相关论文: The Gauss linking integral on the 3-sphere and in …
We study the Euclidean path integral of higher spin gravity on $S^4$. Based on a one-loop analysis, we are led to a gluing formula expressing the $S^4$ path integral in terms of an underlying $S^3$ path integral. We view the three-sphere as…
Wigner's unitary representation of the Lorentz group is extended to a representation of the complex orthosymplectic Lie super group OSp_C(1|2) acting on Minkowski (3,1|4)-dimensional super space essentially by Hermitean conjugation. The…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
In this paper we construct a model for group field cosmology. The classical equations of motion for the non-interactive part of this model generate the Hamiltonian constraint of loop quantum gravity for a homogeneous isotropic universe…
Using spinning we analyze in a geometric way Haefliger's smoothly knotted (4k-1)-spheres in the 6k-sphere. Consider the 2-torus standardly embedded in the 3-sphere, which is further standardly embedded in the 6-sphere. At each point of the…
This paper aims at investigating the influence of space-time curvature on the uncertainty relation. In particular, relying on previous findings, we assume the quantum wave function to be confined to a geodesic ball on a given space-like…
We generate vortex tangles using a Hopf flow on a 3-sphere, in place of the standard torus defined by periodic boundary conditions. These tangles are highly anisotropic, with vortices tending to align along the flow direction. Standard…
Holographic entanglement entropy provides a direct connection between classical geometry and quantum entanglement; however the usual prescription does not apply to theories of higher spin gravity, where standard notions of geometry are no…
These notes are intended to be a pedagogical introduction to higher-form symmetries, which are symmetries whose charged objects are extended operators supported on lines, surfaces, and etc. This subject has been one of the most popular and…
In this paper, we characterize non-hyperbolic 3-component links in the 3-sphere whose exteriors contain essential 3-punctured spheres with non-integral boundary slopes. We also show the existence of embeddings of some multibranched surfaces…
A quantum sl(2,R) coalgebra is shown to underly the construction of a large class of superintegrable potentials on 3D curved spaces, that include the non-constant curvature analogues of the spherical, hyperbolic and (anti-)de Sitter spaces.…
This Thesis reviews some recent developments about higher-spin interactions in flat and constant curvature backgrounds. Particular attention is given to the ambient-space formulation of the problem, both at the cubic and at the quartic…
This paper concerns connections between dynamical systems, knots and helicity of vector fields. For a divergence-free vector field on a closed $3$-manifold that generates an Anosov flow, we show that the helicity of the vector field may be…
We study extremal curves associated with a functional which is linear in the curve's torsion. The functional in question is known to capture the properties of entanglement entropy for two-dimensional conformal field theories with chiral…
We study the relation between the frame-like and metric-like formulation of higher-spin gauge theories in three space-time dimensions. We concentrate on the theory that is described by an SL(3) x SL(3) Chern-Simons theory in the frame-like…
A particle that is constrained to freely move on a hyperspherical surface in an $N\left( \geq 2\right) $ dimensional flat space experiences a curvature-induced gauge potential, whose form was given long ago (J. Math. Phys.…
The Biot-Savart law is used in aerodynamic theory to calculate the velocity induced by curved vortex lines. Explicit formulas are developed, using multivariate Appell hypergeometric functions, for the velocity induced by a general parabolic…
The Kepler problem is a dynamical system that is well defined not only on the Euclidean plane but also on the sphere and on the Hyperbolic plane. First, the theory of central potentials on spaces of constant curvature is studied. All the…
Quantum simulations of the dynamics of QCD have been limited by the complexities of mapping the continuous gauge fields onto quantum computers. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom, we…
We study spherical evolution in scalar-Gauss-Bonnet gravity with additional Ricci coupling and use the gauge-invariant approach of Ref.~\cite{Reall:2021voz} to track well-posedness. Our results show that loss of hyperbolicity when it…