2024/05/23 by Alexander D. Popov, Popov, Alexander D. · 1 citation
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mechanical and Optical Resonators #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2405.14349
openalex publication_date 2024/05/23 · openalex created_date 2024/05/25 · openalex updated_date 2026/07/28
We consider classical and quantum dynamics of relativistic oscillator in Minkowski space ℝ3,1. It is shown that for a non-zero frequency parameter ω the covariant phase space of the classical Klein-Gordon oscillator is a homogeneous Kähler-Einstein manifold Z6=AdS7/U(1)=U(3,1)/U(3)× U(1). In the limit ω→ 0, this manifold is deformed into the covariant phase space T^*H3 of a free relativistic particle, where H3=H3+∪ H-3 is a two-sheeted hyperboloid in momentum space. Quantization of this model with ω≠ 0 leads to the Klein-Gordon oscillator equation which we consider in the Segal-Bargmann representation. It is shown that the general solution of this model is given by functions from the weighted Bergman space of square-integrable holomorphic (for particles) and antiholomorphic (for antiparticles) functions on the Kähler-Einstein manifold Z6. This relativistic model is Lorentz covariant, unitary and does not contain non-physical states.