Related papers: Particles and Quantum Symmetries
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
The connection between the intrinsic angular momentum (spin) of particles and the quantum statistics is established by considering the response of identical particles to a common background radiation field. For this purpose, the Hamiltonian…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
Despite its name, Quantum Field Theory (QFT) has been built to describe interactions between localizable particles. For this reason the actual formalism of QFT is partly based on a suitable generalization of the one already used for systems…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…
We define quantum field theory by taking the Lagrangian action to be given as a sequence of mathematically well-defined functionals written in terms of operator fields fulfilling given \hbox{local} commutation relations. The renormalized…
Orthofermi statistics is characterized by an exclusion principle which is more ``exclusive'' than Pauli's exclusion principle: an orbital state shall not contain more than one particle, no matter what the spin direction is. The wavefunction…
We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A…
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…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
The aim of these notes is to elucidate some aspects of quantum field theory in curved spacetime, especially those relating to the notion of particles. A selection of issues relevant to wave-particle duality is given. The case of a generic…
Quantum coherence is the outcome of the superposition principle. Recently, it has been theorized as a quantum resource, and is the premise of quantum correlations in multipartite systems. It is therefore interesting to study the coherence…
We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum…
The real Hilbert space formalism developed within the quaternionic quantum mechanics ($\mathbb H$QM) is fully applied to the simple model of the autonomous particle. This framework permits novel insights within the usual description of the…
We discuss some algebraic aspects of quantum permutation groups, working over arbitrary fields. If $K$ is any characteristic zero field, we show that there exists a universal cosemisimple Hopf algebra coacting on the diagonal algebra $K^n$:…
A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of…
We give an account of the current state of the approch to quantum field theory via Hopf algebras and Hochschild cohomology. We emphasize the versatility and mathematical foundation of this algebraic structure, and collect algebraic…
The quantum deformation of the Hopf algebra describes the skeleton of quantum field theory, namely its characterizing feature consisting in the existence of infinitely many unitarily inequivalent representations of the canonical commutation…