<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>?</mml:mi></mml:math> -deformed complex fields and discrete symmetries

We present a construction of $\ensuremath{\kappa}$-deformed complex scalar field theory with the objective shedding light on way discrete symmetries and $CPT$ invariance are affected by deformation. Our starting point is observation that, in order to have an appropriate action Lorentz antiparticle states, these should be described four-momenta living complement portion de Sitter group manifold which particle belong. Once equations motions properly worked out from deformed action, we obtain that characterized different mass-shell constraints, leading subtle form departure invariance. The remaining part our work dedicated detailed description Poincar\'e field.