External Fields and Related Effects

Even considering various violations, we basically expect that the relativity, CPT and many other would-be violated invariances are still present in a sense. Their violations used to be suggested in the form of a kind of external field of a classical (caused by matter or dark matter) or quantum (condensate) origin. We refer here to such a field as a violating field. The violating field can have a certain simple form in a specific frame and the result in other frames can be foimd by an appropriate Lorentz transformation. 

However, the same effects can be obtained if we assume that 

Meanwhile, because of the gauge invariance we caimot observe any constant homogeneous potential since the related strength of the electric field is zero. Does it mean that such a term is not observable at all The answer depends on how we treat different particles and what kind of problem we study. If, e.g., we consider the muon in the same way, but if two effective potentials are not the same (He Ufi), we should be able to observe their difference. The decay of muon and antimuon should have slightly different kinematics and the difference in their lifetime caused by the different phase volume of the decay product, would be proportional to Hg — Ui. To understand that we can have in mind so unrealistically large value of this difference that a muon would decay, but an antimuon would not. 

If we do parametrization more rigorously and introduce yo, instead of q (or more correctly to deal with the substitute 

As we could see above, the violating term is similar to the electric potential, but it is a kind of a selective field which should interact differently with different kinds of particles and only the differences can be observed. 

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