Parasupersymmetry and N-fold supersymmetry in quantum many-body systems. I: General formalism and second order

$\mathcal{N}$-FOLD PARASUPERSYMMETRY

“…An 'N -fold generalization' of quasi-parasupersymmetry proposed in Ref. [9] is also straightforward.…”

“…As we pointed out in Ref. [9], an apparent drawback of the (generalized) BDCF formalism is that the relations (8) do not reduce to the ordinary N -fold supersymmetric anti-commutation relation {Q − , Q + } = C 1 P N (H) when p = 1, in contrast to the RSTK relation (7). For this reason, we only consider the (generalized) RSTK formalism in this paper.…”

“…We note that this system exactly reduces to the parasupersymmetric quantum system of Rubakov-Spiridonov (RS) type [4] when N = 1 and R 1 + R 2 = 0. In our previous paper [9], we found that the RS model admits a generalized 2-fold superalgebra. In the following, we show that the above N -fold parasupersymmetric system also satisfies a novel non-linear algebra.…”

“…In this letter, we report on a new type of non-linear supersymmetries, called N -fold parasupersymmetry, which is a generalization of both N -fold supersymmetry [1, 2,3] and parasupersymmetry [4,5,6,7,8]. In our previous paper [9], we generically formulated parasupersymmetry and showed that parasupersymmetric quantum systems as well as N -fold supersymmetric ones are weakly quasi-solvable. The latter fact implies that corresponding higher-dimensional quantum field theories, if exist, would satisfy some kinds of perturbative non-renormalization theorems, as in the case of ordinary supersymmetric quantum field theory, since quasi-solvability is a one-dimensional analog and, in a sense, a generalization of the theorems [2].…”

“…For the formulation, we fully employ the general formalism of parafermionic algebra and parasupersymmetry previously proposed by us in Ref. [9] and omit technical details of them in this letter. Hence, for the details see Ref.…”