Theoretical aspects of the DFR quantum spacetime (2021)
A systematic study of the Doplicher-Fredenhaguen-Roberts (DFR) Quantum Spacetime is presented. This work is based on the original quantized spacetime described by Doplicher, Fredenhaguen, and Roberts in Commun. Math. Phys. 172. I motivate the DFR Quantum Spacetime to obtain Spacetime Uncertainty Relations from the Principle of Gravitational Stability against localization of events and the hoop conjecture. I outline the characteristics of regular representations fulfilling the Quantum Conditions and show how an algebra can be constructed to describe the DFR Quantum Spacetime. I outline how there is a one-to-one correspondence between the representation of the algebra and the regular realizations. I also present how in the classical limit, the commutative Minkowski space is recovered.