The scalar sector in the Myers-Pospelov model

TL;DR

This paper develops a perturbative approach to the scalar sector in the Myers-Pospelov model, addressing Lorentz violation, constructing a positive-definite Hamiltonian, and deriving modified propagators for future interaction studies.

Contribution

It introduces a second-order perturbative expansion that accounts for higher-order time derivatives and Lorentz violation, enabling consistent quantization and analysis of the model.

Findings

Constructed a hermitian positive-definite Hamiltonian.

Derived modified dispersion relations with an upper momentum bound.

Calculated the free scalar propagator including Lorentz-violating effects.

Abstract

We construct a perturbative expansion of the scalar sector in the Myers-Pospelov model, up to second order in the Lorentz violating parameter and taking into account its higher-order time derivative character. This expansion allows us to construct an hermitian positive-definite Hamiltonian which provides a correct basis for quantization. Demanding that the modified normal frequencies remain real requires the introduction of an upper bound in the magnitude |k| of the momentum, which is a manifestation of the effective character of the model. The free scalar propagator, including the corresponding modified dispersion relations, is also calculated to the given order, thus providing the starting point to consider radiative corrections when interactions are introduced.