Stochastic semiclassical fluctuations in Minkowski spacetime

The semiclassical Einstein-Langevin equations which describe the dynamics of stochastic perturbations of the metric induced by quantum stress-energy fluctuations of matter fields in a given state are considered on the background of the ground state of semiclassical gravity, namely, Minkowski spacetime and a scalar field in its vacuum state. The relevant equations are explicitly derived for massless and massive fields arbitrarily coupled to the curvature. In doing so, some semiclassical results, such as the expectation value of the stress-energy tensor to linear order in the metric perturbations and particle creation effects, are obtained. We then solve the equations and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. In the conformal field case, explicit results are obtained. These results hint that gravitational fluctuations in stochastic semiclassical gravity have a non-perturbative behavior in some characteristic correlation lengths.

La géométrie analytique générale.

Available on demand as hard copy or computer file from Cornell University Library.

Fondamenti di geometria a più dimensioni e a più specie di unità rettilinee esposti in forma elementare. Lezioni per la scuola di magistero in matematica.

Available on demand as hard copy or computer file from Cornell University Library.

Schatten class Toeplitz operators on generalized Fock spaces

In this paper we characterize the Schatten p class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range p>0.

Generalized interval vector spaces and interval optimization

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω

Mathematics Subject Classification: 26A16, 26A33, 46E15.

Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators

2000 Mathematics Subject Classification: 35E45

Fractional Derivatives in Spaces of Generalized Functions

MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

On generalized orlicz sequence spaces of Fourier coefficients for trigonometric gap series. I.

We investigate the operator associating with a function fєLp2π, 1generalized Orlicz sequence space lϕ.

Common priors for generalized type spaces

The notion of common prior is well-understood and widely-used in the incomplete information games literature. For ordinary type spaces the common prior is de�fined. Pint�er and Udvari (2011) introduce the notion of generalized type space. Generalized type spaces are models for various bonded rationality issues, for �nite belief hierarchies, unawareness among others. In this paper we de�ne the notion of common prior for generalized types spaces. Our results are as follows: the generalization (1) suggests a new form of common prior for ordinary type spaces, (2) shows some quantum game theoretic results (Brandenburger and La Mura, 2011) in new light.

Generalized type spaces

Ordinary type spaces (Heifetz and Samet, 1998) are essential ingredients of incomplete information games. With ordinary type spaces one can grab the notions of beliefs, belief hierarchies and common prior etc. However, ordinary type spaces cannot handle the notions of finite belief hierarchy and unawareness among others. In this paper we consider a generalization of ordinary type spaces, and introduce the so called generalized type spaces which can grab all notions ordinary type spaces can and more, finite belief hierarchies and unawareness among others. We also demonstrate that the universal generalized type space exists.