Related papers: On the mathematics and physics of Mixed Spin P-Fie…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
We investigate the phase structure of four-dimensional quantum gravity coupled to Ising spins or Gaussian scalar fields by means of numerical simulations. The quantum gravity part is modelled by the summation over random simplicial…
In the framework of light-cone gauge approach, bosonic and fermionic mixed-symmetry continuous-spin fields in AdS space and flat space are considered. For such fields, the light-cone gauge actions are found. Realization of relativistic…
We examine some recent developments in noncommutative geometry, including spin geometries on noncommutative tori and their quantization by the Shale-Stinespring procedure, as well as the emergence of Hopf algebras as a tool linking index…
The $sp(2M)$ invariant unfolded system is considered in the periodic twistor-like spinor space. Complete set of non-trivial charges corresponding to the global symmetry compatible with the periodicity conditions is constructed. Residual…
The geometrical formulation of gravity is not unique and can be set up in a variety of spacetimes. Even though the gravitational sector enjoys this freedom of different geometrical interpretations, consistent matter couplings have to be…
Topological quantum field theories containing matter fields are constructed by twisting $N=2$ supersymmetric quantum field theories. It is shown that $N=2$ chiral (antichiral) multiplets lead to topological sigma models while $N=2$ twisted…
In a recent article [Phys. Rev. Lett. 97 (2006), 107206], we have presented a class of states which is suitable as a variational set to find ground states in spin systems of arbitrary spatial dimension and with long-range entanglement.…
We summarize recent developments at the interface of quantum gravity and quantum information, and discuss applications to the quantum geometry of space in loop quantum gravity. In particular, we describe the notions of link entanglement,…
We introduce an algebraic system which can be used as a model for spaces with geodesic paths between any two of their points. This new algebraic structure is based on the notion of mobility algebra which has recently been introduced as a…
This PhD thesis is the conclusion of some of my works carried out at the Centre de Physique Th\'eorique, under the supervision of Serge Lazzarini. Two subjects are presented in the manuscript, both aiming at studying the effect of the spin…
In special-relativistic physics, spacetime is imbued with a fixed, non-dynamical metric tensor. A path to gravitational theory is to promote this tensor to a genuine dynamical field. An alternative description of special-relativistic…
We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…
We study the problem of interacting theories with (partially)-massless and conformal higher spin fields without matter in three dimensions. A new class of theories that have partially-massless fields is found, which significantly extends…
A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the…
We show how to incorporate massive spinning fields into the Euclidean path integral of three-dimensional quantum gravity via its Chern-Simons formulation. The coupling of the spinning fields to gravity is captured by a Wilson spool, a…
For Connes' spectral triples, the group of automorphisms lifted to the Hilbert space is defined and used to fluctuate the metric. A few commutative examples are presented including Chamseddine and Connes' spectral unification of gravity and…
In order to search for the magnetic ground state of surface nanostructures we extended first principles adiabatic spin dynamics to the case of fully relativistic electron scattering. Our method relies on a constrained density functional…
This work demonstrates that a complete description of the interaction of matter and all forces, gravitational and non-gravitational, can in fact be realized within a quantum affine algebraic framework. Using the affine group formalism, we…
We study a very general four dimensional Field Theory model describing the dynamics of a massless higher spin $N$ symmetric tensor field particle interacting with a geometrical background.This model is invariant under the action of an…