Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Fermionic Casimir effect in the presence of compact dimension in field theory with Lorentz invariance violation

Ar Rohim, Apriadi Salim Adam

Abstract

In this study, we investigate the effect of the Lorentz invariance violation on the Casimir energy and pressure of the massive fermion field in the presence of the compact dimensions with topological $R^4\times S^1$, referring to the Kaluza-Klein model. In the system, the Dirac field is confined between two parallel plates with the geometry described by MIT bag boundary conditions, and the compactified dimension satisfies quasi-periodic boundary conditions. We investigate two directions of the Lorentz violation, namely, space- and time-like. The results reveal that in the space-like vector case, the Lorentz violation's strength and the extra dimension affect the Casimir energy and pressure. In contrast, in the time-like vector case, they are only affected by the extra dimension. We also propose an indirect method to estimate the size of the extra dimension by comparing the frequency shift of the massless fermionic case to that of the scaled experimental data for the electromagnetic field.

Fermionic Casimir effect in the presence of compact dimension in field theory with Lorentz invariance violation

Abstract

In this study, we investigate the effect of the Lorentz invariance violation on the Casimir energy and pressure of the massive fermion field in the presence of the compact dimensions with topological , referring to the Kaluza-Klein model. In the system, the Dirac field is confined between two parallel plates with the geometry described by MIT bag boundary conditions, and the compactified dimension satisfies quasi-periodic boundary conditions. We investigate two directions of the Lorentz violation, namely, space- and time-like. The results reveal that in the space-like vector case, the Lorentz violation's strength and the extra dimension affect the Casimir energy and pressure. In contrast, in the time-like vector case, they are only affected by the extra dimension. We also propose an indirect method to estimate the size of the extra dimension by comparing the frequency shift of the massless fermionic case to that of the scaled experimental data for the electromagnetic field.

Paper Structure

This paper contains 12 sections, 97 equations, 18 figures.

Table of Contents

  1. Introduction
  2. Model
  3. Casimir energy
  4. Time-like vector case
  5. Space-like vector case in $x^{3}$-direction
  6. Space-like vector case in $x^5$-direction
  7. Casimir Pressure
  8. Space-like vector case in $x^3$-direction
  9. Space-like vector case in $x^5$-direction
  10. Frequency shift and size of the extra dimension
  11. Summary and outlook
  12. Vacuum energy for the case of $x^{1}$ and $x^{2}$-directions

Figures (18)

  • Figure 1: Plot of the scaled Casimir energy ${E}_{\rm Cas.}/(L^2m^3)$ as a function of $ma$ and $q/a$ for two values of parameter $\beta$ with a fixed value of Lorentz violation intensity $\lambda=0.1$. In the left panel, we use $\beta=0$ while in the right panel, we use $\beta=0.5$. This figure shows the Lorentz violation in the $x^3$-direction.
  • Figure 2: Plot of the scaled Casimir energy ${E}_{\rm Cas.}/(L^2m^3)$ as a function of $ma$ for various values of the Lorentz violation's intensity $\lambda=0,0.05,0.1$ with fixed $q/a=0.5$ and two values of $\beta$. In the left panel, we use $\beta=0$ while in the right panel, we use $\beta=0.5$. This figure shows the Lorentz violation in the $x^3$-direction.
  • Figure 3: Plot of the scaled Casimir energy ${E}_{\rm Cas.}/(L^2m^3)$ as a function of $q/a$ for various values of the Lorentz violation's intensity $\lambda=0,0.05,0.1$ with fixed $m/a=0.5$ and two values of $\beta$. In the left panel, we use $\beta=0$ while in the right panel, we use $\beta=0.5$. This figure shows the Lorentz violation in the $x^3$-direction.
  • Figure 4: The left panel shows the scaled Casimir energy ${E}_{\rm Cas.}/(L^2m^3)$ as a function of parameter $\beta$ for three values of Lorentz violation's intensity $\lambda=0, 0.05,0.1$ with $\beta=0$ whereas the right panel shows the scaled Casimir energy as a function of $ma$ for various values of $\beta=0,0.25, 0.5$ with fixed $q/a=0.5$ and $\lambda=0.1$. This figure shows the Lorentz violation in $x^3$-direction.
  • Figure 5: Plot of the scaled Casimir energy ${E}_{\rm Cas.}/(L^2m^3)$ as a function of $ma$ and $q/a$ for two values of parameter $\beta$ with a fixed value of Lorentz violation intensity $\lambda=0.1$. In the left panel, we use $\beta=0$ whereas in the right panel, we use $\beta=0.5$. This figure shows the Lorentz violation in the $x^5$-direction.
  • ...and 13 more figures