Related papers: Spin-Statistics Theorem and Geometric Quantisation
A specific algebraic coupling model involving multiple quantization axes is presented in which previously indistinguishable SU(2) symmetry groups become distinguishable when coupled into a SU(3) group structure. The model reveals new…
It is proved from stated assumptions of nonrelativistic quantum mechanics based on the Schroedinger equation that identical spin-zero particles must obey symmetric statistics.
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
We reconsider the effect of indistinguishability on the reduced density operator of the internal degrees of freedom (tracing out the spatial degrees of freedom) for a quantum system composed of identical particles located in different…
In this note we present preliminary study on the relation between the quantum entanglement of boundary states and the quantum geometry in the bulk in the framework of spin networks. We conjecture that the emergence of space with non-zero…
The adaptation of Wigner's induced representation for a relativistic quantum theory making possible the construction of wavepackets and admitting covariant expectation values for the coordinate operator x^\mu introduces a foliation on the…
In this sequel to my previous paper, "Is String Theory in Knots?" I explore ways of constructing symmetries through an algebraic stepping process using knotted graphs. The hope is that this may lead to an algebraic formulation of string…
Spin, $s$ in quantum theory can assume only half odd integer or integer values. For a given $s$, there exist $n=2s+1$ states $|s,m\rangle$, $m=s,s-1,........,-s$. A statistical assembly of particles (like a beam or target employed in…
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,…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
It is quite common to use the generalized probabilistic theories (GPTs) as generic models to reconstruct quantum theory from a few basic principles and to gain a better understanding of the probabilistic or information theoretic foundations…
We demonstrate a fundamental relation between the structures of physical space and of quantum theory: the set of quantum correlations in a rotational prepare-and-measure scenario can be derived from covariance alone, without assuming…
The spin-statistics connection, quantum gravity and other physical considerations suggest that classical space-time topology is not an immutable attribute and can change in quantum physics. The implementation of topology change using…
We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann's standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the…
In the free case, it is possible to define quantum fields which describe particles with integer or half-integer spin larger than one. It is shown that particles with integer spin must have Bose statistic and particles with half-integer-spin…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
Spin networks, the quantum states of discrete geometry in loop quantum gravity, are directed graphs whose links are labeled by irreducible representations of SU(2), or spins. Cosmic strings are 1-dimensional topological defects carrying…
The majority of current understanding of the quantum correlations is in the field of non-relativistic quantum mechanics. To develop quantum information and computation tasks fully, one must inevitably take into account the relativistic…
Using concepts of geometric orthogonality and linear independence, we logically deduce the form of the Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of the spin-1/2 system. Rather than a…