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Yang-Mills-Higgs models with higher order derivatives

Models with higher order derivative terms in the kinetic energy appear not only as effective theories, they can be considered as elementary, renormalizable models in their own right. The extension of Higgs mechanism is discussed for Yang-Mills-Higgs models where the kinetic energy of the scalar field contains higher order derivatives. The connection term of the covariant derivatives generates a local potential for the gauge field in the phase with spontaneously broken global gauge symmetry which may break Lorentz symmetry in the vacuum. Relativistic, massless gauge bosons spectrum is found for small fluctuations where the only remnant of the breakdown of the Lorentz symmetry is a shift of the energy induced by the expectation value of the temporal component of the gauge field, reminiscent of a chemical potential.