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Fischer decomposition for massless fields of spin 1 in dimension 4

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Abstract
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.
Keywords
Fischer decomposition, Massless fields, Spin 1

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Please use this url to cite or link to this publication:

Chicago
Brackx, Fred, Hennie De Schepper, Lukas Krump, and Vladimir Souček. 2018. “Fischer Decomposition for Massless Fields of Spin 1 in Dimension 4.” Complex Analysis and Operator Theory 12 (2): 439–456.
APA
Brackx, Fred, De Schepper, H., Krump, L., & Souček, V. (2018). Fischer decomposition for massless fields of spin 1 in dimension 4. COMPLEX ANALYSIS AND OPERATOR THEORY, 12(2), 439–456.
Vancouver
1.
Brackx F, De Schepper H, Krump L, Souček V. Fischer decomposition for massless fields of spin 1 in dimension 4. COMPLEX ANALYSIS AND OPERATOR THEORY. PICASSOPLATZ 4, BASEL, 4052, SWITZERLAND: SPRINGER BASEL AG; 2018;12(2):439–56.
MLA
Brackx, Fred, Hennie De Schepper, Lukas Krump, et al. “Fischer Decomposition for Massless Fields of Spin 1 in Dimension 4.” COMPLEX ANALYSIS AND OPERATOR THEORY 12.2 (2018): 439–456. Print.
@article{8562028,
  abstract     = {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.},
  author       = {Brackx, Fred and De Schepper, Hennie and Krump, Lukas and Sou\v{c}ek, Vladimir},
  issn         = {1661-8254},
  journal      = {COMPLEX ANALYSIS AND OPERATOR THEORY},
  keyword      = {Fischer decomposition,Massless fields,Spin 1},
  language     = {eng},
  number       = {2},
  pages        = {439--456},
  publisher    = {SPRINGER BASEL AG},
  title        = {Fischer decomposition for massless fields of spin 1 in dimension 4},
  url          = {http://dx.doi.org/10.1007/s11785-017-0697-x},
  volume       = {12},
  year         = {2018},
}

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