Relativistic Adiabatic Approximation and Geometric Phase

Abstract

A relativistic analogue of the quantum adiabatic approximation is developed for Klein-Gordon fields minimally coupled to electromagnetism, gravity and an arbitrary scalar potential. The corresponding adiabatic dynamical and geometrical phases are calculated. The method introduced in this paper avoids the use of an inner product on the space of solutions of the Klein-Gordon equation. Its practical advantages are demonstrated in the analysis of the relativistic Landau level problem and the rotating cosmic string.

Plain LaTeX

Cited by in corpus (15)

• Relativistic Landau Levels in the Rotating Cosmic String Spacetime
• Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation
• Geometric Phase for Neutral Particle in the Presence of a Topological Defect
• Landau Quantization in the Spinning Cosmic String Spacetime
• Transfer Matrices as Non-Unitary S-Matrices, Multimode Unidirectional Invisibility, and Perturbative Inverse Scattering
• Gravitational Geometric Phase in the Presence of Torsion
• A New Class of Adiabatic Cyclic States and Geometric Phases for Non-Hermitian Hamiltonians
• Feshbach-Villars oscillator (FVO) in Kaluza-Klein Theory (KKT)
• Statistical proerties of the two-dimensional Feshbach-illars oscillator (FVO) in the rotating cosmic string
• Hamilton Operator and the Semiclassical Limit for Scalar Particles in an Electromagnetic Field
• Scalar particle in general inertial and gravitational fields and conformal invariance revisited
• Fluctuation, time-correlation function and geometric Phase
• Pseudo-Hermitian continuous-time quantum walks
• Perturbative Calculation of the Adiabatic Geometric Phase and Particle in a Well with Moving Walls
• An anisotropic rotating cosmic string with Lorentz violation: thermodynamics and Landau levels