Related papers: Introduction to abelian anyons in planar systems
We review aspects of classical and quantum mechanics of many anyons confined in an oscillator potential. The quantum mechanics of many anyons is complicated due to the occurrence of multivalued wavefunctions. Nevertheless there exists, for…
I review the quantum kinematics of identical particles, which suggests new possibilities, beyond bosons and fermions, in 2+1 dimensions; and how simple flux-charge constructions embody the new possibilities, leading to both abelian and…
We construct a field theory for anyons in the lowest Landau level starting from the $N$-particle description, and discuss the connection to the full field theory of anyons defined using a statistical gauge potential. The theory is…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
The Landau problem in the noncommutative plane is discussed in the context of realizations of the two-fold centrally extended planar Galilei group and the anyon theory.
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
This paper is meant to be an informal introduction to Quantum Groups, starting from its origins and motivations until the recent developments. We call in particular the attention on the newly descovered relationship among quantum groups,…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the…
A topological quantum field theory of non-abelian differential forms is investigated from the point of view of its possible applications to description of polynomial invariants of higher-dimensional two-component links. A path-integral…
We consider the analog in one spatial dimension of the Bose-Fermi transmutation for planar systems. A quantum mechanical system of a spin 1/2 particle coupled to an abelian gauge field, which is classically invariant under gauge…
Strongly correlated fractional quantum Hall liquids support fractional excitations, which can be understood in terms of adiabatic flux insertion arguments. A second route to fractionalization is through the coupling of weakly interacting…
The theory of causal fermion systems is an approach to describe fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. We here give a…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
This textbook introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting…
In this talk I describe a recently introduced field-theoretical approach that can be used as an alternative framework to study one-dimensional systems of highly correlated particles.
A set of localized, non-Abelian anyons - such as vortices in a p_x + i p_y superconductor or quasiholes in certain quantum Hall states - gives rise to a macroscopic degeneracy. Such a degeneracy is split in the presence of interactions…
A universal quantum computer can be constructed using abelian anyons. Two qubit quantum logic gates such as controlled-NOT operations are performed using topological effects. Single-anyon operations such as hopping from site to site on a…
The Lagrangian model for anyon, presented in [6], is extended to include interactions with external, homogeneous electromagnetic field. Explicit electric and magnetic moment terms for the anyon are introduced in the Lagrangian. The…
We explain the use of category theory in describing certain sorts of anyons. Yoneda's lemma leads to a simplification of that description. For the particular case of Fibonacci anyons, we also exhibit some calculations that seem to be known…