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M.: Dirac equation from the Hamiltonian and the case with a gravitational
, 2006
"... Starting from an interpretation of the classicalquantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies in the same form to a free particle, to one in an electromag ..."
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Starting from an interpretation of the classicalquantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies in the same form to a free particle, to one in an electromagnetic field, and to one subjected to geodesic motion in a static metric, and leads to the same, usual form of the Dirac equation—in special coordinates. To use the equation in the staticgravitational case, we need to rewrite it in more general coordinates. This can be done only if the usual, spinor transformation of the wave function is replaced by the 4vector transformation. We show that the latter also makes the flatspacetime Dirac equation Lorentzcovariant, although the Dirac matrices are not invariant. Because the equation itself is left unchanged in the flat case, the 4vector transformation does not alter the main physical consequences of that equation in that case. However, the equation derived in the staticgravitational case is not equivalent to the standard (FockWeyl) gravitational extension of the Dirac equation. 1
Minimal spatiotemporal extent of events, neutrinos, and the cosmological constant problem
, 2005
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Interaction of Gravitational Waves with Quantum Coherent Systems
, 2005
"... I would like to thank my parents. Although I think they are bemused about my efforts to study Physics, they nevertheless convey encouragement. I would also like to thank Assoc. Prof. Michael Morgan for agreeing to supervise me in this project and for his patience and guidance. Thanks also to Dr. Dav ..."
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I would like to thank my parents. Although I think they are bemused about my efforts to study Physics, they nevertheless convey encouragement. I would also like to thank Assoc. Prof. Michael Morgan for agreeing to supervise me in this project and for his patience and guidance. Thanks also to Dr. David Paganin for helping me maintain a general sense of perspective and for invaluable encouragement. i Accelerating masses are predicted to emit radiation as gravitational waves. It has been suggested that these waves may interact differently with quantum mechanical systems than with classical matter. The possibility that a quantum system may act as a novel transducer between electromagnetism and gravitational waves is investigated. A proposed mechanism for interconversion between the two fields is studied whereby a term due to the presence of the gravitational field appears in the Hamiltonian of the quantum mechanical system. The term is analogous to the vector potential of the electromagnetic field to which it is seen to couple.