Related papers: An introduction to quantum symmetries
The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be…
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…
We study quantum automorphism group of vertex-transitive graphs using intertwinner spaces of the magic unitary matrix associated to this quantum subgroups of $S_n^+$. We also give some applications to quantum symmetries of circulant graphs…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
This is a short, self-contained expository survey, focused on algebraic and analytic aspects of quantum groups. Topics covered include the definition of ``quantum group,'' the Yang-Baxter equation, quantized universal enveloping algebras,…
The geometric realizations of Lusztig's symmetries of symmetrizable quantum groups are given in this paper. This construction is a generalization of that in [19].
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…
This is an elementary introduction to basic tools of supersymmetry: the spacetime symmetries, gauge theory and its application in gravity, spinors and superalgebras. Special attention is devoted to conformal and anti-de Sitter algebras.
This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.
In several of the class A Bianchi models, minisuperspaces admit symmetries. It is pointed out that they can be used effectively to complete the Dirac quantization program. The resulting quantum theory provides a useful platform to…
This is an introduction to loop quantum cosmology (LQC) reviewing mini- and midisuperspace models as well as homogeneous and inhomogeneous effective dynamics.
This thesis is focused on some solvable quantum mechanical models and their associated symmetries.
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
This article is a short introduction to the general topic of quantum spin systems. After a brief sketch of the history of the subject, the standard mathematical framework for formulating problems and results in quantum spin systems is…
These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…
These notes provide an introduction to standard topics on quantum computation and communication for those who already have a basic knowledge of quantum mechanics. The main target audience are professional physicists as well as advanced…
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…
A notion of a quantum automorphism group of a finite quantum group, generalising that of a classical automorphism group of a finite group, is proposed and a corresponding existence result proved.
This is a survey of what is known and/or conjectured about the prime and primitive spectra of quantum algebras, of quantized coordinate rings in particular. The topological structure of these spectra, their relations to classical affine…
These notes deal with finite-dimensional normed algegras, some basic examples, and the definition of the spectrum.