Trace Dynamics and a non-commutative special relativity |
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Authors: | Kinjalk Lochan TP Singh |
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Institution: | Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India |
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Abstract: | Trace Dynamics is a classical dynamical theory of non-commuting matrices in which cyclic permutation inside a trace is used to define the derivative with respect to an operator. We use the methods of Trace Dynamics to construct a non-commutative special relativity. We define a line-element using the Trace over space–time coordinates which are assumed to be operators. The line-element is shown to be invariant under standard Lorentz transformations, and is used to construct a non-commutative relativistic dynamics. The eventual motivation for constructing such a non-commutative relativity is to relate the statistical thermodynamics of this classical theory to quantum mechanics. |
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