Archive for December, 2007


Quantization of relativistic fields without zero-point energy 

1. A complex scalar field

Zahid Zakir [1]


      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