*T***– ****и**** ***CP***–****symmetric quantization of fields**** without zero-point energy**

*T*

*CP*

**without zero-point energy**

**Abstract**

The standard replacement of negatively-frequency operators of relativistic fields to operators of antiparticles leads to incomplete time-reversal in field’s observables. In fact, a correct transition to the operators of antiparticles occurs only at a full* T- *or* CP-*transformation of matrix elements. Then the operators of observables of *T* – or *CP*-symmetric fields with standard Lagrangians appear as normal-ordered and the zero-point energy and the zero-point charge do not arise. The rules* *for the *CP-*symmetric quantization of fields are formulated and also the theorem about vanishing of the zero-point energy is proved. The theorem is in agreement with all known experiments since in fact the contributions of real sources are observed only. The divergent zero-point energy and zero-point charge appear only at using of the Lagrangians symmetrized under the complex-conjugate field operators, while the standard Lagrangians without such symmetrization lead to the required vanishing vacuum energy. At spontaneous symmetry breaking the vacuum zero-point energy and zero-point charge do not appear only if the remained scalar field is complex one and in this case the Standard Model predicts a pair boson-antiboson with hypercharge.

*PACS*: 03.70.+k; 11.10.-z; 11.30.Er

*Key words*: *vacuum energy, vacuum fluctuations, Casimir effect, time reversal, charge conjugation, cosmological constant*

Vol. **1**, No 1 , p. 11 – 27, v1, 22 September 2006

Online: TPAC: 2091-002 v2, 28 September 2012; DOI: 10.9751/TPAC.2091-002

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

1. New result:

The standard replacement of negatively-frequency operators of relativistic fields to operators of antiparticles leads to incomplete time-reversal in field’s observables.

2. New result:

In fact, a correct transition to the operators of antiparticles occurs only at a full CPT-transformation of matrix elements.

3. New result:

The operators of observables of T – or CP-symmetric fields with standard Lagrangians appear as normal-ordered and the zero-point energy and the zero-point charge do not arise.

4. New result:

The rules for the CP-symmetric quantization of fields are formulated and also the theorem about vanishing of the zero-point energy is proved.

The theorem is in agreement with all known experiments since in fact the contributions of real sources are observed only.

5. New result:

At spontaneous symmetry breaking the vacuum zero-point energy and zero-point charge do not appear only if the remained scalar field is complex one and in this case the Standard Model predicts a boson-antiboson pair with hypercharge.

6. New result:

In the standard treatment of QFT it has been postulated a direct identification of the negative-frequency operators in field operators by positive-frequency operators of charge-conjugate particles, i.e. antiparticles, and then the exclusion of the negative-frequency operators has been supposed to be completed.

For the minimal Lagrangian (3) this leads to a paradoxical result that for obeying the charge conjugation symmetry conditions the creation-annihilation operators should commutate. This means that the standard identification of the different frequency sign operators in (28) contradicts to the C-invariance of the theory and, therefore, is inadmissible.

It is shown,that this paradox can be solved at more accurate elimination of the negative frequency operators so that the zero-point energy and the zero-point charge do not arise due to the symmetry properties.