Dirac Field on Moyal-Minkowski Spacetime and Non-commutative Potential Scattering

被引：0
作者：
Markus Borris
Rainer Verch
机构：
[1] Universität Leipzig,Institut für Theoretische Physik
来源：
Communications in Mathematical Physics | 2010年 / 293卷
关键词：
Dirac Equation; Dirac Operator; Minkowski Spacetime; Noncommutative Geometry; Charge Conjugation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：399 / 448
页数：49
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