Physics – Mathematical Physics
Scientific paper
2008-12-03
Commun.Math.Phys.293:399-448,2010
Physics
Mathematical Physics
60 pages, 1 figure
Scientific paper
10.1007/s00220-009-0905-2
The quantized free Dirac field is considered on Minkowski spacetime (of general dimension). The Dirac field is coupled to an external scalar potential whose support is finite in time and which acts by a Moyal-deformed multiplication with respect to the spatial variables. The Moyal-deformed multiplication corresponds to the product of the algebra of a Moyal plane described in the setting of spectral geometry. It will be explained how this leads to an interpretation of the Dirac field as a quantum field theory on Moyal-deformed Minkowski spacetime (with commutative time) in a setting of Lorentzian spectral geometries of which some basic aspects will be sketched. The scattering transformation will be shown to be unitarily implementable in the canonical vacuum representation of the Dirac field. Furthermore, it will be indicated how the functional derivatives of the ensuing unitary scattering operators with respect to the strength of the non-commutative potential induce, in the spirit of Bogoliubov's formula, quantum field operators (corresponding to observables) depending on the elements of the non-commutative algebra of Moyal-Minkowski spacetime.
Borris Markus
Verch Rainer
No associations
LandOfFree
Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering 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 Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-625972