Related papers: Nonlinear Supersymmetry
This article reviews the subject of supersymmetry and its breaking. The emphasis is on recent developments in metastable, dynamical supersymmetry breaking, which permit the construction of promising models of particle physics.
We consider quantum models corresponding to superymmetrizations of the two-dimensional harmonic oscillator based on worldline $d=1$ realizations of the supergroup SU$(\,{\cal N}/2\,|1)$, where the number of supersymmetries ${\cal N}$ is…
We study in general spacetime dimension the symmetry of the theory obtained by gauging a non-anomalous finite normal Abelian subgroup $A$ of a $\Gamma$-symmetric theory. Depending on how anomalous $\Gamma$ is, we find that the symmetry of…
Some problems related to an algebraic approach to quantum statistics are discussed. Generalized quantum statistics is described as a result of interactions. The Fock space representation is discussed. The problem of existence of…
Supersymmetry is one of the most important and indispensable ingredients of modern theoretical physics. However, the absence, at least at the time of publishing this review, of experimental verification of supersymmetry in elementary…
In this note, we revisit a classical problem related to the density of nonlinear statistics. We obtain a new representation of densities and, for the first time, a necessary and sufficient condition for the existence of densities is…
We introduce the notion of algebraic higher symmetry, which generalizes higher symmetry and is beyond higher group. We show that an algebraic higher symmetry in a bosonic system in $n$-dimensional space is characterized and classified by a…
In this paper we generalize previous results on anomaly resolution to noninvertible symmetries. Briefly, given a global symmetry G of some theory with a 't Hooft anomaly rendering it ungaugeable, the idea of anomaly resolution is to extend…
Higher dimensional supersymmetric quantum mechanics is studied. General properties of the two dimensional case are presented. For three spatial dimesions or higher, a spin structure is shown to arise naturally from the nonrelativistic…
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…
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration…
Nuclear supersymmetry is reviewed and some of its applications and extensions are discussed, together with a proposal for new, more stringent and precise tests to probe the supersymmetry classification, in particular, correlations between…
We outline an approach that streamlines considerably the construction and analysis of well-behaved nonlinear quantum dynamics, with completely positive extensions to entangled systems. A few notes are added on the issue of quantum…
Using the basic ingredient of supersymmetry, we develop a simple alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wave functions do not involve tedious…
These five lectures collect elementary facts about 4D supersymmetric theories with emphasis on N=1 supersymmetry, as well as the basic notions of supersymmetric quantum mechanics. Contents: I. From symmetries to supersymmetry; II. Basic…
Starting with assumptions both simple and natural from "physical" point of view we present a direct construction of transformations preserving wide class of (anti)commutation relations which describe Euclidean/Minkowski superspace…
We define a semi-Hopf algebra which is more general than a Hopf algebra. Then we construct the supersymmetry algebra via the adjoint action on this semi-Hopf algebra. As a result we have a supersymmetry theory with quantum gauge group,…
Superconducting quantum symmetries in extended single-band 1-dimensional Hubbard models are shown to originate from the classical (pseudo-)spin SO(4) symmetry of a class of models of which the standard Hubbard model is a special case.…
We analyse some quantum multiplets associated with extended supersymmetries. We study in detail the general form of the causal (anti)commutation relations. The condition of positivity of the scalar product imposes severe restrictions on the…
In this talk we use nonlinear realizations to study the spontaneous partial breaking of rigid and local supersymmetry.