Abstract
We consider the concept of deformed gauge invariance. The described formalism allows the vector gauge bosons to be massive independently of Higgs mechanism. It also allows the possibility for the variability of gauge coupling constants in space-time.
Highlights
Deformed Non-Abelian Gauge InvarianceWe proceed to the case of non-abelian gauge
We consider the concept of deformed gauge invariance
The mass problem for elementary particles in general, and for gauge vector bosons in particular, has been of actual character in many aspects, mostly in the construction of various unification models based on gauge invariance principle [1]-[7] where the Higgs mechanism for mass creation plays a crucial role
Summary
We proceed to the case of non-abelian gauge. Let {φ ( x)} be some matter field multiplet obeying the transformation law under gauge transformation φi M a being representation matrices of the symmetry algebra [ ] M a , Mb = ifabc M c (16). The covariant derivative is introduced by the formula:. ∑ Aμ ≡ Aμa M a a with the gauge fields Aμa ( x) transforming according to the rule:. The deformed field strength Fμ(υga) is constructed from the conventional one. In a similar way as Equation (5), namely:. The invariant Lagrangian for gauge fields should be:. By performing further calculations in a similar way as for the U (1) -gauge with the deformed Lorentz gauge condition. Taken into account the same expression (13) for mass mA will be obtained
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