Dual numbers and supersymmetric mechanics

Abstract

We show that dual numbers, apart from the known practical applications to the description of a rigid body movements in three dimensional space and natural presence in abstract differential algebra, play a role in field theory and are related to supersymmetry as well. Relevant models are considered.

On Special Spacelike Hybrid Numbers

“…Using equalities (1) and (2) we define the hybrid numbers multiplication. Moreover, by (1) and (2) we can find the product of any two hybrid units as presented in Table 1.…”

On the Basic Structures of Dual Space

“…In 1994, by using dual numbers, Cheng [5] introduced the C H programming language. These numbers play an important role in field theory as well [12]. The most interesting use of dual numbers in field theory can be shown in a series of articles by Wald et al [22].…”

Nilpotent quantum mechanics and SUSY

“…In a natural way, the formalism we present, suits the analysis of entanglement in multiqubit systems. The applicability of nilpotent commuting variables is not restricted only to the quantum mechanics, but they are also of use in the quantumˇeld theory and statistical physics [3,4]. In the context of the description of qubit systems, the formalism of functions of η variables Å functions of theˇrst order nilpotent commuting variables, η 2 = 0, gives natural language to address the entanglement questions for multiqubit systems.…”