Sep
05

Rotatory quantization of charge-conjugation symmetric systems.

1. Harmonic oscillators

       Zahid Zakir [1]

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. The same system also can be presented as a particle with positive and negative frequencies and, if to consider that a sign of mass of the particle coincides with a sign of its frequency, then the norm of negative frequency states remains positive.

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, v1, 5 September 2011

Online: TPAC: 3900-021 v2, 28 September 2012; DOI: 10.9751/TPAC.3900-021

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[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

One Response to “TPAC: 3900-021 v2, Vol. 6, p. 14–30”

  1. Zahid Zakir
    October 10th, 2012 at 03:12 | #1

    1. New result:
    In the Lagrangian unsymmetrized and symmetrized orderings of complex conjugate operators of momentum lead to different charge operators and are not equivalent at interaction with a gauge field.
    It is shown that due to C-symmetry conditions the zero-point charge does not arise in both orderings and in the first case the zero-point energy disappears.

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