4.2 Article

Covariant coordinate transformations and scalar-field - matter interactions

Publisher

WALTER DE GRUYTER GMBH
DOI: 10.1515/zna-2022-0165

Keywords

CPT-symmetry violation; Klein-Gordon fields; Lorentz invariance

Funding

  1. Universidad de Los Andes, Santiago, Chile [FAI 12.19]

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We propose a classical Lorentz invariant model for the interaction between local scalar fields and matter, where the spatial and temporal coordinates of a particle are modified by a background Klein-Gordon field. We discuss two examples at the quantum mechanical level to help understand the basics of the theory.
We propose a classical Lorentz invariant model of local scalar-field - matter interactions where the zeroth component of the space-time coordinates of a particle is modified by a background Klein-Gordon field. This model is not directly explained in terms of the standard model (SM) because the CPT symmetry is generally broken with a Hermitian Hamiltonian. Our ultimate goal (which is not explored here) is to construct a quantum field theory approach to tackle the matter-antimatter asymmetry problem. To understand the basics of the theory, two examples are discussed only at the quantum mechanical level: (i) a (quantum) harmonic oscillator with the occurrence of negative-energy eigenvalues where the effective energy-masses of the 'particle and antiparticle' are not symmetric with respect to the non-physical zero-energy mode of the oscillator; (ii) a Dirac particle in an electromagnetic (EM) linear potential.

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