One-loop renormalization of a Lorentz-violating scalar field theory with a kink in 1+1 dimensions

Shokri, Hanie; Moazzemi, Reza

doi:10.22055/jrmbs.2025.20198

One-loop renormalization of a Lorentz-violating scalar field theory with a kink in 1+1 dimensions

Document Type : Full length research Paper

Authors

Hanie Shokri ¹

Reza Moazzemi ²

¹ Department of Physics, University of Qom, Qom, Iran

² Department of Physics, University of Qom, Qom, Iran.

10.22055/jrmbs.2025.20198

Abstract

This article investigates the renormalization of a scalar field theory with Lorentz symmetry violation in two spacetime dimensions. This theory is suitable for describing a kink as a nontrivial background of space. As we know, the standard theory of the kink is generally renormalizable with only one mass counter-term in two spacetime dimensions. Here we introduce a Lorentz violation term, which has non-removable effects. We show that, up to one-loop order, in addition to a modification of the mass counter-term, to obtain a renormalized theory, the theory needs a field strength renormalization counter-term. These modifications directly affect the radiative corrections of physical quantities.

Keywords

Scalar field theory

Violation of Lorentz symmetry

Renormalization

soliton

Kink

Subjects

Fundamental particle physics

[1] C. Escobar, L. Medel, and A. Martín-Ruiz, Casimir effect in Lorentz-violating scalar field theory: A local approach. Phys. Rev. D, 101 (2020) 095011. 10.1103/PhysRevD.101.095011

[2] V.A. Kostelecký, Gravity, Lorentz violation, and the standard model. Phys. Rev. D, 69 (2004) 105009. 10.1103/PhysRevD.69.105009.

[3] D. Colladay, and V.A. Kostelecký, CPT violation and the standard model. Phys. Rev. D, 55 (1997) 6760. 10.1103/PhysRevD.55.6760

[4] D. Colladay, and V.A. Kostelecký, Lorentz-violating extension of the standard model. Phys. Rev. D, 58 (1998) 116002. 10.1103/PhysRevD.58.116002.

[5] V.A Kostelecký, and M. Mewes, Electrodynamics with Lorentz-violating operators of arbitrary dimension. Phys. Rev. D, 80 (2009) 015020. 10.1103/PhysRevD.80.015020.

[6] M. Barreto, D. Bazeia, and R. Menezes, Defect structures in Lorentz and CPT violating scenarios. Phys. Rev. D, 73 (2006) 065015. 10.1103/PhysRevD.73.065015

[7] R. Moazzemi, M.M. Ettefaghi, and A. Mojavezi, Kink properties in Lorentz-violating scalar field theory. Nucl. Phys. B, 965 (2021) 115343. doi.org/10.1103/PhysRevD.97.055048.

[8] S. Coleman, Quantum sine-Gordon equation as the massive Thirring model. Phys. Rev. D, 11 (1975) 2088, DOI: 10.1103/PhysRevD.11.2088.

[9] A. Mojavezi, R. Moazzemi, and M.E. Zomorrodian, NLO radiative correction to the Casimir energy in Lorentz-violating scalar field theory. Nucl. Phys. B, 941 (2019) 145. 10.1016/j.nuclphysb.2019.02.021.