TPAC: 3900-022, Vol. 6, No 2, p. 31–47
Rotatory quantization of charge-conjugation symmetric systems. 2. Harmonic and magneto-harmonic rotators
Abstract
For soft rotators the lack of a radial component of velocity is a defining property and it allows to simplify quantization of harmonic and magneto-harmonic rotators. Operators of observables of soft rotators are normal ordered due to symmetries of the system, energy spectrum is linear under frequency and equidistant, and in the ground state there is no zero-point energy from rotational modes. It coincides with a generalization of the uncertainty relations for systems with non-hermitian canonical variables where the restrictions on fluctuations depend on state’s charge. Applications of the new formalism to quantization of waves at collective rotations of one-dimensional chain of harmonic rotators allows to model fields with charge-conjugation and gauge symmetries. For the rotating modes there is a crossing symmetry between states with opposite rotation directions, and arising of negative-frequency modes are positive-frequency states of antiquanta with replaced initial and final states. The commutators and causal correlators (propagators) of generalized coordinates of the harmonic rotator are derived.
PACS: 03.65.Ge, 11.30.Er, 1130.Ly, 11.90.+t
Key words: discrete symmetries, rotations, charge-conjugation symmetry, Landau levels, chain of rotators, propagators
Vol. 6, No 2, p. 31–47, 5 September 2011.