Integral Formulas for Higher Order Conformally Invariant Fermionic Operators

  • Chao DingEmail author


In this paper, we establish higher order Borel–Pompeiu formulas for conformally invariant fermionic operators in higher spin theory, which is the theory of functions on m-dimensional Euclidean space taking values in arbitrary irreducible representations of the Spin group. As applications, we provide higher order Cauchy’s integral formulas for those fermionic operators. This paper continues the work of building up basic integral formulas for conformally invariant differential operators in higher spin theory.


Fermionic operators Stokes’ theorem Borel–Pompeiu formula Cauchy’s integral formula 

Mathematics Subject Classification

Primary 30Gxx Secondary 42Bxx 46F12 58Jxx 



The author is grateful to the anonymous referees for detailed comments.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mathematics/PhysicsBauhaus-Universität WeimarWeimarGermany

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