Abstract
A Clifford calculus on sections of a Clifford bundle associated with a (pseudo-) Riemannian metric is reviewed. Its use is illustrated by reference to the Einstein — Yang — Mills equations. The formalism highlights the difference between the Kähler and Dirac equations and their separability in a curved space-time is discussed. Some aspects of supersymmetric models are outlined.
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References
C. Chevalley, ‘The Algebraic Theory of Spinors’, Columbia University Press, New York, 1954.
N. Salingaros, Y. Ilamed, Found. of Phys. 14 777 (1984).
N. Salingaros, M. Dresden, Adv. in Appl. Maths. 4 1 (1983); Phys. Rev. Letts. 43 1 (1970).
D. Hestenes, ‘Space-time Algebra’ (Gordon and Breach, New York, 1966); Found. in Phys. 12, 153, 1982.
J.S.R. Chisholm, R.S. Farwell, Proc. R. Soc. London, Ser. A, 377 1 (1981). Il. Nuovo. Cim. 82 145, 185, 210 (1984).
T.T. Truong, H.J. Vega, Phys. Letts. 151B 135 (1985).
P. Budinich, Proc. 8th Inst. Nathiagali, Pakistan (1983). P. Budinich, K. Bugajska, J. Math. Phys. 26 588 (1985). P. Budinich, L. Dabrowski, Lett. in Math. Physics 10 (1985) 7.
C.G. Darwin, Proc. R. Soc. 118 654 (1928). D. Ivaneko and L. Landau, Zeits f. Phys. 48 (1928) 340.
E. Kähler, Rend. Mat. (3-4)21 425 (1962).
W. Graf, Ann. Inst. Henri Poincaré, XXIX 85 (1978).
P. Becher, H. Joos, Zeit. Phys. C. Particles and Fields 15, 343, (1982). J.M. Rabin, Nucl. Phys. B201, 315 (1982). T. Banks, Y. Dothan and D. Horn, Phys. Lett. 117B (1982) 413. A.K. Common,‘Reduction of Dirac-Kahler Equation to Dirac Equation’, University of Kent Preprint.
I.M. Benn, R.W. Tucker, Comm. Math. Phys. 89 341 (1983).
P. Basarab-Horwath, R.W. Tucker, Comptes Rendue Acad. Sc. Paris, t, 299, Series I No. 20, 1984.
P. Basarab-Horwath, R.W. Tucker, ‘A Quantisation for Kähler Fields in Static Space-Time’. Lancaster University Preprint (1985).
I.M. Benn, R.W. Tucker, Comm. Math. Phys. 98 53, (1985), Phys. Letts. B130 177 (1983).
I.M. Benn, R.W. Tucker, Phys. Lett. B125 47 (1983) J. Phys. A 16. 4147 (1983).
I.M. Benn, R.W. Tucker, Phys. Lett. B132 325 (1984). II Nuovo. Cim. 88a 273 (1984). Proc. of Colloquium on Differential Geometry. Debrecen. Hungary 1984. J. Phys. A (Math) 16 4123 (1983).
T. Dereli, M. Onder, R.W. Tucker, Clas. Quantum Gray. 1L67 (1984). M. Panahi, R.W. Tucker,’ separation of Dirac and Kahler Equations in Spherically Symmetric Space-Times’. Lancaster University Preprint 1985.
A. Al-Saad, I.M. Benn, ‘Ideal Preserving Lorentzian Connections’, Lancaster University Preprint (1985).
I.M. Benn, B. Dolan, R.W. Tucker, Phvs. Letts. 150B 100 (1985).
I.M. Benn, R.W. Tucker, Phys. Letts. B119 348 (1982).
I.M. Benn, R.W. Tucker, ‘Pure Spinors and Real Clifford Algebras’, Lancaster University Preprint 1984.
I.M. Benn, M. Panahi, R.W. Tucker, Clas. Quantum Gray. 2 L71 (1985).
I.M. Benn, M. Panahi, R.W. Tucker, ‘A Note on the Zero Mode Structure of the Rarita-Schwinger Operator’, Clas. Quantum Gray. 2 L109 (1985).
I.M. Benn, R.W. Tucker, ‘A Modern Introduction to Spinors and Geometry with Applications in Physics’, Adam Hilger Ltd., Techno House, Redcliffe Way, Bristol, BS1 6NX, England. (To be published.)
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© 1986 D. Reidel Publishing Company
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Tucker, R.W. (1986). A Clifford Calculus for Physical Field Theories. In: Chisholm, J.S.R., Common, A.K. (eds) Clifford Algebras and Their Applications in Mathematical Physics. NATO ASI Series, vol 183. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4728-3_16
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DOI: https://doi.org/10.1007/978-94-009-4728-3_16
Publisher Name: Springer, Dordrecht
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