, providing an explanation for the observed loss of charge conjugation symmetry under boosts.

hep-th↗