By Swanhild Bernstein (auth.), F. Brackx, J. S. R. Chisholm, V. Souček (eds.)

ISBN-10: 0792370457

ISBN-13: 9780792370451

ISBN-10: 9401008620

ISBN-13: 9789401008624

In its conventional shape, Clifford research presents the functionality thought for strategies of the Dirac equation. From the start, notwithstanding, the speculation was once used and utilized to difficulties in different fields of arithmetic, numerical research, and mathematical physics. lately, the idea has enlarged its scope significantly through incorporating geometrical tools from international research on manifolds and strategies from illustration conception. New, fascinating branches of the idea are in accordance with conformally invariant, first-order structures except the Dirac equation, or structures which are invariant with appreciate to a gaggle except the conformal team. This ebook represents an up to date overview of Clifford research in its current shape, its functions, and instructions for destiny examine. *Readership:* Mathematicians and theoretical physicists attracted to Clifford research itself, or in its functions to different fields.

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4. 5. 'l/J is a solution of the HS-Dirac equation Qs'l/J only if there exists an element ep E £s-l with DT'l/J = X(ep) Let us denote ep := 6s ('l/J). X 0 Qs 0 Y. 6. Let'l/J be a solution of higher spin Dirac equation Qs'l/J = o , then Let us denote by Pk(S) the space of polynomial k-homogeneous spinor-valued forms in £s. We would like to describe the space M(s) of all solutions of the equation Qs'l/J = 0 on an and its subspace Mk(S) of solutions, which are elements of Pk (s ). The space Mk(S) is a finite dimensional representation space of the group Spin(m), it can be decomposed into irreducible pieces and it is possible to find their representation types, determined by its highest weight.

Harmonic spinors (solutions of the Dirac equation) were studied intensively, only few facts are known about the properties of solutions of the other equations. A special system t: L of first order conformally invariant operators consists of elliptic operators of the first order • This work was supported by grant GAUK No. J13/98113200007 39 F. Brach et al. ), Clifford Analysis and Its Applications, 39--48. © 2001 Klwwer Academic Publishers. 247/2000 an CEZ 40 J BureS which have source and target in the same space of sections and which can be uniquely defined (together with some normalization).

Phys. 149 (1992) 241-262. Branson, T. and B. 0rsted Explicit junctional determinants in four dimensions. Proc. Amer. Math. Soc. 113 (1991) 669-682. , and P. -manifolds. Annals of Math. 142 (1995) 171-212. Connes, A. Noncommutative Geometry. Academic Press, San Diego, 1994. Eastwood, M. and J. Slovak Semi-holonomic Verma modules. J. Alg. 197 (1997) 424-448. M. Ricci: A Mathematica package for doing tensor calculations in differential geometry. edu/ lee/Ricci/. Stein, E. and G. Weiss Generalization of the Cauchy-Riemann equations and representations of the rotation group.

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