Related papers: Many-body States and Operator Algebra for Exclusio…
With an easily applicable criterion based on permutation symmetries of (identically prepared) replicas of quantum states we identify distinct entanglement classes in high-dimensional multi- partite systems. The different symmetry properties…
A general method to easily build global and relative operators for any number n of elementary systems if they are defined for 2 is presented. It is based on properties of the morphisms valued in the tensor products of algebras of the…
We present examples of many-body Wigner quantum systems. The position and the momentum operators ${\bf R}_A$ and ${\bf P}_A,\; A=1,\ldots,n+1$, of the particles are noncanonical and are chosen so that the Heisenberg and the Hamiltonian…
Several quantum systems have been used in the last few years to extend supersymmetry. In this paper we show all this systems fit into the picture of what we call "Number Operator Algebras".
Contents 1. Creation and annihilation operators for the system of indistinguishable particles 1.1 The permutation group and the states of a system of indistinguishable particles 1.2 Dimension of the Hilbert space of a system of…
Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their…
We provide a guiding principle to generate entanglement of quantum many-body states by applying key ideas of the Higgs mechanism to systems without gauge structures. Unitary operators associated with the Higgs mechanism are constructed,…
We consider a number operator-annihilation operator uncertainty as a well behaved alternative to the number-phase uncertainty relation, and examine its properties. We find a formulation in which the bound on the product of uncertainties…
The definitions of para-Grassmann variables and q-oscillator algebras are recalled. Some new properties are given. We then introduce appropriate coherent states as well as their dual states. This allows us to obtain a formula for the trace…
A new representation -which is similar to the Bargmann representation- of the creation and annihilation operators is introduced, in which the operators act like "multiplication with" and like "derivation with respect to" a single real…
It is shown how to construct many-particle quantum-mechanical spectra of particles obeying multispecies exclusion statistics, both in one and in two dimensions. These spectra are derived from the generalized exclusion principle and yield…
We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account…
After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…
We present the microscopic formulation of inclusion statistics, a counterpoint to exclusion statistics in which particles tend to coalesce more than ordinary bosons. We derive the microscopic occupation multiplicities of 1-body quantum…
This is a self-contained and hopefully readable account on the method of creation and annihilation operators (also known as the Fock space representation or the "second quantization" formalism) for non-relativistic quantum mechanics of many…
Second quantization is revisited and creation and annihilation operators are shown to be related, on the same footing both to the algebra ${\it h}(1)$, ${\underline {and}}$ to the superalgebra ${\it osp}(1|2)$ that are shown to be both…
Coherent states are usually defined as eigenstates of an unbounded operator, the so-called annihilation operator. We propose here possible constructions of {\em quasi-coherent states}, which turn out to be {\em quasi} eigenstate of a…
We derive a condition for the existence of completely or exponentially localised Majorana bound states (with the potential for non-Abelian statistics) in a generic many-body system. We discuss the relationship between the existence of these…
We review and develop the many-body spectral theory of ideal anyons, i.e. identical quantum particles in the plane whose exchange rules are governed by unitary representations of the braid group on $N$ strands. Allowing for arbitrary rank…
We investigate the expression of natural numbers in any base from a quantum point of view. In particular, resorting to the one-to-one correspondence between natural numbers and Fock states, we construct a set of multiboson operators and a…