arXiv:hep-th/0112090hep-th
Lorentz invariance with an invariant energy scale
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Abstract
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a non-linear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants, and we highlight the similarities between the group action found and a transformation previously proposed by Fock. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.
Special relativity is defined by invariants on the Minkowski metric ds^2 = dx^2 - dt^2 using general coordinates and setting c to unity. This is a generalization of the Euclid metric ds^2 = dx^2. (In Cartesian coordinates and in 2d, ds^2 = dx^2 + dy^2). Just as the Euclidean…
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