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\(q\)-deformed superspace and \(q\)-extended supersymmetric Hamiltonian with arbitrary superpotential. (English. Russian original) Zbl 0943.58005

J. Math. Sci., New York 94, No. 4, 1611-1619 (1999); translation from Zap. Nauchn. Semin. POMI 235, 260-272 (1996).
The authors consider one of the possible generalizations of supersymmetry (SUSY). For this purpose, they state the \(q\)-superspace formalism and construct the \(q\)-supertransformation group on this \(q\)-superspace. After this, they begin with a standard action for a scalar \(d\)-dimensional real superfield and construct a \(q\)-extended supersymmetric Lagrangian for the component variables of the \(q\)-superfield. After the quantization procedure, the corresponding conserved quantities become \(q\)-supercharges.

MSC:

58C50 Analysis on supermanifolds or graded manifolds
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81T60 Supersymmetric field theories in quantum mechanics