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F.: Dirac equation: Representation independence and tensor transformation
 Braz. J. Phys
, 2008
"... The BargmannPauli hermitizing matrix is used to define and study the probability current and the Hamiltonian operator for a fully general set of Dirac matrices in a flat spacetime with affine coordinates. It is found that the current, as well as the spectrum of the Dirac Hamiltonian, thus all of qu ..."
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Cited by 19 (19 self)
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The BargmannPauli hermitizing matrix is used to define and study the probability current and the Hamiltonian operator for a fully general set of Dirac matrices in a flat spacetime with affine coordinates. It is found that the current, as well as the spectrum of the Dirac Hamiltonian, thus all of quantum mechanics, are independent of that set. These results allow us to show that the tensor Dirac theory, which transforms the wave function as a spacetime vector and the set of Dirac matrices as a thirdorder affine tensor, is physically equivalent to the genuine Dirac theory, based on the spinor transformation. The tensor Dirac theory extends immediately to general coordinate systems, thus to noninertial (e.g. rotating) coordinate systems. Key words: Dirac equation, BargmannPauli hermitizing matrix, Dirac gamma matrices, fourvector wave function.
Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations
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Quantum mechanics for three versions of the Dirac
, 810
"... equation in a curved spacetime ..."
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Two alternative Dirac equations with gravitation
, 2007
"... An analysis of the classicalquantum correspondence shows that it needs to identify a preferred class of coordinate systems. One such class is that of the locallygeodesic systems. If a preferred reference frame is available, another class emerges. From the classical Hamiltonian that rules geodesic ..."
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An analysis of the classicalquantum correspondence shows that it needs to identify a preferred class of coordinate systems. One such class is that of the locallygeodesic systems. If a preferred reference frame is available, another class emerges. From the classical Hamiltonian that rules geodesic motion, the correspondence yields two distinct KleinGordon (KG) equations and two distinct Dirac equations in a general metric, depending on the class selected. Each of the two Dirac equations can be put in generallycovariant form, transforms the wave function as a fourvector, and differs from the standard (FockWeyl) gravitational Dirac equation. One obeys the equivalence principle in the usuallyaccepted sense, which the FockWeyl equation does not. Key words: quantum mechanics in a gravitational field, classicalquantum correspondence, Dirac and KleinGordon equations, preferred reference frame. 1
Interactions Between Real and Virtual Spacetimes
, 2014
"... Here arise the problems of modern physics that theories at the quantum scales have been discontinued. Therefore we should pass through the quantum scales and review phenomena at the sub quantum levels. The question is where to enter the sub quantum levels? Answer is; open a new window for massive ph ..."
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Here arise the problems of modern physics that theories at the quantum scales have been discontinued. Therefore we should pass through the quantum scales and review phenomena at the sub quantum levels. The question is where to enter the sub quantum levels? Answer is; open a new window for massive photons. The reason this answer is that although there are theoretical reasons to accept that the photon is a massless particle. The massless particle is an assumption, also a long series of very different experiments lead to the current experimental upper bound on the photon mass greater than zero. In this article, we analyzed that c is the edge of visible and invisible particles such as virtual photons and graviton. It leads us passing the real spacetime and enter into the virtual spacetime and describe interactions between real spacetime and virtual spacetime and reach to nonobvious space. Keywords: Spacetime, virtual spacetime, nonobvious DOI:10.14331/ijfps.2014.330075