Related papers: Introduction to abelian anyons in planar systems
This is a review of the paper "Anomalies in Quantum Field Theory and Cohomologies of Configuration Spaces" (arXiv:0903.0187).
We propose a construction of anyon systems associated to quantum tori with real multiplication and the embedding of quantum tori in AF algebras. These systems generalize the Fibonacci anyons, with weaker categorical properties, and are…
The mathematical description of stable particle-like systems appearing in relativistic quantum field theory at large, respectively small scales or non-zero temperatures is discussed.
A coincise review about Euclidean (Quantum) Field Theory is presented. It deals with the general structural properties, the connections with Quantum Field Theory, the exploitation in Constructive Quantum Field Theory, and the physical…
I discuss two techniques that can be used in the investigation of the properties of ``colliding" and ``non-colliding" anyons.
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…
This is an expository article on the theory of formal group laws in homotopy theory, with the goal of leading to the connection with higher-dimensional abelian varieties and automorphic forms. These are roughly based on a talk at the…
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
This paper is dedicated to give a concise introduction to the theory of causal fermion systems. After putting the theory of causal fermion systems into the historical context, we recall fundamental physical preliminaries. Afterwards, we…
Anyons in one spatial dimension can be defined by correctly identifying the configuration space of indistinguishable particles and imposing Robin boundary conditions. This allows an interpolation between the bosonic and fermionic limits. In…
We consider the external magnetic field effects on the two types of anyon with fractional statistical parameters $p/q$ with coprimes $p$ and $q$, one with fractional charge $e/q $ and flux $p \phi_0(=hc/e)$(type I), the other with…
A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with…
The first-order, infinite-component field equations we proposed before for non-relativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic…
Proceeding from the main principles of the non-unitary quantum theory of relativistic bi-Hamiltonian systems, a system of Lagrangian fields characterized by a certain dispersion law (mass spectrum of particles), interactions between them…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
This paper provides a thorough introduction to the causal set hypothesis aimed at students, and other interested persons, with some knowledge of general relativity and nonrelativistic quantum mechanics. I elucidate the arguments for why the…
We review one dimensional matrix theory and its variations, collective field theory and quantum phase space description. In the planar limit, these theories become classical and can be easily analyzed. With these descriptions, one…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
A conceptual framework for variational formulations of physical theories is proposed. Such a framework is displayed here just for statics, but it is designed to be subsequently adapted to variational formulations of static field theories…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…