Related papers: Are N=1 and N=2 supersymmetric quantum mechanics e…
One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N-1 complex structures satisfying a Clifford algebra and the constraints on the target space geometry can be formulated in…
A cyclic nature of quantum mechanical clock is discussed as ``quantization of time." Quantum mechanical clock is seen to be equivalent to the relativistic classical clock.
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
Exact solutions to the low-energy effective action of the four-dimensional, N=2 supersymmetric gauge theories with matter (including N=2 super-QCD) are discussed from the three different viewpoints: (i) instanton calculus, (ii) N=2 harmonic…
We extend the differential form representation of N = (n,n) supersymmetric quantum mechanics to the superconformal case. We identify the superalgebras occurring for n = 1,2,4, give necessary and sufficient conditions for their existence,…
We discuss the ways of constructing the exact superpotential for N=1 supersymmetric theories and propose a new approach. As a consequence, a new structure of the superpotential is found.
We construct L-theory with complex coefficients from the geometry of 1|2-dimensional perturbative mechanics. Methods of perturbative quantization lead to wrong-way maps that we identify with those coming from the MSO-orientation of L-theory…
The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…
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. Possible applications of this formalism have been…
We present the general ideas on SuperSymmetric Quantum Mechanics (SUSY-QM) using different representations for the operators in question, which are defined by the corresponding bosonic Hamiltonian as part of SUSY Hamiltonian and its…
We review the calculation and properties of the supersymmetric index for four dimensional N=1 theories, illustrating its physical significance in several examples.
It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a…
The interplay between supersymmetry and classical and quantum computation is discussed. First, it is shown that the problem of computing the Witten index of $\mathcal N \leq 2$ quantum mechanical systems is $\#P$-complete and therefore…
The author's opinion on the interpretation of quantum mechanics is further elucidated. Not only may quantum mechanics be a description of the sub-microscopic world that is profoundly different from what is often asserted, particularly…
Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and…
The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise…
We bring together two topics (quantum mechanics and time passage) with the goal of clarifying questions about each. Specifically, we claim that the formalism of quantum mechanics provides an answer to the question: "What is time passage?".
We present an attempt to formulate the supersymmetric and relativistic quantum mechanics in the sense of realizing supersymmetry on the single particle level, by utilizing the equations of motion which is equivalent to the ordinary 2nd…
A general theory is presented of quantum mechanics of singular, non-autonomous, higher derivative systems. Within that general theory, $n$-th order and $m$-th order Lagrangians are shown to be quantum mechanically equivalent if their…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…