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arXiv · hep-th/0111110

Doubly special quantum and statistical mechanics from quantum $κ$-Poincaré algebra

J. Kowalski-Glikman
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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.

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J. Kowalski-Glikman. 2001-11-12. Doubly special quantum and statistical mechanics from quantum $κ$-Poincaré algebra. https://doi.org/10.1016/s0375-9601(02)00751-x

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