Related papers: Group Theoretical Quantization and the Example of …
The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields…
The review is devoted to topological global aspects of quantal description. The treatment concentrates on quantizations of kinematical observables --- generalized positions and momenta. A broad class of quantum kinematics is rigorously…
One of the obstacles to reconciling quantum theory with general relativity, is constructing a theory which is both consistent with observation, and and gives finite answers at high energy, so that the theory holds at arbitrarily short…
Consider a locally compact group $G=Q\ltimes V$ such that $V$ is abelian and the action of $Q$ on the dual abelian group $\hat V$ has a free orbit of full measure. We show that such a group $G$ can be quantized in three equivalent ways: (1)…
We present a new method for renormalisation group improvement of the effective potential of a quantum field theory with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective…
In order to avoid the difficulties encountered by relativistic quantum theory of single particles, we pursue a deductive development of the theory from physical principles, without canonical quantization, by making use of group-theoretical…
When physical systems are tunable by three classical parameters, level degeneracies may occur at isolated points in parameter space. A topological singularity in the phase of the degenerate eigenvectors exists at these points. When a path…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
We consider here kinematical quantization: a first and often overlooked step in quantization procedures. $\mathbb{R}$, $\mathbb{R}_+$ and the interval are considered, as well as direct (Cartesian) products thereof. Some simple…
In various approaches to quantum gravity continuum spacetime is expected to emerge from discrete geometries through a phase transition. In group field theory, various indications for such a transition have recently been found but a complete…
By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric…
In a previous work we have introduced the concept of quasi-integrable quantum system. In the present one we determine sufficient conditions under which, given an integrable classical system, it is possible to construct a quasi-integrable…
By decomposing the regular representation of a particular (Heisenberg-like) Lie supergroup into irreducible subspaces, we show that not all of them can be obtained by applying geometric quantization to coadjoint orbits with an even…
In this paper we study the problem of determining the homology groups of a quotient of a topological space by an action of a group. The method is to represent the original topological space as a homotopy limit of a diagram, and then act…
We propose a general formula for the group of invertible topological phases on a space $Y$, possibly equipped with the action of a group $G$. Our formula applies to arbitrary symmetry types. When $Y$ is Euclidean space and $G$ a…
A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the renormalization group running scale are…
We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d Riemannian gravity, and discuss briefly the current status…
Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, $A_{\mu}(x)\rightarrow A_{\mu}(x)+\partial_{\mu}\varphi(x)$, into a group law. In…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…