Since the formulation of the String Theory, we adopt that a fundamental symmetry of relativity should be broken at the energy scale bellow the Standard Model of Particle Physics. The symmetry breaking is implemented by the appearance of vector and tensor background that is reminiscent of a phase transition mechanism in high energy; the space-time became anisotropic by the presence of a background. We point out that the Lorentz symmetry breaking occurs only in a active Lorentz frame transformation, giving rise a new nomenclature for coordinate transformation in space-time: the observer and particle transformation. The main goal of this work is to clarify these transformations by a two examples in turn to explore the Lorentz symmetry breaking by a background vector field.
sponteneous symmetry breaking
