A parametrization of the Hamiltonian of the generalized Witten model of the SUSY QM by a single arbitrary function in d = 1 has been obtained for an arbitrary number of the supersymmetries N = 2N . Possible applications of this formalism have been discussed. It has been shown that the N = 1 and 2 conformal SUSY QM is generalized for any N .Recently, the interest to the supersymmetric quantum mechanics [1], [2] has been renewed. Following the Maldacena's conjecture [3] it has been argued [4], that the extended superconformal quantum mechanics [5], [6], [7], [8] describes the dynamics of a D − 0 brane in the near horizon background of the extreme Reisner-Nordstrom black hole. In the framework of the N = 1 SUSY QM the exactly solvable potentials of the common QM were classified and found to be related to the integrability condition called shape invariance [9], [10]. Thereis an exciting connection of the extended SUSY QM to the solution of the Calogero type many body potentials [11]. It has been noted [12], that the N ≥ 4 superconformal Calogero model has not been constructed yet. These motivations lead us to consider an old problem of extending the SUSY QM to an arbitrary number of the supersymmetries N. Unlike the supersymmetric field theories, where the number N is constrained by the spin content ( N = 4 for the SYM, and N = 8 for the SUGRA both in D = 4), the extended SUSY QM appears to have none. Thus, we can consider N as a free parameter in the theory. For the same reason the extended SUSY QM of N > 8 can not be the result of the dimensional reduction of the corresponding field theory. Originally, the SUSY QM was first considered in the algebraic approach by Witten [1], [2] before the superfield approach was developed in [5], [13]. The main advantage of the latter is that it gives the SUSY QM a natural classical foundation. On the other hand, the algebraic approach is more directly related to the quantum mechanical aspects of the theory. Although, it is possible to obtain the results of this paper in both formalisms, we will consider here only the generalization of the Witten model,
In this paper we discuss the possibility of existence of anapole formfactor of the proton. In the framework of hypothesis of violation of discrete symmetries in electromagnetic processes involving composite systems with strong interactions we discuss the results of modern experiments on elastic ep-scattering and recent results on the measurement of radius of proton. In the approach of Poincare invariant quantum mechanics the analysis of experiments on elastic ep-scattering is made and electromagnetic and anapole formfactors of proton are calculated
In this paper we propose to discuss the electromagnetic structure of the nucleon in the framework of the violation hypothesis of discrete symmetries. Analysis is performed with help of the general method of the Lorentz-covariant local operator matrix element parametrization. The proposed analysis allows to solve the problem of the "non-Rosenbluth" behavior of the electromagnetic proton form factors. It is shown that the CP-violation effects give rise to the additional anapole proton form factor.
A free lattice fermion field theory in 1+1 dimensions can be interpreted as SOStype model, whose spins are integer-valued. We point out that the relation between these spins and the fermion field is similar to the abelian bosonization relation between bosons and fermions in the continuum. Though on the lattice the connected 2n-point correlation functions of the integer-valued spins are not zero for any n ≥ 1, the twopoint correlation function of these spins is that of free bosons in the infrared. We also conjecture the form of the Wess-Zumino-Witten chiral field operator in a nonabelian lattice fermion model. These constructions are similar in spirit to the "twistable string" idea of Krammer and Nielsen.--------------------------
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