Doubly special quantum and statistical mechanics from quantum $\kappa$-Poincaré algebra

Abstract

Recently Amelino--Camelia proposed a ``Doubly Special Relativity'' theory with two observer independent scales (of speed and mass) that could replace the standard Special Relativity at energies close to the Planck scale. Such a theory might be a starting point in construction of quantum theory of space-time. In this paper we investigate the quantum and statistical mechanical consequences of such a proposal. We construct the generalized Newton--Wigner operator and find relations between energy/momentum and frequency/wavevector for position eigenstates of this operator. These relations indicate the existence of a minimum length scale. Next we analyze the statistical mechanics of the corresponding systems. We find that depending on the value of a parameter defining the canonical commutational algebra one has to do either with system with maximal possible temperature or with the one, which in the high temperature limit becomes discrete.

11 pages, LaTeX

References in corpus (6)

• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• Deformed Boost Transformations That Saturate at the Planck Scale
• Observer-independent quanta of mass and length
• Some Consequences of the Generalised Uncertainty Principle: Statistical Mechanical, Cosmological, and Varying Speed of Light
• Planck-scale relativity from quantum $\kappa$-Poincaré algebra

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• Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity
• The Soccer-Ball Problem
• Spacetime singularity resolution in Snyder noncommutative space
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• Thermodynamics of Ideal Gas in Doubly Special Relativity
• Natural Cutoffs via Compact Symplectic Manifolds
• Thermodynamics of a photon gas and deformed dispersion relations
• UV and IR quantum-spacetime effects for the Chandrasekhar model
• Gravity's rainbow: a bridge between LQC and DSR
• Deformed Special Relativity from Asymptotically Safe Gravity
• Spectrum of the three dimensional fuzzy well
• Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology
• A fundamental length as a candidate for dark energy: a DSR inspired FRW spacetime
• Compact stars in quantum spacetime
• A cosmological viewpoint on the correspondence between deformed phase-space and canonical quantization
• Universal entropy bound and discrete space-time
• Noncommutative spaces and covariant formulation of statistical mechanics
• Undeformed (additive) energy conservation law in Doubly Special Relativity
• The cosmological implications of a fundamental length: a DSR inspired de-Sitter spacetime
• Entropy bound for the photon gas in noncommutative spacetime
• Thermodynamics of a Photon Gas in Nonlinear Electrodynamics
• Early universe thermostatistics in curved momentum spaces
• Equilibrium properties of blackbody radiation with an ultraviolet energy cut-off
• Planck scale effect on the thermodynamics of photon gas
• Photon gas thermodynamics in dS and AdS momentum spaces
• kappa-Deformed Kinematics and Addition Law for Deformed Velocities