Related papers: A C*-algebraic approach to interacting quantum fie…

In this article a new formulation of the Weyl C*-algebra, which has been invented by Fleischhack, in terms of C*-dynamical systems is presented. The quantum configuration variables are given by the holonomies along paths in a graph.…

Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…

Representations of $C^*$-algebras are realized on section spaces of holomorphic homogeneous vector bundles. The corresponding section spaces are investigated by means of a new notion of reproducing kernel, suitable for dealing with…

In this article, we use Exel's construction to associate a C*-algebra to every shift space. We show that it has the C*-algebra defined in [Carlsen and Matsumoto: Some remarks on the C*-algebras associated with subshifts] as a quotient, and…

In this paper, we construct a universal C*-algebraic quantum group out of an algebraic one. We show that this universal C*-algebraic quantum group has the same rich structure as its reduced companion. This universal C*-algebraic quantum…

We show that certain C*-algebras which have been studied among others by Arzumanian, Vershik, Deaconu, and Renault in connection to a measure preserving transformation of a measure space and/or to a covering map of a compact space are…

A class of interacting classical random fields is constructed using deformed *-algebras of creation and annihilation operators. The fields constructed are classical random field versions of "Lie fields". A vacuum vector is used to construct…

Given a connected and locally compact Hausdorff space X with a good base K we assign, in a functorial way, a C(X)-algebra to any precosheaf of C*-algebras A defined over K. Afterwards we consider the representation theory and the Kasparov…

The treatment of supersymmetry is known to cause difficulties in the C*-algebraic framework of relativistic quantum field theory; several no-go theorems indicate that super-derivations and super-KMS functionals must be quite singular…

Recently, we have constructed a non{linear (polynomial) extension of the 1-mode Heisenberg group and the corresponding Fock and Weyl representations. The transition from the 1-mode case to the current algebra level, in which the operators…

We consider a new class of potentially exotic group C*-algebras $C^*_{PF_p^*}(G)$ for a locally compact group $G$, and its connection with the class of potentially exotic group C*-algebras $C^*_{L^p}(G)$ introduced by Brown and Guentner.…

Based on Koopman formalism for classical statistical mechanics, we propose a formalism to define hybrid quantum-classical dynamical systems by defining (outer) automorphisms of the C*-algebra of hybrid operators and realizing them as linear…

This is a graduate-level introduction to C*-algebras, Hilbert C*-modules, vector bundles, and induced representations of groups and C*-algebras, with applications to quantization theory, phase space localization, and configuration space…

We present a uniqueness theorem for k-graph C*-algebras that requires neither an aperiodicity nor a gauge invariance assumption. Specifically, we prove that for the injectivity of a representation of a k-graph C*-algebra, it is sufficient…

We introduce {\it covariant structures} $\left\{(\A,\k),(\a,\aa),\(\ha,\haa\)\right\}$ formed of a separable $C^*$-algebra $\A$, a measurable twisted action $(\a,\aa)$ of the second-countable locally compact group $\G$\,, a measurable…

We examine the question of quasidiagonality for C*-algebras of discrete amenable groups from a variety of angles. We give a quantitative version of Rosenberg's theorem via paradoxical decompositions and a characterization of…

For any nilpotent Lie group $G$ we provide a description of the image of its $C^*$-algebra through its operator-valued Fourier transform. Specifically, we show that $C^*(G)$ admits a finite composition series such that that the spectra of…

I review the formalism, Feynman rules, and combinatorics that constrain a field to propagate ``classically", strictly in tree diagrams, either by itself, or interacting with other, purely quantum fields. The perturbation theory is…

We review the homotopy algebraic perspective on perturbative quantum field theory: classical field theories correspond to homotopy algebras such as $A_\infty$- and $L_\infty$-algebras. Furthermore, their scattering amplitudes are encoded in…

We give a new definition of the semigroup C*-algebra of a left cancellative semigroup, which resolves problems of the construction by X. Li. Namely, the new construction is functorial, and the independence of ideals in the semigroup does…