Quantization of relativistic fields without zero-point energy
1. A complex scalar field
Abstract
The relativistic fields having opposite sign on frequency modes usually are represented as complex fields only with positive-frequency modes, but with global U(1) symmetry and a charge conjugation (C-symmetry). However, at conventional introduction of operators of antiparticles C-symmetry becomes broken and then a zero-point charge and a vacuum zero-point energy arises. The new method of quantization of relativistic fields without C-symmetry violation is developed. On an example of a complex scalar field it is shown that C-symmetry requirements impose such constraints on bilinear products of ladder operators which lead to new operator identities. They then allow to express the observables through charge-conjugate creation-annihilation operators at once in a normal-ordered form without the zero-point energy and the zero-point charge. It is shown that a self-interaction of a complex scalar field does not change the vacuum energy. As the invariant propagators of particles and antiparticles can be chosen the retarded and advanced propagators accordingly.
PACS: 03.70.+k; 11.10.-z; 11.30.Er
Key words: vacuum energy, vacuum fluctuations, time reversal, charge conjugation
Vol. 2, No 3, p. 22 – 31, v1, 2 December 2007
Online: TPAC: 2527-008 v2, 28 September 2012; DOI: 10.9751/TPAC.2527-008
[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan
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