Casimir effect, loop corrections and topological mass generation for interacting real and complex scalar fields in Minkowski spacetime with different conditions

Abstract

In this paper the Casimir energy density, loop corrections, and generation of topological mass are investigated for a system consisting of two interacting real and complex scalar fields. The interaction considered is the quartic interaction in the form of a product of the modulus square of the complex field and the square of the real field. In addition, it is also considered the self-interaction associated with each field. In this theory, the scalar field is constrained to always obey periodic condition while the complex field obeys in one case a quasiperiodic condition and in other case mixed boundary conditions. The Casimir energy density, loop corrections, and topological mass are evaluated analytically for the massive and massless scalar fields considered. An analysis of possible different stable vacuum states and the corresponding stability condition is also provided. In order to better understand our investigation, some graphs are also presented. The formalism we use here to perform such investigation is the effective potential, which is written as loop expansions via path integral in quantum field theory.

arXiv comment23 pages, 9 figures, accepted for publication in Physical Review D

References in corpus (17)

• Precision Measurement of the Casimir Force from 0.1 to 0.9 microns
• Measurement of the Casimir force between parallel metallic surfaces
• Casimir effect for scalar fields under Robin boundary conditions on plates
• Casimir Energy and Radius Stabilization in Five and Six Dimensional Orbifolds
• Anomalies in electrostatic calibrations for the measurement of the Casimir force in a sphere-plane geometry
• Radiative corrections to the Casimir effect for the massive scalar field
• Results from electrostatic calibrations for measuring the Casimir force in the cylinder-plane geometry
• The Casimir effect for the scalar and Elko fields in a Lifshitz-like field theory
• Thermal Casimir effect for the scalar field in flat spacetime under a helix boundary condition
• Casimir energy and topological mass for a massive scalar field with Lorentz violation
• Loop correction to the scalar Casimir energy density and generation of topological mass due to a helix boundary condition in a scenario with Lorentz violation
• Casimir Effect under Quasi-Periodic Boundary Condition Inspired by Nanotubes
• Dissipation of oscillating scalar backgrounds in an FLRW universe
• Ground state energy and topological mass in spacetimes with nontrivial topology
• Revisiting Vacuum Energy in Compact Spacetimes
• Quantum Brownian motion induced by an inhomogeneous tridimensional space and a $S^1\times R^3$ topological space-time
• Implications of symmetries in the scalar sector

Cited by in corpus (3)

• One-Loop Correction to the Casimir Energy in Lorentz-Violating ${\varphi }^4$ Theory with Rough Membrane Boundaries
• One-Loop Quantum Corrections to the Casimir Effect for Smoothly Rough Plates in the Low-Temperature Regime
• Vacuum energy, temperature corrections and heat kernel coefficients in $(D+1)$-dimensional spacetimes with nontrivial topology