Trace Dynamics as a model for emergent spacetime

Trace Dynamics is a classical theory of non-commuting matrices, which uses cyclic permutation inside a trace to define the derivative with respect to an operator. We have used the methods of Trace Dynamics to construct a non-commutative special relativity. We have defined a line-element using the tr...

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Bibliographic Details
Published in:Journal of physics. Conference series 2014-01, Vol.484 (1), p.12065-4
Main Authors: Lochan, K, Singh, T P
Format: Article
Language:English
Subjects:
Construction
Derivatives
Dynamics
Invariants
Lorentz transformations
Operators
Operators (mathematics)
Permutations
Physics
Relativity
Spacetime
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Summary:Trace Dynamics is a classical theory of non-commuting matrices, which uses cyclic permutation inside a trace to define the derivative with respect to an operator. We have used the methods of Trace Dynamics to construct a non-commutative special relativity. We have defined a line-element using the trace over spacetime coordinates, which are assumed to be operators. The line-element is shown to be invariant under generalized Lorentz transformations, and is used to construct a non-commutative relativistic dynamics. We have been motivated for such an operator structure at a more fundamental level, and attempt to obtain an emergent picture of classical spacetime.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/484/1/012065