Transformations of coordinates and Hamiltonian formalism in deformed special relativity

2003/04/07 by S. Mignemi
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Coordinate time #Cosmology and Gravitation Theories #Covariance #Formalism (music) #General covariance #General relativity #Hamiltonian (control theory) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Observer (physics) #Physics #Poisson bracket #Quantum mechanics #Spacetime #Theoretical physics #Theory of relativity #gr-qc

paper · pdf · doi:10.1103/physrevd.68.065029

published as Phys.Rev. D68 (2003) 065029 · 11 pages, plain LaTeX

arxiv created 2003/04/07 · openalex publication_date 2003/09/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We investigate the transformation laws of coordinates in generalizations of special relativity with two observer-independent scales. The request of covariance leads to simple formulas if one assumes noncanonical Poisson brackets, corresponding to noncommuting spacetime coordinates.

Citations

• Classical and Quantum Mechanics of Free κ-Relativistic Systems
• Two-dimensional gravity with an invariant energy scale
• On the definition of velocity in theories with two observer-independent scales
• Testable scenario for relativity with minimum length
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale