TPAC: 3900-021, Vol. 6, No 2, p. 14–30
Rotatory quantization of charge-conjugation symmetric systems. 1. Harmonic oscillators
Abstract
In a system of a particle and antiparticle in the harmonic potential, represented as an oscillator with a complex generalized coordinate, there is a global U(1) symmetry and the charge conjugation (C-symmetry). It is shown that two pairs of ladder operators, introduced at the frequency decomposition of canonical variables, are not mutually charge-conjugate and that, therefore, their standard interpretation as operators of the charge-conjugate quanta breaks C-symmetry. Operator identities between bilinear products of the ladder operators are discovered, allowing expressing observables through charge-conjugate operators and it is correct to take into account C-symmetry. It is shown that these identities are maintained and at insert of the C-symmetric interactions. In a Lagrangian unsymmetrized and symmetrized orderings of complex conjugate operators of a momentum lead to different charge operators and are not equivalent at interaction with the gauge field. It is shown that due to C-symmetry conditions a zero-point charge does not arise in both orderings and in the first case a zero-point energy disappears also. The contribution of interaction with the gauge field and anharmonic potentials in higher orders of perturbation theory is considered.
PACS: 03.65.Ge, 11.30.Er, 1130.Ly, 11.90.+t
Key words: Hamiltonian dynamics, discrete symmetries, quantization
Vol. 6, No 2, p. 14–30, 5 September 2011.
Only the English abstract wording directly recovered from the 2019 source is included; no extra sentence was back-translated from the Russian version.