Related papers: Rainbow statistics
This is a systematic introduction for physicists to the theory of algebras and groups with braid statistics, as developed over the last three years by the author. There are braided lines, braided planes, braided matrices and braided groups…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Quantum gravity may modify the fundamental symmetries that govern identical particles. In particular, noncommutative spacetime frameworks predict deformations of Bose and Fermi statistics. Here we develop a relativistic quantum field theory…
Within the framework of Tsallis statistics with q ~ 1, we construct a perturbation theory for treating relativistic quantum field systems. We find that there appear initial correlations, which do not exist in the Boltzmann-Gibbs statistics.…
The twist-deformation of the Poincar\'e algebra as symmetry of the field theories on noncommutative space-time with Heisenberg-like commutation relation is discussed in connection to the relation between a sound approach to the twist and…
We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
In this study, we construct a 1+1-dimensional, relativistic, free, complex scalar Quantum Field Theory on the noncommutative spacetime known as lightlike $\kappa$-Minkowski. The associated $\kappa$-Poincar\'e quantum group of isometries is…
We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability distributions and observables, with random variables. An…
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 develop a rigorous connection between statistical properties of an interference pattern and the coherence properties of the underlying quantum state. With explicit examples, we demonstrate that even for inaccurate reconstructions of…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
Non-Hermitian quantum theories have been applied in many other areas of physics. In this note, I will briefly review recent developments in the formulation of non-Hermitian quantum field theories, highlighting features that are unique…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
The description of thermal or non-equilibrium systems necessitates a quantum field theory which differs from the usual approach in two aspects: 1.The Hilbert space is doubled; 2.Stable quasi-particles do not exist in interacting systems. A…
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
It is seen that issues of unitarity raised by the evolution of the wave function in curved spacetime can be resolved by describing the evolution of quantum states in Minkowski tangent space. The treatment adheres closely to the orthodox…
We develop a general framework for quantum field theory on noncommutative spaces, i.e., spaces with quantum group symmetry. We use the path integral approach to obtain expressions for $n$-point functions. Perturbation theory leads us to…
The existence of a minimum time uncertainty is usually argued to be a consequence of the combination of quantum mechanics and general relativity. Most of the studies that point to this result are nonetheless based on perturbative…