Related papers: Area spectrum in Lorentz covariant loop gravity
Covariant loop gravity comes out of the canonical analysis of the Palatini action and the use of the Dirac brackets arising from dealing with the second class constraints (``simplicity'' constraints). Within this framework, we underline a…
Lorentz covariance is the fundamental principle of every relativistic field theory which insures consistent physical descriptions. Even if the space-time is noncommutative, field theories on it should keep Lorentz covariance. In this…
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area…
A loop quantization of the diagonal class A Bianchi models starting from the complex-valued self-dual connection variables is presented in this paper. The basic operators in the quantum theory correspond to areas and generalized holonomies…
The ingoing and outgoing null expansions associated to a spatial 2-sphere are quantized in the spherically symmetric model of loop quantum gravity. It is shown that the resulting expansion operators are self-adjoint in the kinematical…
Quantum harmonic analysis on phase space is shown to be linked with localization operators. The convolution between operators and the convolution between a function and an operator provide a conceptual framework for the theory of…
In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to…
We study relationships between different formulations of the local principle. Also we establish a connection among the local principle and the non-commutative Fourier transform approach to the investigation of convolution operator algebras.…
We construct an irreducible representation of the canonical commutation relations by operators on a certain Banach space over a local field of characteristic p. The Carlitz polynomials forming the basis of the space are shown to be the…
We calculate Wilson loops on boundaries of Lifshitz-like dual backgrounds with different scaling parameters, assuming existence of a field theory dual to string theory in the bulk. We consider scaling parameters to be variable quantities…
We study numerically the first order radiative corrections to the self-energy, in covariant loop quantum gravity. We employ the recently developed 'sl2cfoam-next' spinfoam amplitudes library, and some original numerical methods. We analyze…
Witten described how a path integral quantization of Wilson Loop observables will define Jones polynomial type of link invariants, using the Chern-Simons gauge theory in $\mathbb{R}^3$. In this gauge theory, a compact Lie group ${\rm G}$,…
The parity operator for a parity-symmetric quantum field theory transforms as an infinite sum of irreducible representations of the homogeneous Lorentz group. These representations are connected with Wilson polynomials.
Results that illuminate the physical interpretation of states of nonperturbative quantum gravity are obtained using the recently introduced loop variables. It is shown that: i) While local operators such as the metric at a point may not be…
We give a prescription to define in Loop Quantum Gravity the electric field operator related to the scale factor of an homogeneous and isotropic cosmological space-time. This procedure allows to link the fundamental theory with its…
The Lorentz covariance of a non-linear, time-dependent relativistic wave equation is demonstrated; the equation has recently been shown to have highly interesting and significant empirical consequences. It is established here that an…
We present a systematic technique for constructing Lorentz covariant orbital-spin ($LS$) bases for matrix elements of local operators and the associated form factors, thereby extending the traditional multipole expansion to a Lorentz…
In this paper the relativistic quantum mechanics is considered in the framework of the nonstandard synchronization scheme for clocks. Such a synchronization preserves Poincar{\'e} covariance but (at least formally) distinguishes an inertial…
I investigate the relation between an operative definition of the area of a surface specified by matter fields and the area operators recently introduced in the canonical/loop approach to Quantum Gravity and in Rovelli's variant of the…
In this article, we study the quantum theory of gravitational boundary modes on a null surface. These boundary modes are given by a spinor and a spinor-valued two-form, which enter the gravitational boundary term for self-dual gravity.…