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Lin ZHU Xiu Hong FENG Yan Lin YU 《数学学报(英文版)》2007,23(9):1629-1638
In this paper, we give identifications of bispinor space with Grassmann algebra, and with Clifford algebra. The multiplication in Clifford algebra provides an action on them. Lastly we have researched on the geometry of bispinor space, and define Dirac operators to get a Pythagoras equality. 相似文献
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We have shown in a previous paper that the Dirac bispinor can vary like a four-vector and that Quantum Electrodynamics (QED) can be reproduced with this form of behaviour.(1) In Part I of this paper, we show that QED with the same transformational behaviour also holds in an alternative space we call M-space. We use the four-vector behaviour to model the two-body interaction in M and show that this has similar physical properties to the usual model in L which it predicts. In Part II of this paper we use M-space to show that QED can be reduced to two simple rules for a two-body interaction. 相似文献
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H. Arodź 《Physics letters. A》2019,383(12):1242-1246
The Hilbert space of states of the relativistic Majorana particle consists of normalizable bispinors with real components, hence the usual momentum operator can not be defined in this space. For this reason, we introduce the axial momentum operator, as a new observable for this particle. In the Heisenberg picture, the axial momentum contains a component which oscillates with the amplitude proportional to , where E is the energy and m the mass of the particle. The presence of the oscillations discriminates between the massive and massless Majorana particle. Furthermore, we show how the eigenvectors of the axial momentum, called the axial plane waves, can be used as a basis for obtaining the general solution of the evolution equation, also in the case of free Majorana field. Here a novel feature is a coupling of modes with the opposite momenta, again present only in the case of massive particle or field. 相似文献
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S. S. De 《International Journal of Theoretical Physics》2002,41(7):1307-1325
The electromagnetic field and its interaction with the leptons is introduced in Finsler space. This space is also considered as the microlocal space-time of the extended hadrons. The field equations for the Finsler space have been obtained from the classical field equations by quantum generalization of this space-time below a fundamental length-scale. On the other hand, the classical field equations are derived from a property of the fields on the autoparallel curve of the Finsler space. The field equations for the associated spaces of the Finsler space, which are macroscopic spaces, such as the large-scale space-time of the universe and the usual Minkowski space-time, can also be obtained for the case of Finslerian bispinor fields separable as the direct products of fields depending on the position coordinates with those depending on the directional arguments. The equations for the coordinate-dependent fields are the usual field equations with the cosmic time-dependent masses of the leptons. The other equations of the directional variable-dependent fields are solved here. Also, the lepton current and the continuity equation are considered. The form-invariance of the field equations under the general coordinate transformations of the Finsler spaces has been discussed. 相似文献
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There is a well-known way to generalize the Riemann-Roch operator for Kahler manifold to that for Hermitian manifold. In this paper we show a slightly different way to get a generalized Riemann-Roch operator, which is just the Dirac operator. The difference between the two operators is that the latter one enables the so-called Pythagoras equalities. 相似文献
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