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30

Quantization of complex harmonic oscillator and the zero-point energy vanishing effect

Zahid Zakir [1]

Abstract

      The system of two harmonic oscillators with different sign frequencies is presented as a positive-frequency oscillator with a complex generalized coordinate where there are a global U(1) symmetry and a charge conjugation symmetry (C-symmetry). It is shown that two pairs of ladder operators, appearing at the frequency decomposition of canonical variables, are not mutually charge-conjugate and their standard interpretation as operators of charge-conjugate quanta breaks the C-symmetry. Bilinear operator identities for the ladder operators are found allowed the theory to obey the C-symmetry restrictions and to express observables through the mutually charge-conjugate operators. These identities hold for C-symmetric interactions also. It is shown that C-symmetry eliminates a ground state zero-point charge and a zero-point energy. The uncertainty relations are generalized for non-hermitian canonical variables and it is shown that the charge-conjugation symmetric ground states do not quantized. It is shown that the C-symmetric interactions do not contribute to the ground state energy in all orders of perturbation theory.

PACS: 03.65.Ge, 11.30.Er, 1130.Ly, 11.90. + t

Key words: Hamiltonian dynamics, discrete symmetries, quantization, oscillator, uncertainty relations

Vol. 2, No 2,  p. 9 – 21, v1,   30 November 2007

Online: TPAC: 2525-007 v2,  18 September 2012; DOI: 10.9751/TPAC.2525-007


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

      zahidzakir@theor-phys.org