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The well-known Yang-Mills theory with one $ S^{1} / Z_{2}$ universal extradimension (UED) is generalized to an arbitrary number of spatial extradimensions through a novel compactification scheme. In this paper, theRiemannian flat based manifold under consideration contains $ n $ spatial extradimensions defined by $ n $ copies of the orbifold $ S^{1} / Z_{2}$. In thisapproach, we present the gauge structure and the mass spectrum of the effectivefour-dimensional theory. We introduce the concept of standard and nonstandardgauge transformations of the effective theory, and explicitly identify theemergence of massive vector fields in the same number as massless('pseudo-Goldstone') scalars in the compactified theory, verifying that aHiggs-like mechanism operates in the compactification process. It is foundthat, in contrast with the one UED scenario, in cases with two or more UEDsthere emerge massive scalar fields. Besides, at phase-space level, theHamiltonian analysis yields that the higher-dimensional and compactifiedtheories are classically equivalent using the fundamental concept of canonicaltransformation. This work lays the ground for a wider study on these theoriesconcerning their quantization and predictive power at the level of quantumfluctuations.

Yang-Mills theories with an arbitrary number of compactified extra dimensions