- The paper derives analytical expressions for Helmholtz free energy and Casimir pressure using the zeta function method in finite temperature settings.
- It demonstrates that Lorentz-violating corrections vary with boundary conditions and critical exponents, affecting attractive and repulsive forces between plates.
- Results highlight asymptotic limits, revealing Stefan-Boltzmann behavior at high temperatures and distinct modifications for Dirichlet and mixed conditions.
Overview of Finite Temperature Casimir Effect in Lorentz-Violating Scalar Theory
This paper explores the finite temperature Casimir effect generated by a complex scalar field that infringes upon Lorentz invariance through an aether-like, CPT-even approach facilitated by a constant space-like vector. The scalar field is described by a modified Klein-Gordon equation incorporating higher-order derivative terms tied to the vector. The paper primarily focuses on two configurations: the scalar field meeting Dirichlet boundary conditions and mixed boundary conditions on parallel plates. Utilizing the zeta function technique, the author derives analytical expressions for Helmholtz free energy and Casimir pressure under finite temperature conditions, examining distinct asymptotic limits of small plate distance, high temperature, and large mass.
Analytical Framework and Boundary Conditions
The scalar field model integrates a space-like unit vector to engage higher-order derivatives, breaking Lorentz symmetry and causing space-time anisotropy. The examination encompasses both parallel and perpendicular orientations of this vector in relation to the plates. The Helmholtz free energy and Casimir pressure calculations are performed using the generalized zeta function technique. This technique effectively compiles temperature effects on the quantum vacuum of the modified Klein-Gordon model, contrasting Dirichlet and mixed boundary conditions.
Key Results and Implications
Analytic results for free energy and Casimir pressure are produced across three asymptotic limits and distinct boundary conditions, revealing varying influences of Lorentz violation. For Dirichlet boundary conditions in the small plate distance limit, the Lorentz violating correction to the Casimir pressure weakens plates' attraction for even critical exponents while the high temperature limit showcases Stefan-Boltzmann-like behavior. Mixed boundary conditions present reverse signs compared to Dirichlet in small plate distance and large mass limits, with temperature-driven repulsion more potent under Dirichlet.
In terms of analytical implications, Lorentz-violating corrections manifest differently contingent on the critical exponent, the unit vector orientation, and the boundary conditions applied. Even values of critical exponent afford a weakening effect on pressure while odd values augment it under similar conditions. Numerically distinct expressions were derived for critical exponents ε = 2 and ε = 3, enabling a granular understanding of Lorentz violation's impacts across configurations.
Relevance to Quantum Field Theory and Future Directions
The paper contributes to the ongoing research of Lorentz-violating fields in quantum field theory, offering meticulous quantification of finite temperature adjustments to the Casimir effect among scalar fields. The incorporation of space-like vectors invites broader contemplation about Lorentz violation's practical applications and theoretical repercussions, potentially influencing future explorations in quantum gravity frameworks.
Prospective studies might explore experimental verification of these theoretical predictions, as well as expand investigations to encompass Neumann boundary conditions and elaborate further on interplay with other quantum fields and gauge theories. The analytical precision introduced paves the way for examining real-world space-time anisotropies potentially observable at lower energies, enriching the dialogue around fundamental symmetries in quantum physics.