Related papers: A New Approach to Spin and Statistics
The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important \qo{Pauli Exclusion Principle} but by the adoption of the complex standard relativistic quantum field…
A number of interesting features of the ground states of quantum spin chains are analized with the help of a functional integral representation of the system's equilibrium states. Methods of general applicability are introduced in the…
Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realise and investigate topological quantum spin liquid phases. This new and exciting direction brings about important research…
We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of…
We present a construction of integrable quantum spin chains where local spin-spin interactions are weighted by ``position''-dependent potential containing abelian non-local spin dependance. This construction applies to the previously…
Rigidity results for asymptotically locally hyperbolic manifolds with lower bounds on scalar curvature are proved using spinor methods related to the Witten proof of the positive mass theorem. The argument is based on a study of the Dirac…
The problem of fermions in 1+1 dimensions in the presence of a pseudoscalar Coulomb potential plus a mixing of vector and scalar Coulomb potentials which have equal or opposite signs is investigated. We explore all the possible signs of the…
We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in…
Here we explore the possibility to obtain a non-relativistic proof of the spin-statistics theorem. First, we examine the structure of axioms and theorems involved in a relativistic Schwinger-like proof of the spin-statistics relation.…
We present a coherent proof of the spin-statistics theorem in path integral formulation. The local path integral measure and Lorentz invariant local Lagrangian, when combined with Green's functions defined in terms of time ordered products,…
The three-dimensional universal complex Clifford algebra is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the…
We investigate with the help of Clifford algebraic methods the Mandelbrot set over arbitrary two-component number systems. The complex numbers are regarded as operator spinors in D\times spin(2) resp. spin(2). The thereby induced (pseudo)…
Many years ago Friedman and Sorkin [1] established the existence of certain topological solitonic excitations in quantum gravity called (topological) geons. Geons can have quantum numbers like charge and can be tensorial or spinorial having…
We propose a novel quantum technique to search for unmodeled anomalies in multidimensional binned collider data. We propose associating an Ising lattice spin site with each bin, with the Ising Hamiltonian suitably constructed from the…
In this article, an introduction to the nonlinear equations for completely symmetric bosonic higher spin gauge fields in anti de Sitter space of any dimension is provided. To make the presentation self-contained we explain in detail some…
Clock-spin models are attracting great interest, due to both their rich phase diagram and their connection to parafermions. In this context, we derive an exact local mapping from clock-spin to fermionic partition functions. Such mapping,…
Based on the results of part I, we obtain the general form of the addition theorem for spin spherical harmonics and give explicit results in the cases involving one spin-$s'$ and one spin-$s$ spherical harmonics with $s',s=1/2$, 1, 3/2, and…
We prove that every unitary invertible quantum field theory satisfies a generalization of the famous spin-statistics theorem. To formulate this extension, we define a `higher spin' action of the stable orthogonal group $O$ on appropriate…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
The analytical relations in position, momentum and four-dimensional spaces are established for the expansion and one-range addition theorems of relativistic complete orthonormal sets of exponential type spinor wave functions and Slater…