Exploring the landscape of very special relativity

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2020
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In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.
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Tesis (PhD in Physics)--Pontificia Universidad Católica de Chile, 2020
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https://doi.org/10.7764/tesisUC/FIS/46087
 https://repositorio.uc.cl/handle/11534/46087
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3.10 Tesis doctorado