Basic quantum mechanics for three Dirac equations in a curved spacetime

Details Basic quantum mechanics for three Dirac equations in a curved spacetime Basic quantum mechanics for three Dirac equations in a curved spacetime

2008-07-03

arxiv.org/abs/0807.0570v3

Brazilian J. of Physics, vol. 40, No. 2, pp. 242-255 (2010)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

35 pages (standard 12pt format). v3: Introduction reinforced, a few wording improvements in the body, former appendix removed

Scientific paper

We study the basic quantum mechanics for a fully general set of Dirac matrices in a curved spacetime by extending Pauli's method. We further extend this study to three versions of the Dirac equation: the standard (Dirac-Fock-Weyl or DFW) equation, and two alternative versions, both of which are based on the recently proposed linear tensor representations of the Dirac field (TRD). We begin with the current conservation: we show that the latter applies to any solution of the Dirac equation, iff the field of Dirac matrices $\gamma ^\mu $ satisfies a specific PDE. This equation is always satisfied for DFW with its restricted choice for the $\gamma ^\mu $ matrices. It similarly restricts the choice of the $\gamma ^\mu $ matrices for TRD. However, this restriction can be achieved. The frame dependence of a general Hamiltonian operator is studied. We show that in any given reference frame with minor restrictions on the spacetime metric, the axioms of quantum mechanics impose a unique form for the Hilbert space scalar product. Finally, the condition for the general Dirac Hamiltonian operator to be Hermitian is derived in a general curved spacetime. For DFW, the validity of this hermiticity condition depends on the choice of the $\gamma ^\mu $ matrices.

Affiliated with

Also associated with

No associations

Rating

Basic quantum mechanics for three Dirac equations in a curved spacetime does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Basic quantum mechanics for three Dirac equations in a curved spacetime, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Basic quantum mechanics for three Dirac equations in a curved spacetime will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-115901