Related papers: Gauge transformations and quasitriangularity
An important property of a Hopf algebra is its quasitriangularity and it is useful various applications. This property is investigated for quantum groups $sl_2$ at roots of 1. It is shown that different forms of the quantum group $sl_2$ at…
We define a simplified version of Regge quantum gravity where the link lengths can take on only two possible values, both always compatible with the triangle inequalities. This is therefore equivalent to a model of Ising spins living on the…
Analyses which use loop calculations to put constraints on anomalous trilinear gauge boson couplings (TGC's) often give bounds which are much too stringent. The reason has nothing to do with gauge invariance, in contrast to the recent…
We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzezinski and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. We…
We derive a new implementation of linear covariant gauges on the lattice, based on a minimizing functional that can be interpreted as the Hamiltonian of a spin-glass model in a random external magnetic field. We show that our method solves…
A novel canonical transformation is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum phase…
The study of charged and neutral boson vertices has been performed in different production channels at the LEP experiments. Decay rates and kinematic properties of these events are exploited to set constraints on the corresponding gauge…
We show how to construct Hamiltonian lattice theories with one exact supersymmetry on arbitrary triangulations of curved space in any number of dimensions. Both bosons and fermions satisfy discrete K\"{a}hler-Dirac equations. The…
Strongly coupled gauge theories provide an ultra-violet realization of new physics models for physics beyond the Standard Model of particle physics arising from composite dynamics. Depending on the gauge group and matter content, they are…
Quantum link models (QLMs) are extensions of Wilson-type lattice gauge theories, and show rich physics beyond the phenomena of conventional Wilson gauge theories. Here we explore the physics of $U(1)$ symmetric QLMs, both using a more…
Quasi-lattices are introduced in terms of 'join' and 'meet' operations. It is observed that quasi-lattices become lattices when these operations are associative and when these operations satisfy 'modularity' conditions. A fundamental…
We develop a quantum duality principle for coisotropic subgroups of a (formal) Poisson group and its dual: namely, starting from a quantum coisotropic subgroup (for a quantization of a given Poisson group) we provide functorial recipes to…
Atomic many-body phase transitions and quantum criticality have recently attracted much attention in non-standard optical lattices. Here we perform an experimental study of finite-temperature superfluid transition of bosonic atoms confined…
We propose a general formulation of simplicial lattice gauge theory inspired by the finite element method. Numerical tests of convergence towards continuum results are performed for several SU(2) gauge fields. Additionaly, we perform…
Gauge theories with finite gauge groups have applications to quantum simulation and quantum gravity. Recently, the exact number of gauge-invariant states was computed for pure gauge theories on arbitrary lattices. In this work, we…
An enlarged group G of nonlinear transformations, modeled on the general linear group GL(2,R), leads to a beautiful, apparently unremarked symmetry between the wave function's phase and the logarithm of its amplitude. Equations Doebner and…
In recent years, there has been a growing interest in flatband systems which exhibit macroscopic degeneracies. These systems offer a valuable mathematical framework for the extreme sensitivity to perturbations and interactions. This…
We describe how to overcome some problems that usually prevent from obtaining an efficient algorithm to fix a generic covariant gauge on the lattice. This gauge is the lattice equivalent of the generic gauge usually adopted in perturbative…
Let $\Gamma$ be a finite group acting faithfully and linearly on a vector space $V$. Let $T(V)$ ($S(V)$) be the tensor (symmetric) algebra associated to $V$ which has a natural $\Gamma$ action. We study generalized quadratic relations on…
We obtain lattice models whose continuum limits correspond to $N=2$ superconformal coset models. This is done by taking the well known vertex model whose continuum limit is the $G \times G/G$ conformal field theory, and twisting the…