The three-dimensional Klein–Gordon oscillator exhibits an algebraic structure known from supersymmetric quantum mechanics. supersymmetry is unbroken with a vanishing Witten index, and it utilized to derive the spectral properties of oscillator, which closely related that nonrelativistic harmonic in three dimensions. Supersymmetry also enables us closed-form expression for energy-dependent Green...

Semiclassical methods provide important tools for approximating solutions in quantum mechanics. In several cases these are intriguingly exact rather than approximate, as has been shown by direct calculations on particular systems. this paper we prove that the long-conjectured exactness of supersymmetry-based semiclassical quantization condition broken supersymmetry is a consequence additive sha...

In these Lectures, we present a pedagogical introduction to weak scale supersymmetry phenomenology. A basic understanding of the Standard Model and of the ideas behind Grand Unification, but no prior knowledge of supersymmetry, is assumed. Topics covered include: • What is supersymmetry and why do we bother with it? • Working with a supersymmetric theory: A toy example

A many variable q-calculus is introduced using the formalism of braided covector algebras. Its properties when certain of its deformation parameters are roots of unity are discussed in detail, and related to fractional supersymmetry. The special cases of two dimensional supersymmetry and fractional supersymmetry are developed in detail. PACS 02.10T, 11.30P, 03.65F. e-mail: [email protected]...

These lectures give an introduction to the problem of finding a realistic and natural extension of the standard model based on spontaneously broken supersymmetry. Topics discussed at some length include the effective field theory paradigm, coupling constants as superfield spurions, gauge mediated supersymmetry breaking, and anomaly mediated supersymmetry breaking, including an extensive introdu...

We show that theories in the confining, free magnetic, and conformal phases can break supersymmetry through dynamical effects. To illustrate this, we present theories based on the gauge groups SU(n) × SU(4) × U(1) and SU(n) × SU(5) × U(1) with the field content obtained by decomposing an SU(m) theory with an antisymmetric tensor and m− 4 antifundamentals. Supported in part by DOE under cooperat...

Abstract. We show how spontaneous supersymmetry breaking in the vacuum state of higher-derivative supergravity is transmitted, as explicit soft supersymmetry-breaking terms, to the effective Lagrangian of the standard electroweak model. The general structure of the soft supersymmetry breaking terms is presented and a new scenario for understanding the gauge hierarchy problem, based on the funct...

We review mechanisms of dynamical supersymmetry breaking. Several observations that narrow the search for possible models of dynamical supersymmetry breaking are summarized. These observations include the necessary and sufficient conditions for supersymmetry breaking. The two conditions are based on non-rigorous arguments, and we show examples where they are too restrictive. Dynamical effects p...

In this paper I review the multiplet calculus of N = 1, D = 1 local supersymmetry with applications to the construction of models for spinning particles in background fields, and models with space-time supersymmetry. New features include a non-linear realization of the local supersymmetry algebra and the coupling to anti-symmetric tensor fields of both odd and even rank. The non-linear realizat...

We present a simple four-dimensional model in which anomaly mediated supersymmetry breaking naturally dominates. The central ingredient is that the hidden sector is near a strongly-coupled infrared fixed-point for several decades of energy below the Planck scale. Strong renormalization effects then sequester the hidden sector from the visible sector. Supersymmetry is broken dynamically and requ...