Search results for "Classical"
showing 10 items of 2294 documents
Fractal Spacetime Structure in Asymptotically Safe Gravity
2005
Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective dimensionality of 2. The original argument leading to this result was based upon the anomalous dimension of Newton's constant. In the present paper we demonstrate that also the spectral dimension equals 2 microscopically, while it is equal to 4 on macroscopic scales. This result is an exact consequence of asymptotic safety and does not rely on any truncation. Contact is made with recent Monte Carlo simulations.
On the physical contents of q-deformed Minkowski spaces
1994
Some physical aspects of $q$-deformed spacetimes are discussed. It is pointed out that, under certain standard assumptions relating deformation and quantization, the classical limit (Poisson bracket description) of the dynamics is bound to contain unusual features. At the same time, it is argued that the formulation of an associated $q$-deformed field theory is fraught with serious difficulties.
General invertible transformation and physical degrees of freedom
2017
An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However, if the transformation depends on field derivatives, the equivalence between the two systems is nontrivial due to the appearance of higher derivative terms in the equations of motion. To address this problem, we prove the following theorem on the relation between an invertible transformation and Euler-Lagrange equations: If the field transformation is invertible, then any solution of the original set of Euler-Lagrange equations is mapped to a solution of …
Continuous-variable entanglement sharing in noninertial frames
2007
We study the distribution of entanglement between modes of a free scalar field from the perspective of observers in uniform acceleration. We consider a two-mode squeezed state of the field from an inertial perspective, and analytically study the degradation of entanglement due to the Unruh effect, in the cases of either one or both observers undergoing uniform acceleration. We find that for two observers undergoing finite acceleration, the entanglement vanishes between the lowest frequency modes. The loss of entanglement is precisely explained as a redistribution of the inertial entanglement into multipartite quantum correlations among accessible and unaccessible modes from a non-inertial p…
Deterministic Quantization by Dynamical Boundary Conditions
2010
We propose an unexplored quantization method. It is based on the assumption of dynamical space-time intrinsic periodicities for relativistic fields, which in turn can be regarded as dual to extra-dimensional fields. As a consequence we obtain a unified and consistent interpretation of Special Relativity and Quantum Mechanics in terms of Deterministic Geometrodynamics.
Generalized Slow Roll in the Unified Effective Field Theory of Inflation
2017
We provide a compact and unified treatment of power spectrum observables for the effective field theory (EFT) of inflation with the complete set of operators that lead to second-order equations of motion in metric perturbations in both space and time derivatives, including Horndeski and GLPV theories. We relate the EFT operators in ADM form to the four additional free functions of time in the scalar and tensor equations. Using the generalized slow roll formalism, we show that each power spectrum can be described by an integral over a single source that is a function of its respective sound horizon. With this correspondence, existing model independent constraints on the source function can b…
Renormalization group analysis of the gluon mass equation
2014
In the present work we carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass. A detailed, all-order analysis of the complete kernel appearing in this particular equation reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained sol…
Renormalized stress-energy tensor for spin-1/2 fields in expanding universes
2014
We provide an explicit expression for the renormalized expectation value of the stress-energy tensor of a spin-$1/2$ field in a spatially flat FLRW universe. Its computation is based on the extension of the adiabatic regularization method to fermion fields introduced recently in the literature. The tensor is given in terms of UV-finite integrals in momentum space, which involve the mode functions that define the quantum state. As illustrative examples of the method efficiency, we see how to compute the renormalized energy density and pressure in two interesting cosmological scenarios: a de Sitter spacetime and a radiation-dominated universe. In the second case, we explicitly show that the l…
Quantum Backreaction on Three-Dimensional Black Holes and Naked Singularities
2016
We analytically investigate backreaction by a quantum scalar field on two rotating Ba\~nados-Teitelboim-Zanelli (BTZ) geometries: that of a black hole and that of a naked singularity. In the former case, we explore the quantum effects on various regions of relevance for a rotating black hole space-time. We find that the quantum effects lead to a growth of both the event horizon and the radius of the ergosphere, and to a reduction of the angular velocity, compared to the unperturbed values. Furthermore, they give rise to the formation of a curvature singularity at the Cauchy horizon and show no evidence of the appearance of a superradiant instability. In the case of a naked singularity, we f…
Quantum walk on a cylinder
2016
We consider the 2D alternate quantum walk on a cylinder. We concentrate on the study of the motion along the open dimension, in the spirit of looking at the closed coordinate as a small or "hidden" extra dimension. If one starts from localized initial conditions on the lattice, the dynamics of the quantum walk that is obtained after tracing out the small dimension shows the contribution of several components, which can be understood from the study of the dispersion relations for this problem. In fact, these components originate from the contribution of the possible values of the quasi-momentum in the closed dimension. In the continuous space-time limit, the different components manifest as …