Fischer Decomposition for Massless Fields of Spin 1 in Dimension 4
The massless field equations for lower integer and half-integer values of spin in Minkowski space are fundamental equations in mathematical physics. Their counterpart in Euclidean spacetime is a system of elliptic equations, which was already studied from the viewpoint of function theory in the fram...
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| Veröffentlicht in: | Complex analysis and operator theory 2018-02, Vol.12 (2), p.439-456 |
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| creator | Brackx, F. De Schepper, H. Krump, L. Souček, V. |
| description | The massless field equations for lower integer and half-integer values of spin in Minkowski space are fundamental equations in mathematical physics. Their counterpart in Euclidean spacetime is a system of elliptic equations, which was already studied from the viewpoint of function theory in the framework of so-called Hodge systems for differential forms of various degrees. In dimension 4 it is possible to substitute spinor calculus for the usual tensor notation. In the present paper we concentrate on the case of the massless field equation for spin 1 in dimension 4, and we treat, in a spinor formalism, a fundamental concept of its function theory: the Fischer decomposition of polynomial spinor fields, for which we give simple and independent proofs. |
| doi_str_mv | 10.1007/s11785-017-0697-x |
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Their counterpart in Euclidean spacetime is a system of elliptic equations, which was already studied from the viewpoint of function theory in the framework of so-called Hodge systems for differential forms of various degrees. In dimension 4 it is possible to substitute spinor calculus for the usual tensor notation. 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| subjects | Analysis Calculus Decomposition Euclidean geometry Mathematical analysis Mathematics Mathematics and Statistics Minkowski space Operator Theory |
| title | Fischer Decomposition for Massless Fields of Spin 1 in Dimension 4 |
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