Related papers: A noncommutative de Finetti theorem: Invariance un…
An exchangeable random matrix is a random matrix with distribution invariant under any permutation of the entries. For such random matrices, we show, as the dimension tends to infinity, that the empirical spectral distribution tends to the…
Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…
In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential…
In the last decades, noncommutative spacetimes and their deformed relativistic symmetries have usually been studied in the context of field theory, replacing the ordinary Minkowski background with an algebra of noncommutative coordinates.…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
Feynman's formulation of quantum theory is remarkable in its combination of formal simplicity and computational power. However, as a formulation of the abstract structure of quantum theory, it is incomplete as it does not account for most…
We point out that the quantum de Finetti representation, unique for infinitely extendable exchangeable systems, assigns a non-zero Quantum Discord to uncorrelated systems and thus cannot serve as an universal prior distribution in the…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
We show an organized form of quantum de Finetti theorem for Boolean independence. We define a Boolean analogue of easy quantum groups for the categories of interval partitions, which is a family of sequences of quantum semigroups. We…
Adelic quantum mechanics is form invariant under an interchange of real and p-adic number fields as well as rings of p-adic integers. We also show that in adelic quantum mechanics Feynman's path integrals for quadratic actions with rational…
A version of the classical Vieta theorem for free noncommuting variables is given. It leads to a new start in a construction of noncommutative symmetric functions
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
According to symmetrization postulate for a system of identical particles, wave function has to be completely symmetric or completely anti-symmetric. In this paper we want to mathematically justify this postulate ignoring the spin part of…
Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parametrizing isomorphism classes of geometric objects (vector bundles, polarized…
We show that the strength of non-commutativity could play a role in determining the boundary condition of a physical problem. As a toy model we consider the inverse square problem in non-commutative space. The scale invariance of the system…
We show that the supersymmetric algebra of Witten's quantum mechanics is invariant under a given point canonical transformation. It is shown that Witten's supersymmetric quantum mechanics can be isospectral or not to the seed Hamiltonian…
We consider the quantum dynamics of a test particle in noncommutative space under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. A prescription for quantizing the classical Hamiltonian for…
The space-time symmetry of noncommutative quantum field theories with a deformed quantization is described by the twisted Poincar\'e algebra, while that of standard commutative quantum field theories is described by the Poincar\'e algebra.…
In this paper we provide a method for constructing joint distributions for an arbitrary set of observables on finite dimensional Hilbert spaces irrespective of whether the observables commute or not. These distributions have a number of…
We introduce a new natural notion of convergence for permutations at any specified scale, in terms of the density of patterns of restricted width. In this setting we prove that limits may be chosen independently at a countably infinite…