Re: dirac equation in curved spacetime

On Sep 19, 6:27 am, Oh No <N...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
Thus spake vivishek <vivishek.sud...@xxxxxxxxx>>Is there a single, well-accepted form of the dirac equation for a free
particle in curved spacetime? If not, what are the various
possibilities constructed so far?

Its form is determined by manifest covariance, but of course it may be
treated either as a wave equation or an operator equation as usual. Here
is a selection of papers.

arXiv:0706.4413
Title: Quantum wave equations in curved space-time from wave mechanics
Authors: Mayeul Arminjon

arXiv:hep-th/0610207
Title: On bound states of Dirac particles in gravitational fields
Authors: Nicolas Boulanger, Fabien Buisseret, Philippe Spindel

arXiv:gr-qc/0603099
Title: Electromagnetic and gravitational self-force on a relativistic
particle from quantum fields in curved space
Authors: Chad R. Galley, B. L. Hu, Shih-Yuin Lin

arXiv:hep-th/0411016
Title: Symmetries and supersymmetries of the Dirac operators in curved
spacetimes
Authors: I. I. Cotuaescu, M. Visinescu

arXiv:gr-qc/0409080 [ps, pdf, other]
Title: $\bar{SL}(4,R)$ Embedding for a 3D World Spinor Equation
Authors: Djordje Sijacki

arXiv:gr-qc/0209096
Title: Gravity, torsion, Dirac field and computer algebra using MAPLE
and REDUCE

arXiv:gr-qc/0103056 [ps, pdf, other]
Title: Application of linear hyperbolic PDE to linear quantum fields in
curved spacetimes: especially black holes, time machines and a new semi-
local vacuum concept
Authors: Bernard S. Kay (York)

arXiv:gr-qc/0010065 [ps, pdf, other]
Title: The phase of a quantum mechanical particle in curved spacetime
Authors: P.M. Alsing, J.C. Evans, K.K. Nandi

arXiv:gr-qc/0008047 [ps, pdf, other]
Title: A new approach to electromagnetic wave tails on a curved
spacetime

arXiv:gr-qc/9708041 [ps, pdf, other]
Title: Gravity from Dirac Eigenvalues
Authors: Giovanni Landi, Carlo Rovelli

arXiv:gr-qc/9612034 [ps, pdf, other]
Title: General Relativity in terms of Dirac Eigenvalues
Authors: Giovanni Landi, Carlo Rovelli

Regards

--
Charles Francis
moderator sci.physics.foundations.
substitute charles for NotI to email


Also take a look at "Quantum Fields in Curved Space" by Birrell and
Davies.

And it's not going to be the equation of "a free particle" anymore but
of a field.
Curvature does not uniformly conserve the notion of particles.

.

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