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GENERAL MASSLESS FIELD EQUATIONS FOR HIGHER SPIN IN DIMENSION 4
  • Roman Lavicka,
  • vladimir soucek,
  • Wei Wang
Roman Lavicka
Charles University
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vladimir soucek
Charles University, Prague
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Wei Wang
Zhejiang University
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Abstract

Massless field equations are fundamental in particle physics. In Clifford analysis, the Euclidean version of these equations has been dealt with but it is not clear, even in dimension 4, what should be the right analogue of massless field equations for fields with values in a general irreducible Spin(4)-module. The main aim of the paper is to explain that a good possibility is to take the so-called generalized Cauchy-Riemann equations proposed a long time ago by E. Stein and G. Weiss. For this choice of the equations, we show that their polynomial solutions form different irreducible Spin(4)-modules. This is an important step in developing the corrresponding function theory.

Peer review status:ACCEPTED

26 Sep 2020Submitted to Mathematical Methods in the Applied Sciences
27 Sep 2020Submission Checks Completed
27 Sep 2020Assigned to Editor
03 Oct 2020Reviewer(s) Assigned
05 Feb 2021Review(s) Completed, Editorial Evaluation Pending
05 Feb 2021Editorial Decision: Revise Minor
17 Feb 20211st Revision Received
18 Feb 2021Submission Checks Completed
18 Feb 2021Assigned to Editor
18 Feb 2021Reviewer(s) Assigned
27 May 2021Review(s) Completed, Editorial Evaluation Pending
28 May 2021Editorial Decision: Accept