Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOperator Spin Foam Models
122
0
0.0
(
0
)
Added by
Marcin Kisielowski M.Sc.
Publication date
2010
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as the main tool. An equivalence relation we impose in the set of the operator spin foams allows to split the faces and the edges of the foams. The consistency with that relation requires introduction of the (familiar for the BF theory) face amplitude. The operator spin foam models are defined quite generally. Imposing a maximal symmetry leads to a family we call natural operator spin foam models. This symmetry, combined with demanding consistency with splitting the edges, determines a complete characterization of a general natural model. It can be obtained by applying arbitrary (quantum) constraints on an arbitrary BF spin foam model. In particular, imposing suitable constraints on Spin(4) BF spin foam model is exactly the way we tend to view 4d quantum gravity, starting with the BC model and continuing with the EPRL or FK models. That makes our framework directly applicable to those models. Specifically, our operator spin foam framework can be translated into the language of spin foams and partition functions. We discuss the examples: BF spin foam model, the BC model, and the model obtained by application of our framework to the EPRL intertwiners.
rate research
Read More
The Lorentzian Engle-Pereira-Rovelli-Livine/Freidel-Krasnov (EPRL/FK) spinfoam model and the Conrady-Hnybida (CH) timelike-surface extension can be expressed in the integral form $int e^S$. This work studies the analytic continuation of the spinfoam action $S$ to the complexification of the integration domain. Our work extends our knowledge from the real critical points well-studied in the spinfoam large-$j$ asymptotics to general complex critical points of $S$ analytic continued to the complexified domain. The complex critical points satisfying critical equations of the analytic continued $S$. In the large-$j$ regime, the complex critical points give subdominant contributions to the spinfoam amplitude when the real critical points are present. But the contributions from the complex critical points can become dominant when the real critical point are absent. Moreover the contributions from the complex critical points cannot be neglected when the spins $j$ are not large. In this paper, we classify the complex critical points of the spinfoam amplitude, and find a subclass of complex critical points that can be interpreted as 4-dimensional simplicial geometries. In particular, we identify the complex critical points corresponding to the Riemannian simplicial geometries although we start with the Lorentzian spinfoam model. The contribution from these complex critical points of Riemannian geometry to the spinfoam amplitude give $e^{-S_{Regge}}$ in analogy with the Euclidean path integral, where $S_{Regge}$ is the Riemannian Regge action on simplicial complex.
The canonical ``loop formulation of quantum gravity is a mathematically well defined, background independent, non perturbative standard quantization of Einsteins theory of General Relativity. Some among the most meaningful results of the theory are: 1) the complete calculation of the spectrum of geometric quantities like the area and the volume and the consequent physical predictions about the structure of the space-time at the Plank scale; 2) a microscopical derivation of the Bekenstein-Hawking black-hole entropy formula. Unfortunately, despite recent results, the dynamical aspect of the theory (imposition of the Wheller-De Witt constraint) remains elusive. After a short description of the basic ideas and the main results of loop quantum gravity we show in which sence the exponential of the super Hamiltonian constraint leads to the concept of spin foam and to a four dimensional formulation of the theory. Moreover, we show that some topological field theories as the BF theory in 3 and 4 dimension admits a spin foam formulation. We argue that the spin-foams/spin-networks formalism it is the natural framework to discuss loop quantum gravity and topological field theory.
A spin-foam model is derived from the canonical model of Loop Quantum Gravity coupled to a massless scalar field. We generalized to the full theory the scheme first proposed in the context of Loop Quantum Cosmology by Ashtekar, Campiglia and Henderson, later developed by Henderson, Rovelli, Vidotto and Wilson-Ewing.
We compute the regularized temperature for a spacetime foam model, consisting on S^4 instantons, in quantum gravity. Assuming that thermal equilibrium takes place with some amount of radiation - with thermal fields in the SU(2)xU(1) gauge theory - we obtain the remarkable result that the squared value of this temperature exactly coincides with the electroweak coupling constant at the energy scale of the gauge bosons W. This is consistent with the classical ADM result that the electrical charge should be equal to its finite gravitational self energy.
It was found recently that the anisotropies in the homogeneous Bianchi I cosmology considered within the context of a specific Horndeski theory are damped near the initial singularity instead of being amplified. In this work we extend the analysis of this phenomenon to cover the whole of the Horndeski family. We find that the phenomenon is absent in the K-essence and/or Kinetic Gravity Braiding theories, where the anisotropies grow as one approaches the singularity. The anisotropies are damped at early times only in more general Horndeski models whose Lagrangian includes terms quadratic and cubic in second derivatives of the scalar field. Such theories are often considered as being inconsistent with the observations because they predict a non-constant speed of gravitational waves. However, the predicted value of the speed at present can be close to the speed of light with any required precision, hence the theories actually agree with the present time observations. We consider two different examples of such theories, both characterized by a late self-acceleration and an early inflation driven by the non-minimal coupling. Their anisotropies show a maximum at intermediate times and approach zero at early and late times. The early inflationary stage exhibits an instability with respect to inhomogeneous perturbations, suggesting that the initial state of the universe should be inhomogeneous. However, more general Horndeski models may probably be stable.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
