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Statistical Thermodynamics for a Non-commutative Special Relativity: Emergence of a Generalized Quantum Dynamics

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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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Acknowledgements

This publication was made possible through the support of a grant from the John Templeton Foundation. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation.

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Authors and Affiliations

  1. Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India

    Kinjalk Lochan & Tejinder P. Singh

  2. Inst. of Math. Sciences, IV Cross Road, CIT Campus Taramani, Chennai, 600113, India

    Seema Satin

Authors
  1. Kinjalk Lochan
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  2. Seema Satin
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  3. Tejinder P. Singh
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Correspondence to Tejinder P. Singh.

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Lochan, K., Satin, S. & Singh, T.P. Statistical Thermodynamics for a Non-commutative Special Relativity: Emergence of a Generalized Quantum Dynamics. Found Phys 42, 1556–1572 (2012). https://doi.org/10.1007/s10701-012-9683-3

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  • DOI: https://doi.org/10.1007/s10701-012-9683-3

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