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Clifford algebras, Dirac equation, properties of solutions of the Dirac
equation on Rn.
Monogenic functions, Cauchy theorem and Cauchy integral formula.
Taylor and Laurent series.
Residuum of monogenic functions, residuum theorem.
Conformal invariance.
Last update: T_MUUK (16.05.2013)
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Students should pass an examination. Last update: Lávička Roman, doc. RNDr., Ph.D. (23.06.2021)
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[1] F. Brackx, R. Delanghe, F. Sommen: Clifford analysis, Pitman, London, 1982. [2] R. Delanghe, F. Sommen, V. Souček, Clifford algebra and spinor- valued functions, Kluwer Academic Publishers, Dordrecht, 1992. [3] J.E. Gilbert, M.A.M. Murray, Clifford Algebras and Dirac Operators in Harmonic Analysis, Cambridge University Press, Cambridge, 1991. [4] P. Lounesto, Clifford Algebras and Spinors, Cambridge University Press, 1997 (Second edition, 2001). Last update: Lávička Roman, doc. RNDr., Ph.D. (11.10.2016)
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Requirements to the exam correspond to the syllabus to the extent to which topics were covered during the course. Last update: Lávička Roman, doc. RNDr., Ph.D. (23.06.2021)
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Clifford algebra of a vector space with a scalar product, Spin group, spinor representations, spinor fields, the Dirac operator. Monogenic functions, connection with harmonic functions, Cauchy theorem, Cauchy integral formula and its applications, Morera theorem, Taylor and Laurent series, residue, residue theorem. Conformal maps in Euclidean space, action of conformal transformations on monogenic functions, conformal invariance. Last update: Lávička Roman, doc. RNDr., Ph.D. (13.09.2013)
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