ﻻ يوجد ملخص باللغة العربية
In this work, we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to $SU(2)$-invariant spin-network states. Our results do not depend on the physical interpretation of the spin network; however, they are mainly motivated by the fact that spin-network states can describe states of quantum geometry, providing a gauge-invariant basis for the kinematical Hilbert space of several background-independent approaches to quantum gravity. The first result is, by itself, the existence of a regime in which we show the emergence of a typical state. We interpret this as the proof that in that regime there are certain (local) properties of quantum geometry which are universal. Such a set of properties is heralded by the typical state, of which we give the explicit form. This is our second result. In the end, we study some interesting properties of the typical state, proving that the area law for the entropy of a surface must be satisfied at the local level, up to logarithmic corrections which we are able to bound.
We start from a static, spherically symmetric space-time in the presence of an electrostatic field and construct the mini-superspace Lagrangian that reproduces the well known Reissner - Nordstrom solution. We identify the classical integrals of motio
We explicitly construct and characterize all possible independent loop states in 3+1 dimensional loop quantum gravity by regulating it on a 3-d regular lattice in the Hamiltonian formalism. These loop states, characterized by the (dual) angular momen
The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to develop
It is well known in the literature that vacuum fluctuations can induce a random motion of particles which is sometimes called quantum Brownian motion or quantum stochastic motion. In this paper, we consider Lorentz Invariance Violation (LIV) in an ac
The problem of finding null geodesics in a stationary Lorentzian spacetime is known to to be equivalent to finding the geodsics of a Randers-Finlser structure. This latter problem is equivalent to finding the motion of charged particles moving on a R