The foundations of the theory of functions of commuting and anticommuting variables were laid in the well-known work A Note to the Quantum Dynamical Principle by J. Schwinger  published in 1953. Schwinger presented the analysis for commuting and anticommuting variables on the physical level of strictness. He assumed that there existed a set of points (which was later called a superspace) on which commuting and anticommuting coordinates were given and a differential calculus was constructed. This set was similar in many respects to Newton’s differential calculus. However, the superspace was not defined on the mathematical level of strictness (although the work  contained a remark concerning the construction of a superspace, namely, it was proposed to define a superspace as a subset of the algebra of quantum field operators).
KeywordsPhysical Theory Pseudo Differential Operator Grassmann Algebra Mathematical Level Mathematical Construction
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