A. D. Popov

activity

20232026

collaborators

6 papers

quant-ph2026

Discrete symmetries in classical and quantum oscillators

Alexander D. Popov

We consider the nature of the wave function using the example of a harmonic oscillator. We show that the eigenfunctions $ψ_{n} = z^{n}$ of the quantum Hamiltonian in the complex Bargma…

hep-th2025

Dirac particles, spin and photons

Alexander D. Popov

We describe relativistic particles with spin as points moving in phase space $X = T^{*} R^{1, 3} \times C_{L}^{2} \times C_{R}^{2}$ , where $T^{*} R^{1, 3} = R^{1, 3} \times R^{1, 3}$ is the space of coor…

hep-th2024

Klein-Gordon oscillators and Bergman spaces

Alexander D. Popov

We consider classical and quantum dynamics of relativistic oscillator in Minkowski space $R^{3, 1}$ . It is shown that for a non-zero frequency parameter $ω$ the covariant p…

math-ph2024

Antiparticles in non-relativistic quantum mechanics

Alexander D. Popov

Non-relativistic quantum mechanics was originally formulated to describe particles. Using ideas from the geometric quantization approach, we show how the concept of antiparticles c…

hep-th2024

On Dirac equations on phase spaces

Alexander D. Popov

We consider Dirac equations on relativistic phase spaces $T^{*} R^{p - 1, 1}$ , where $R^{p - 1, 1}$ is Minkowski space with $p = 2, 4$ . We use the geometric quantization ap…

hep-th2023

Quantum connection, charges and virtual particles

Alexander D. Popov

Geometrically, quantum mechanics is defined by a complex line bundle $L_{ℏ}$ over the classical particle phase space $T^{*} R^{3} ≅ R^{6}$ with coordinates $x^{a}$ and momenta $p_{a}$ …