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The electron-positron scattering process is investigated in the context ofvery special relativity (VSR). This theory assumes that the true symmetry ofnature is not the full Lorentz group, but some of its subgroups, such as thesubgroups $SIM(2)$ and $HOM(2)$. In this context, the cross-section forelectron-positron scattering at finite temperature is calculated. The effectsof temperature are introduced using the Thermo Field Dynamics (TFD) formalism.Our result shows that the cross-section is changed due to both effects, the VSRcontributions and temperature effects. An estimated value for the VSR parameterusing experimental data available in the literature is discussed.

Temperature effects for $e^-+e^+\rightarrow \mu^-+\mu^+$ scattering in very special relativity