Related papers: Introducci\'on a la supersimetr\'ia
These are introductory notes on symmetries in quantum field theory and how they apply to particle physics. The notes cover the fundamentals of group theory, their representations, Lie groups, and Lie algebras, along with an elaborate…
Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction…
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum…
These notes describe some links between the group $\mathrm{SL}_2(\mathbb{R})$, the Heisenberg group and hypercomplex numbers---complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
Supersymmetric quantum mechanical models are computed by the Path integral approach. In the $\beta\rightarrow0$ limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of…
Motivated by Quantum Bayesianism I give background for a general epistemic approach to quantum mechanics, where complementarity and symmetry are the only essential features. A general definition of a symmetric epistemic setting is…
We introduce and define the quantum affine $(m|n)$-superspace (or say quantum Manin superspace) $A_q^{m|n}$ and its dual object, the quantum Grassmann superalgebra $\Omega_q(m|n)$. Correspondingly, a quantum Weyl algebra $\mathcal…
We give a new interpretation for the super loop space that has been used to formulate supersymmetry. The fermionic coordinates in the super loop space are identified as the odd generators of the Weil algebra. Their bosonic superpartners are…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
This is a survey of the work of Seiberg and Witten on 4-dimensional N=2 supersymmetric Yang-Mills theory and of some of its recent extensions, written for mathematicians. The point of view is that of algebraic geometry and integrable…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
This set of lectures contain a brief review of some basic supersymmetry and its representations, with emphasis on superspace and superfields. Starting from the Poincar\'e group, the supersymmetric extensions allowed by the Coleman-Mandula…
We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors…
These lecture notes were created for a graduate-level course on quantum simulation taught at Leibniz University Hannover in 2013. The first part of the course discusses various state of the art methods for the numerical description of…
Introductory lectures on the phenomenology of the minimal supersymmetric Standard Model. The emphasis is on general signatures for supersymmetry and on the motivation for constructing supersymmetric models. These lectures are intended for…
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
This is the first Internet course on elementary quantum mechanics written in Spanish ("castellano") for the benefit of Spanish speaking students. I thank my eight Mexican students at the Institute of Physics, University of Guanajuato, Leon,…
We study the supersymmetric quantum mechanical systems that arise from discrete light cone quantization of theories with minimal supersymmetry in various dimensions. These systems, which have previously arisen in the study of black hole…