Istituto Lombardo - Accademia di Scienze e Lettere - Rendiconti di Scienze
A brief introduction to the scientic work of Stephen Hawking and to his contributions to our unde... more A brief introduction to the scientic work of Stephen Hawking and to his contributions to our understanding of the interplay between general relativity and quantum theory.
The perturbative approach to nonlinear Sigma models and the associated renormalization group flow... more The perturbative approach to nonlinear Sigma models and the associated renormalization group flow are discussed within the framework of Euclidean algebraic quantum field theory and of the principle of general local covariance. In particular we show in an Euclidean setting how to define Wick ordered powers of the underlying quantum fields and we classify the freedom in such procedure by extending to this setting a recent construction of Khavkine, Melati and Moretti for vector valued free fields. As a by-product of such classification, we provide a mathematically rigorous proof that, at first order in perturbation theory, the renormalization group flow of the nonlinear Sigma model is the Ricci flow.
No. In a number of papers Green and Wald argue that the standard FLRW model approximates our Univ... more No. In a number of papers Green and Wald argue that the standard FLRW model approximates our Universe extremely well on all scales, except close to strong field astrophysical objects. In particular, they argue that the effect of inhomogeneities on average properties of the Universe (backreaction) is irrelevant. We show that this latter claim is not valid. Specifically, we demonstrate, referring to their recent review paper, that (i) their two-dimensional example used to illustrate the fitting problem differs from the actual problem in important respects, and it assumes what is to be proven; (ii) the proof of the trace-free property of backreaction is unphysical and the theorem about it fails to be a mathematically general statement; (iii) the scheme that underlies the trace-free theorem does not involve averaging and therefore does not capture crucial non-local effects; (iv) their arguments are to a large extent coordinate-dependent, and (v) many of their criticisms of backreaction frameworks do not apply to the published definitions of these frameworks. It is No proof that backreaction is irrelevant 2 therefore incorrect to infer that Green and Wald have proven a general result that addresses the essential physical questions of backreaction in cosmology.
Nonlinear sigma models are quantum field theories describing, in the large deviation sense, rando... more Nonlinear sigma models are quantum field theories describing, in the large deviation sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton–Perelman Ricci flow. By exploiting the heat kernel embedding introduced by Gigli and Mantegazza, we show that the Wasserstein geometry of the space of probability measures over Riemannian metric measure spaces provides a natural setting for discussing the relation between nonlinear sigma models and Ricci flow theory. In particular, we analyze the embedding of Ricci flow into a heat kernel renormalization group flow for dilatonic nonlinear sigma models, and characterize a non-trivial generalization of the Hamilton–Perelman version of the Ricci flow. We discuss in detail the monotonicity and gradient flow properties of this extended flow.
In the framework of simplicial models, we construct and we fully characterize a scalar boundary c... more In the framework of simplicial models, we construct and we fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analysed from a string theory perspective as tools to deal with open/closed string dualities.
... Hamilton's flow Mauro Carfora and Annalisa Marzuoli Dipartimento di Fisica N... more ... Hamilton's flow Mauro Carfora and Annalisa Marzuoli Dipartimento di Fisica Nucleare e Teorica, Universita di Pavia, Via Bassi 6, 27100 Pavia, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Via Bassi 6, 27100 Pavia, Italy ...
Advances in Theoretical and Mathematical Physics, 2002
Our goal here is to present a detailed analysis connecting the anomalous scaling properties of 2D... more Our goal here is to present a detailed analysis connecting the anomalous scaling properties of 2D simplicial quantum gravity to the geometry of the moduli space M g , N0 of genus g Riemann surfaces with N 0 punctures. In the case of pure gravity we prove that the scaling properties of the set of dynamical triangulations with N 0 vertices are directly provided by the large N 0 asymptotics of the Weil-Petersson volume of M g , N0 , recently discussed by Manin and Zograf. Such a geometrical characterization explains why dynamical triangulations automatically take into account the anomalous scaling properties of Liouville theory. In the case of coupling with conformal matter we briefly argue that the anomalous scaling of the resulting discretized theory should be related to the Gromov-Witten invariants of the moduli space M g , N0 (X, β) of stable maps from (punctured Riemann surfaces associated with) dynamical triangulations to a (smooth projective) manifold X parameterizing the conformal matter configurations.
We will show how the study of randomly triangulated surfaces merges with the study of open/closed... more We will show how the study of randomly triangulated surfaces merges with the study of open/closed string dualities. In particular we will discuss the Conformal Field Theory which arises in the open string sector and its implications.
