Related papers: Some New Unifications in Supersymmetry and Higher …
The present lectures contain an introduction to low energy supersymmetry, a new symmetry that relates bosons and fermions, in particle physics. The Standard Model of fundamental interactions is briefly reviewed, and the motivation to…
It is well known that bosons and fermions exhibit opposite behaviors when experiencing interference, in the sense that bosons have a tendency to bunch whereas fermions have a tendency to antibunch. Recently, this complementarity was…
Supersymmetric theories are reviewed in the context of field theories. The gauge hierarchy problem in attempting the unification of all fundamental interactions is the strongest motivation of modern development of supersymmetry. Starting…
A fundamental pillar of quantum mechanics concerns indistinguishable quantum particles. In three dimensions they may be classified into fermions or bosons, having, respectively, antisymmetric or symmetric wave functions under particle…
It is commonly believed that there are only two types of particle exchange statistics in quantum mechanics, fermions and bosons, with the exception of anyons in two dimension. In principle, a second exception known as parastatistics, which…
Parity is ubiquitous, but not always identified as a simplifying tool for computations. Using parity, having in mind the example of the bosonic/fermionic Fock space, and the framework of Z_2-graded (super) algebra, we clarify relationships…
In quantum theory, particles in three spatial dimensions come in two different types: bosons or fermions, which exhibit sharply contrasting behaviours due to their different exchange statistics. Could more general forms of probabilistic…
Usual quantum statistics is written in Fock space but it is not an algebraic theory. We show that at a deeper level it can be algebraically formalized defining the different statistics as (multi-mode) coherent states of the appropriate (but…
We construct new integrable coupled systems of N=1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence…
Composite structure of particles somewhat modifies their statistics, compared to the pure Bose- or Fermi-ones. The spin-statistics theorem, so, is not valid anymore. Say, $\pi$-mesons, excitons, Cooper pairs are not ideal bosons, and,…
In the Bargmann-Fock representation the coordinates $z^i$ act as bosonic creation operators while the partial derivatives $\partial_{z^j}$ act as annihilation operators on holomorphic $0$-forms as states of a $D$-dimensional bosonic…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
In contrast to classical physics, quantum mechanics divides particles into two classes-bosons and fermions-whose exchange statistics dictate the dynamics of systems at a fundamental level. In two dimensions quasi-particles known as 'anyons'…
A deformed $q$-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the algebra…
We introduce a concise quantum operator formula for bosonization in which the Lie group structure appears in a natural way. The connection between fermions and bosons is found to be exactly the connection between Lie group elements and the…
We show how, using multipartite entanglement, the symmetries among bosons and fermions of the Standard Model of particle physics emerge. Fermions belong to tripartite maximally entangled classes starting with basic chiral right and left…
The present lectures contain an introduction to possible new physics beyond the Standard Model. Having in mind first of all accelerator experiments of the nearest future we concentrate on supersymmetry, a new symmetry that relates bosons…
Making use of a simple unitary transformation we change the hamiltonian of a particle coupled to an one dimensional gas of bosons or fermions to a new form from which the many body degrees of freedom can be easily traced out. The effective…
There are at least three physical arguments for some form of supersymmetry, based on experiment and observation, but conventional supersymmetry (SUSY) has not been observed up to surprisingly high experimental limits. Here we consider a…
\noindent In our contribution to this volume we deal with \emph{discrete} symmetries: these are symmetries based upon groups with a discrete set of elements (generally a set of elements that can be enumerated by the positive integers). In…