Related papers: Example of q-deformed Field Theory
In recent decades, there have been increasing interests in quantum statistics beyond the standard Fermi-Dirac and Bose-Einstein statistics, such as the fractional statistics, quon statistics, anyon statistics and quantum groups, since they…
We consider 2+1 dimensional noncommutative models of scalar and fermionic fields coupled to the Chern-Simons field. We show that, at least up to one loop, the model containing only a fermionic field in the fundamental representation…
This lecture consists of two sections. In section 1 we consider the simplest version of a q-deformed Heisenberg algebra as an example of a noncommutative structure. We first derive a calculus entirely based on the algebra and then formulate…
Various applications of Chern-Simons theory in algebraic topology, in particular knot theory, condensed matter physics and cosmology are reviewed. Special attention is paid to appearances of Chern-Simons actions in the theory of the…
The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the…
We study the thermodynamics of the relativistic Quantum Field Theory of massive fermions in three space-time dimensions coupled to an Abelian Maxwell-Chern-Simons gauge field. We evaluate the specific heat at finite temperature and density…
We propose the quantum simulation of a fermion and an antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add-up of bosonic…
In a minimalistic view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind: 1-particle solutions (wavefunctions) of the equation of motion in the presence of an…
We analyse the Abelian $N=1$ super-Chern-Simons model coupled to parity-preserving matter in linear and non-linear gauges with exact BRST invariance. Then we analyse the theory in field/antifield formulation to discuss the model at quantum…
Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.
The algebraic and geometric structures of deformations are analyzed concerning topological field theories of Schwarz type by means of the Batalin-Vilkovisky formalism. Deformations of the Chern-Simons-BF theory in three dimensions induces…
A deformed boson mapping of the Marumori type is derived for an underlying $su(2)$ algebra. As an example, we bosonize a pairing hamiltonian in a two level space, for which an exact treatment is possible. Comparisons are then made between…
We examine Chern-Simons theory written on a noncommutative plane with a `hole', and show that the algebra of observables is a nonlinear deformation of the $w_\infty$ algebra. The deformation depends on the level (the coefficient in the…
We construct a quantum theory of free fermion field based on the generalized uncertainty principle using supersymmetry as a guiding principle. A supersymmetric field theory with a real scalar field and a Majorana fermion field is given…
A framework is proposed that allows to write down field theories with a new energy scale while explicitly preserving Lorentz invariance and without spoiling the features of standard quantum field theory which allow quick calculations of…
We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions, by investigating the $q\to 1$ limit of the q-deformed affine $\hat{sl(2)}$ symmetry of the sine-Gordon theory, this limit occurring at the…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
We propose the bosonization of a many-body fermion theory in D spatial dimensions through a noncommutative field theory on a (2D-1)-dimensional space. This theory leads to a chiral current algebra over the noncommutative space and…
A class of quantum field theories invariant with respect to the action of an odd vector field Q on a source supermanifold $\Sigma$ is considered. We suppose that Q satisfies the conditions under which an integral of any Q-invariant function…
A simple exposition of the rarely discussed fact that a set of free boson fields describing different, i.e. kinematically different particle types can be quantized with mutual anticommutation relations is given by the explicit construction…