Related papers: Nonlinear Supersymmetry
We discuss the cosmological constant problem in the light of dilatation symmetry and its possible anomaly. For dilatation symmetric quantum theories realistic asymptotic cosmology is obtained provided the effective potential has a…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
The N=1 Volkov-Akulov model of nonlinear supersymmetry is explicitly related to a vector supermultiplet model with a Fayet-Iliopoulos D term of linear supersymmetry. The physical significance of the results is discussed briefly.
We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying algebraic structure of the Z_2-graded uniform topological symmetries of type (1,1) and…
We discuss how the stochastic approach for supersymmetric theories leads to new ways of characterizing anomalies in how supersymmetry can be broken.
Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland (2005a,b) is surveyed and clarified. The…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
We consider a gauge symmetry in a quantum Hilbert space. The symmetry leads to that of the heat-kernel and of the anomaly formulae which were previously obtained by the authors. This greatly simplifies and clarifies the structure of the…
We analyze general structure of N-fold supersymmetry which provides a systematic framework to construct weakly quasi-solvable quantum mechanical systems. Main ingredients of our analysis are dimensional analysis and introduction of an…
We exploit the hidden symmetry structure of a recently proposed non-Hermitian Hamiltonian and of its Hermitian equivalent one. This sheds new light on the pseudo-Hermitian character of the former and allows access to a generalized quantum…
Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection,…
We analyse the relation between anomalies in their manifestly supersymmetric formulation in superspace and their formulation in Wess-Zumino (WZ) gauges. We show that there is a one-to-one correspondence between the solutions of the…
Algebraic relations that characterize quantum statistics (Bose-Einstein statistic, Fermi-Dirac statistic, supersymmetry, parastatistic, anyonic statistic, ...) are reformulated herein in terms of a new algebraic structure, which we call…
We consider how the problem of determining normal forms for a specific class of nonholonomic systems leads to various interesting and concrete bridges between two apparently unrelated themes. Various ideas that traditionally pertain to the…
At an elementary level, we present some non-perturbative aspects of non-abelian gauge theories in four dimensional space-time. Some rigorous results have been obtained in the framework of supersymmetric theories, and a very rich physics…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
In this work we report a new result that appears when one investigates the route that starts from a scalar field theory and ends on a supersymmetric quantum mechanics. The subject has been studied before in several distinct ways and here we…
We extend Tanaka theory to the context of supergeometry and obtain an upper bound on the supersymmetry dimension of geometric structures related to strongly regular bracket-generating distributions on supermanifolds and their structure…
In these lectures I present a basic introduction to supersymmetry, especially to N=1 supersymmetric gauge theories and their renormalization, in the Wess-Zumino gauge. I also discuss the various ways supersymmetry may be broken in order to…
We examine various generalizations, e.g. exactly solvable, quasi-exactly solvable and non-Hermitian variants, of a quantum nonlinear oscillator. For all these cases, the same mass function has been used and it has also been shown that the…