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Clifform calculus with applications to classical field theories

A Dimakis and F Muller-Hoissen

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The authors present a concise introduction to Clifford algebraic techniques and calculus with Clifford-algebra-valued differential forms (which they call 'clifforms'). Some examples of applications demonstrate the efficiency of these methods. These comprise Dirac-Kahler operators, Lie group and Kaluza-Klein geometry, Gauss-Bonnet Lagrangians, their dimensional reduction, and on-minimal couplings of gravity and an Abelian gauge field generated in this way. Furthermore, they formulate the four-dimensional Einstein equations as a clifform equation and relate it to certain spinor equations.


PACS

02.10.Ud Linear algebra

04.20.-q Classical general relativity

02.20.Qs General properties, structure, and representation of Lie groups

04.50.-h Higher-dimensional gravity and other theories of gravity

MSC

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

22Exx Lie groups (For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90)

83E15 Kaluza-Klein and other higher-dimensional theories

15A66 Clifford algebras, spinors

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 11 (November 1991)



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