Related papers: Quantum Groups, Strings and HTSC materials II
A new non-perturbative approach to quantum field theory --- D-theory --- is proposed, in which continuous classical fields are replaced by discrete quantized variables which undergo dimensional reduction. The 2-d classical O(3) model…
The loop representation of quantum gravity has many formal resemblances to a background-free string theory. In fact, its origins lie in attempts to treat the string theory of hadrons as an approximation to QCD, in which the strings…
Motivated by the formalism of string bit models, or quantum matrix models, we study a class of simple Hamiltonian models of quantum gravity type in two space-time dimensions. These string bit models are special cases of a more abstract…
Relational particle models are useful toy models for quantum cosmology and the problem of time in quantum general relativity. This paper shows how to extend existing work on concrete examples of relational particle models in 1-d to include…
In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge…
A set of $n$ coherent states is introduced in a quantum system with $d$-dimensional Hilbert space $H(d)$. It is shown that they resolve the identity, and also have a discrete isotropy property. A finite cyclic group acts on the set of these…
In this lecture I summarize recent developments on strings propagating in curved spacetime. Exact conformal field theories that describe gravitational backgrounds such as black holes and more intricate gravitational singularities have been…
A major goal of the quantum simulation of high-energy physics (HEP) is to probe real-time nonperturbative far-from-equilibrium quantum processes underlying phenomena such as hadronization in quantum chromodynamics (QCD). The quantum…
Quantum fields are shown to provide an example of infinite-dimensional quantum groups. A dictionary is established between quantum field and quantum group concepts: the expectation value over the vacuum is the counit, Wick's theorem is the…
The formalism of matrix product states is used to perform a numerical study of 1+1 dimensional QED -- also known as the (massive) Schwinger model -- in the presence of an external static `quark' and `antiquark'. We obtain a detailed picture…
The Hubbard model, which augments independent-electron band theory with a single parameter to describe electron-electron correlations, is widely regarded to be the `standard model' of condensed matter physics. The model has been remarkably…
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as…
Projecting a quantum theory onto the Hilbert subspace of states with energies below a cutoff $\overline{E}$ may lead to an effective theory with modified observables, including a noncommutative space(time). Adding a confining potential well…
String theory on 2-d charged black holes corresponding to (SL(2)xU(1)_L)/U(1) exact asymmetric quotient CFTs are investigated. These backgrounds can be embedded, in particular, in a two dimensional heterotic string. In the extremal case,…
Cosmic strings are linear concentrations of energy that form whenever phase transitions in the early universe break axial symmetries as originally shown by Kibble. They are the result of frustrated order in the quantum fields responsible…
Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a…
The purpose of this talk is to review some considerations by the present author on the possible role of a simple space-time uncertainty relation toward nonperturbative string theory. We first motivate the space-time uncertainty relation as…
One important yet exceedingly rare property of the cuprate high-temperature superconductors is the presence of a single correlated $d$ band in the low-energy spectrum, leading to the one-band Hubbard model as the minimal description. In…
These notes are based on lectures serving the advanced graduate education of the Delta Institute of Theoretical Physics in the Netherlands in autumn 2021. The goal is to explain in a language that can be understood by non-specialists very…
String theory has been initially derived from motivations coming from strong interaction phenomenology,but its application faced deep conceptual and practical difficulties. The strong interactions found their theoretical foundation…