Four-vector vs. four-scalar representation of the Dirac wave function

Details Four-vector vs. four-scalar representation of the Dirac wave function Four-vector vs. four-scalar representation of the Dirac wave function

2010-12-10

arxiv.org/abs/1012.2327v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages (standard 12pt). v2: version accepted for publication in Int. J. Geom. Meth. Mod. Phys. Some emphasis and a clarifica

Scientific paper

In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincar\'e group. This is not an option in a curved spacetime. Therefore, in the equation proposed independently by Fock and Weyl, the four complex components of the Dirac wave function transform as scalars under a general coordinate transformation. Recent work has shown that a covariant complex four-vector representation is also possible. Using notions of vector bundle theory, we describe these two representations in a unified framework. We prove theorems that relate together the different representations and the different choices of connections within each representation. As a result, either of the two representations can account for a variety of inequivalent, linear, covariant Dirac equations in a curved spacetime that reduce to the original Dirac equation in a Minkowski spacetime. In particular, we show that the standard Dirac equation in a curved spacetime, with any choice of the tetrad field, is equivalent to a particular realization of the covariant Dirac equation for a complex four-vector wave function.

Affiliated with

Also associated with

No associations

Rating

Four-vector vs. four-scalar representation of the Dirac wave function 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 Four-vector vs. four-scalar representation of the Dirac wave function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Four-vector vs. four-scalar representation of the Dirac wave function will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-108270