Bosonic symmetries of the massless Dirac equation. (English) Zbl 0915.35092
Summary: The results of spin 1 symmetries of massless Dirac equation are proved completely in the space of 4-component Dirac spinors on the basis of unitary operator in this space connecting this equation with the Maxwell equations containing gradient-like sources. Nonlocal representations of the conformal group are found, which generate the transformations under which the massless Dirac equation is invariant. The Maxwell equations with gradient-like sources are proved to be invariant with respect to fermionic representations of Poincaré and conformal groups and to be the kind of Maxwell equations with maximally symmetrical properties. Brief consideration of an application of these equations in physics is discussed.
MSC:
| 35Q40 | PDEs in connection with quantum mechanics |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 58J70 | Invariance and symmetry properties for PDEs on manifolds |
Keywords:
Poincaré group; Dirac equation; Maxwell equations; gradient-like sources; fermionic representations; conformal groupsReferences:
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