On the Fock Transformation in Nonlinear Relativity

Abstract

In this paper, we propose a new deformed Poisson brackets which leads to the Fock coordinate transformation by using an analogous procedure as in Deformed Special Relativity. We therefore derive the corresponding momentum transformation which is revealed to be different from previous results. Contrary to the earlier version of Fock's nonlinear relativity for which plane waves cannot be described, our resulting algebra keeps invariant for any coordinate and momentum transformations the four dimensional contraction $p_{\mu }{x}^{\mu }$, allowing therefore to associate plane waves for free particles. As in Deformed Special Relativity, we also derive a canonical transformation with which the new coordinates and momentum satisfy the usual Poisson brackets and therefore transform like the usual Lorentz vectors. Finally, we establish the dispersion relation for Fock's nonlinear relativity.

10 pages, no figures

References in corpus (2)

• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• A possible Reinterpretation of Einstein's Equations

Cited by in corpus (6)

• The Theory of Thermodynamic Relativity
• Maxwell's equations in the context of the Fock transformation and the magnetic monopole
• Exact form of Maxwell's equations and Dirac's magnetic monopole in Fock's nonlinear relativity
• Quantum Field Theory in fractal space-time with negative Hausdorff-Colombeau dimensions.The solution cosmological constant problem
• Maxwell's equations and Lorentz force in doubly special relativity
• Exact form of the generalized Lorentz force in Fock's nonlinear relativity