The irreducible unitary representation of the noncompact SL(2, C) is discussed by a method based on the use of the homogeneous functions. The mat¡ elements of the finite transformations are calculated explicitly. The method is very eonvenient for applications in physics and the results of GELFAND and NAIMAI~K are obtained in a very simple way.

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 spacetime.

Based on the mechanism for mass creation in the space-time with extradimensions proposed in our previous work, (arXiv: 1301.1405 [hep-th] 2013) we consider now the mass spectrum of vector bosons in extradimensions. It is shown that this spectrum is completely determined by some function of compactification length and closely related to the metric of extradimensions.

In this work we consider a mechanism for mass creation based on the periodicity condition dictated from the compactification of extradimensions. It is shown that the existence and the compactification of extradimensions are the origin for creating particle mass in ordinary 4-dimensional space-time. Mass of Higgs particles themselves would be also originated from the geometric topology of extradimensions.

The mass spectrum for spinor fields in extra dimensions is considered within the framework of the mass creation mechanism proposed in our previous works (Duc and Giao 2013; Duc and Giao J. Mod. Phys. 4(N7), 991, 2013; Duc et al. J. Phys Sci. Appl. (USA) 4(N1), 60, 2014; Duc and Giao J. Mod. Phys. 5(N6), 2014). It is shown that a single spinor field in the whole space-time with extradimensions corresponds to a set of multiplets of effective spinor fields in ordinary 4-dimensional space-time with masses obeying the sum rule expressed in terms of metric for extradimensions and parameter functions dictated from the periodicity conditions.