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arXiv · 1203.6518

Statistical thermodynamics for a non-commutative special relativity: Emergence of a generalized quantum dynamics

Kinjalk Lochan·Seema Satin·Tejinder P. Singh
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Abstract

There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter degrees of freedom are treated as classical matrices with arbitrary commutation relations, and a space-time line element is defined using a trace. In the present paper, following the theory of Trace Dynamics, we construct a statistical thermodynamics for the non-commutative special relativity, and show that one arrives at a generalized quantum dynamics in which space and time are non-classical and have an operator status. In a future work, we will show how standard quantum theory on a classical space-time background is recovered from here.

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Kinjalk Lochan, Seema Satin, Tejinder P. Singh. 2012-03-29. Statistical thermodynamics for a non-commutative special relativity: Emergence of a generalized quantum dynamics. https://doi.org/10.1007/s10701-012-9683-3

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