Related papers: Statistics and Quantum Group Symmetries
We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the…
Preparation of molecular quantum gas promises novel applications including quantum control of chemical reactions, precision measurements, quantum simulation and quantum information processing. Experimental preparation of colder and denser…
We give a simplified description of quantum affine algebras in their loop presentation. This description is related to Drinfeld's new realization via halves of vertex operators. We also define an idempotent version of the quantum affine…
We show that boson correlations from quantum states with a Glauber-Sudarshan representation of their density matrix which provides a well-behaved probability distribution -- including coherent states, thermal states, and all states that can…
We present extensive \textit{ab initio} path integral Monte Carlo (PIMC) simulations of two-dimensional quantum dipole systems in a harmonic confinement, taking into account both Bose- and Fermi-statistics. This allows us to study the…
We introduce and study certain asymptotic invariants associated with fusion algebras (equipped with a dimension function), which arise naturally in the representation theory of compact quantum groups. Our invariants generalise the analogous…
We use a noncommutative generalization of Fourier analysis to define a broad class of pseudo-probability representations, which includes the known bosonic and discrete Wigner functions. We characterize the groups of quantum unitary…
Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can results in significant overhead due to the exponentially growing size of some…
Given a symmetry group acting on a principal fibre bundle, symmetric states of the quantum theory of a diffeomorphism invariant theory of connections on this fibre bundle are defined. These symmetric states, equipped with a scalar product…
Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can…
Infinite statistics in which all representations of the symmetric group can occur is known as a special case of quon theory. However, the validity of relativistic quon theories is still in doubt. In this paper we prove that there exists a…
Exact supersymmetry can be maintained on nonanticommutative superspace with a twisted coproduct on the supergroup.We show that the usual exchange statistics for the superfields is not compatible with the twisted action of the superpoincare…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
We discuss the relation between dimensional reduction in quantum field theories at finite temperature and a familiar quantum mechanical phenomenon that quantum effects become negligible at high temperatures. Fermi and Bose fields are…
The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…
For a set of quantum states generated by the action of a group, we consider the graph obtained by considering two group elements adjacent whenever the corresponding states are non-orthogonal. We analyze the structure of the connected…
This contribution, to be published in Imagine Math 8 to celebrate Michele Emmer's 75th birthday, can be seen as the second part of my previous considerations on the relationships between topology and physics (Mouchet, 2018). Nevertheless,…
This paper suggests that traditional fermi-bose quantum field theories (QFT) in 3+1-D, like the standard model of physics, may often be exactly equivalent to the limiting case of a family of bosonic QFT (BQFT) which generate soliton…
Through the example of the quantum symplectic 4-sphere, we discuss how the notion of twisted spectral triple fits into the framework of quantum homogeneous spaces.
Both the topics of entanglement and particle statistics have aroused enormous research interest since the advent of quantum mechanics. Using two pairs of entangled particles we show that indistinguishability enforces a transfer of…