Grassmann Mechanics, Multivector Derivatives and Geometric Algebra

A method of incorporating the results of Grassmann calculus within the framework of geometric algebra is presented, and shown to lead to a new concept, the multivector Lagrangian. A general theory for multivector Lagrangians is outlined, and the crucial role of the multivector derivative is emphasised. A generalisation of Noether’s theorem is derived, from which conserved quantities can be found conjugate to discrete symmetries.

C. J. L. Doran, A. N. Lasenby and S. F. Gull. Grassmann Mechanics, Multivector Derivatives and Geometric Algebra, In Z. Oziewicz, A. Borowiec and B. Jancewicz, editors, Spinors, Twistors, Clifford Algebras and Quantum Deformations (Kluwer Academic, Dordrecht, 1993), p. 215-226