Effective action in DSR1 quantum field theory

We present the one-loop effective action of a quantum scalar field with DSR1 space-time symmetry as a sum over field modes. The effective action has real and imaginary parts and manifest charge conjugation asymmetry, which provides an alternative theoretical setting to the study of the particle-antiparticle asymmetry in nature. We report here a recent result concerning the one-loop effective action of doublyrelativistic theory of type 1 (DSR1) [1, 2]. To set the stage for this result we start by discussing analogous results in usual relativistic theory described by the Poincare algebra. Then we consider the κ-deformed Poincare algebra in standard basis and in bicrossproduct basis [3, 4, 5, 6]. The latter is the mathematical setting of DSR1 theory [2]. It is usually assumed that local space-time symmetries are completely described by the Poincare algebra, whose defining commutation relations between the basis elements we exhibit here with the purpose of comparison with the deformed algebras that we consider in the present work. In usual notation we have [P, P ν ] = 0 , i[P, J] = gP σ − gP ρ , i[J , J ] = gJ − gJ − gJ + gJ , (1) where we identify P 0 as the energy, P i (i = 1, 2, 3) as the components of momentum three-vector, J i = eJ/2 (i = 1, 2, 3) as the components of angular-momentum three-vector and K = J i0 (i = 1, 2, 3) as the components of the boost three-vector. The first Casimir invariant of this algebra is the relation between energy and momentum given by PμP μ = P − P 2 0 = −m 2 , (2) where m is a positive real scalar which labels the irreducible representation of the algebra under consideration. For this case m is the mass of the field excitation, i.e., its marcus@if.ufrj.br farina@if.ufrj.br jayme@ime.eb.br siqueira@if.ufrj.br