Clifford Algebras and the Dirac-Bohm Quantum Hamilton-Jacobi Equation |
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Authors: | B J Hiley R E Callaghan |
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Institution: | (1) Birkbeck College, University of London, London, UK |
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Abstract: | In this paper we show how the dynamics of the Schr?dinger, Pauli and Dirac particles can be described in a hierarchy of Clifford
algebras, C1,3, C3,0{\mathcal{C}}_{1,3}, {\mathcal{C}}_{3,0}, and C0,1{\mathcal{C}}_{0,1}. Information normally carried by the wave function is encoded in elements of a minimal left ideal, so that all the physical
information appears within the algebra itself. The state of the quantum process can be completely characterised by algebraic
invariants of the first and second kind. The latter enables us to show that the Bohm energy and momentum emerge from the energy-momentum
tensor of standard quantum field theory. Our approach provides a new mathematical setting for quantum mechanics that enables
us to obtain a complete relativistic version of the Bohm model for the Dirac particle, deriving expressions for the Bohm energy-momentum,
the quantum potential and the relativistic time evolution of its spin for the first time. |
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Keywords: | |
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