Superalgebraic representation of Dirac matrices

作者：Monakhov V V^*

来源：Theoretical and Mathematical Physics, 2016, 186(1): 70-82.

DOI：10.1134/S0040577916010062

• Grassmann algebra
• Clifford algebra
• quantum field theory
• generalized matrix algebra
• Dirac matrix
• spinor
• superspace
• supersymmetry

We consider a Clifford extension of the Grassmann algebra in which operators are constructed from products of Grassmann variables and derivatives with respect to them. We show that this algebra contains a subalgebra isomorphic to a matrix algebra and that it additionally contains operators of a generalized matrix algebra that mix states with different numbers of Grassmann variables. We show that these operators are extensions of spin-tensors to the case of superspace. We construct a representation of Dirac matrices in the form of operators of a generalized matrix algebra.

• 出版日期2016-1