Model of a quantum particle in spacetime.

DOI10.1088/0305-4470/34/19/318zbMATH Open1129.81327arXivhep-th/0012209OpenAlexW2014190943MaRDI QIDQ2735738

Publication date: 4 September 2001

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Abstract: Doplicher, Fredenhagen, and Roberts (1994, 1995) proposed a simple model of a particle in quantum spacetime. We give a new formulation of the model and propose some small changes and additions which improve the physical interpretation. In particular, we show that the internal degrees of freedom e and m of the particle represent external forces acting on the particle. To obtain this result we follow a constructive approach. The model is formulated as a covariance system. It has projective representations in which not only the spacetime coordinates but also the conjugated momenta are two-by-two noncommuting. These momenta are of the form P_mu-(b/c)A_mu, where b is the charge of the particle. The electric and magnetic fields obtained from the vector potential A_mu coincide with the variables e and m postulated by DFR. Similarly, the spacetime position operators are of the form Q_mu-(al^2/hbar c) Omega_mu where a is a generalized charge, l a fundamental length, and with vector potentials Omega_mu which are in some sense dual w.r.t. the A_mu.

Full work available at URL: https://arxiv.org/abs/hep-th/0012209

Mathematics Subject Classification ID

Noncommutative geometry methods in quantum field theory (81T75) General quantum mechanics and problems of quantization (81S99) Noncommutative geometry in quantum theory (81R60)