Abstract
We analyze the algebra of Dirac observables of the relativistic particle in four space-time dimensions. We show that the position observables become noncommutative and the commutation relations lead to a structure very similar to the noncommutative geometry of deformed special relativity (DSR). In this framework, it appears natural to consider the 4D relativistic particle as a five-dimensional massless particle. We study its quantization in terms of wave functions on the 5D light cone. We introduce the corresponding five-dimensional action principle and analyze how it reproduces the physics of the 4D relativistic particle. The formalism is naturally subject to divergences (due to the 5D representation), and we show that DSR arises as a natural regularization: the 5D light cone is regularized as the de Sitter space. We interpret the fifth coordinate as the particle's proper time while the fifth moment can be understood as the mass. Finally, we show how to formulate the Feynman propagator and the Feynman amplitudes of quantum field theory in this context in terms of Dirac observables. This provides new insights for the construction of observables and scattering amplitudes in DSR.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.