Related papers: The Fine Structure of SU(2) Intertwiners from U(N)…
The character problems of SU(2) and SU(1,1) are reexamined from the standpoint of a physicist by employing the Hilbert space method which is shown to yield a completely unified treatment for SU(2) and the discrete series of representations…
We introduce a spin chain based on finite-dimensional spin-1/2 SU(2) representations but with a non-hermitian `Hamiltonian' and show, using mostly analytical techniques, that it is described at low energies by the SL(2,R)/U(1) Euclidian…
We introduce a classical limit of the dynamics of quantum spin systems based on coherent states of SU($N$), where $N$ is the dimension of the local Hilbert space. This approach, that generalizes the well-known Landau-Lifshitz dynamics from…
The complete classification of the nilpotent orbits of ${\rm SO}(2,2)^2$ in the representation ${\bf (2,2,2,2)}$, achieved in \cite{Dietrich:2016ojx}, is applied to the study of multi-center, asymptotically flat, extremal black hole…
We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in…
We prove that the Novikov conjecture holds for any discrete group admitting an isometric and metrically proper action on an admissible Hilbert-Hadamard space. Admissible Hilbert-Hadamard spaces are a class of (possibly infinite-dimensional)…
We investigate the structure of the moduli space of multiple BPS non-Abelian vortices in U(N) gauge theory with N fundamental Higgs fields, focusing our attention on the action of the exact global (color-flavor diagonal) SU(N) symmetry on…
Let G be either SU(p,2) with p>=2, Sp(2,R) or SO(p,2) with p>=3. The symmetric spaces associated to these G's are the classical bounded symmetric domains of rank 2, with the exceptions of SO*(8)/U(4) and SO*(10)/U(5). Using the…
A refined notion of curvature for a linear system of Hermitian vector spaces, in the sense of Grothendieck, leads to the unitary classification of a large class of analytic Hilbert modules. Specifically, we study Hilbert sub-modules, for…
The intrinsic symmetries of physical systems have been employed to reduce the number of degrees of freedom of systems, thereby simplifying computations. In this work, we investigate the properties of $\mathcal{M}SU(2^N)$,…
This work focuses on non-compact groups and their applications to quantum gravity, mainly through the use of tensor operators. First, the mathematical theory of tensor operators for a Lie group is recast in a new way which is used to…
We analyze mathematical and physical properties of a previously introduced [J. Phys. A47, 115302 (2014)] family of $U(4)$ coherent states (CS). They constitute a matrix version of standard spin $U(2)$ CS when we add an extra (pseudospin)…
The emergence of nontrivial symmetries for black holes minisuperspaces has been recently pointed out. These Noether symmetries possess non-null charges and hence map physical solutions to different ones. The symmetry group is isomorphic to…
We obtain the following characterization of Hilbert spaces. Let $E$ be a Banach space whose unit sphere $S$ has a hyperplane of symmetry. Then $E$ is a Hilbert space iff any of the following two conditions is fulfilled: a) the isometry…
We derive a collective field theory of the singlet sector of the Sp(2N) sigma model. Interestingly the hamiltonian for the bilocal collective field is the same as that of the O(N) model. However, the large-N saddle points of the two models…
We prove that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C). For hyperbolic integer homology spheres this comes with the definition,…
The pure braid group \Gamma of a quadruply-punctured Riemann sphere acts on the SL(2,C)-moduli M of the representation variety of such sphere. The points in M are classified into \Gamma-orbits. We show that, in this case, the monodromy…
What is the bulk Hilbert space of quantum gravity? In this paper, we resolve this problem in 2d JT gravity, both with and without matter, providing an explicit definition of a non-perturbative Hilbert space specified in terms of metric…
We study closed, connected, spin 4-manifolds up to stabilisation by connected sums with copies of $S^2 \times S^2$. For a fixed fundamental group, there are primary, secondary and tertiary obstructions, which together with the signature…
We propose a new method to solve the Killing spinor equations of eleven-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1,10) gauge symmetry of the supercovariant derivative. We give the…