We investigate the scale-dependence of Eulerian volume averages of scalar functions on Riemannian... more We investigate the scale-dependence of Eulerian volume averages of scalar functions on Riemannian three-manifolds. We propose a complementary view of a Lagrangian scaling of variables as opposed to their Eulerian averaging on spatial domains. This program explains rigorously the origin of the Ricci deformation flow for the metric, a flow which, on heuristic grounds, has been already suggested as a possible candidate for averaging the initial data set for cosmological spacetimes.
ABSTRACT This book contains papers presented at a conference on general relativity and gravitatio... more ABSTRACT This book contains papers presented at a conference on general relativity and gravitational physics. Topics covered include non-perturbative quantum gravity: a status report and stochastic quantization in curved space time.
By exploiting a correspondence between Random Regge triangula- tions (i.e., Regge triangulations ... more By exploiting a correspondence between Random Regge triangula- tions (i.e., Regge triangulations with variable connectivity) and punc- tured Riemann surfaces, we propose a possible characterization of the SU(2) Wess-Zumino-Witten model on a triangulated surface of genus g. Techniques of boundary CFT are used for the analysis of the quantum amplitudes of the model at level � = 1. These techniques
Istituto Lombardo - Accademia di Scienze e Lettere - Rendiconti di Scienze
A brief introduction to the scientic work of Stephen Hawking and to his contributions to our unde... more A brief introduction to the scientic work of Stephen Hawking and to his contributions to our understanding of the interplay between general relativity and quantum theory.
The perturbative approach to nonlinear Sigma models and the associated renormalization group flow... more The perturbative approach to nonlinear Sigma models and the associated renormalization group flow are discussed within the framework of Euclidean algebraic quantum field theory and of the principle of general local covariance. In particular we show in an Euclidean setting how to define Wick ordered powers of the underlying quantum fields and we classify the freedom in such procedure by extending to this setting a recent construction of Khavkine, Melati and Moretti for vector valued free fields. As a by-product of such classification, we provide a mathematically rigorous proof that, at first order in perturbation theory, the renormalization group flow of the nonlinear Sigma model is the Ricci flow.
No. In a number of papers Green and Wald argue that the standard FLRW model approximates our Univ... more No. In a number of papers Green and Wald argue that the standard FLRW model approximates our Universe extremely well on all scales, except close to strong field astrophysical objects. In particular, they argue that the effect of inhomogeneities on average properties of the Universe (backreaction) is irrelevant. We show that this latter claim is not valid. Specifically, we demonstrate, referring to their recent review paper, that (i) their two-dimensional example used to illustrate the fitting problem differs from the actual problem in important respects, and it assumes what is to be proven; (ii) the proof of the trace-free property of backreaction is unphysical and the theorem about it fails to be a mathematically general statement; (iii) the scheme that underlies the trace-free theorem does not involve averaging and therefore does not capture crucial non-local effects; (iv) their arguments are to a large extent coordinate-dependent, and (v) many of their criticisms of backreaction frameworks do not apply to the published definitions of these frameworks. It is No proof that backreaction is irrelevant 2 therefore incorrect to infer that Green and Wald have proven a general result that addresses the essential physical questions of backreaction in cosmology.
Nonlinear sigma models are quantum field theories describing, in the large deviation sense, rando... more Nonlinear sigma models are quantum field theories describing, in the large deviation sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton–Perelman Ricci flow. By exploiting the heat kernel embedding introduced by Gigli and Mantegazza, we show that the Wasserstein geometry of the space of probability measures over Riemannian metric measure spaces provides a natural setting for discussing the relation between nonlinear sigma models and Ricci flow theory. In particular, we analyze the embedding of Ricci flow into a heat kernel renormalization group flow for dilatonic nonlinear sigma models, and characterize a non-trivial generalization of the Hamilton–Perelman version of the Ricci flow. We discuss in detail the monotonicity and gradient flow properties of this extended flow.
In the framework of simplicial models, we construct and we fully characterize a scalar boundary c... more In the framework of simplicial models, we construct and we fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analysed from a string theory perspective as tools to deal with open/closed string dualities.
... Hamilton's flow Mauro Carfora and Annalisa Marzuoli Dipartimento di Fisica N... more ... Hamilton's flow Mauro Carfora and Annalisa Marzuoli Dipartimento di Fisica Nucleare e Teorica, Universita di Pavia, Via Bassi 6, 27100 Pavia, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Via Bassi 6, 27100 Pavia, Italy ...
Advances in Theoretical and Mathematical Physics, 2002
Our goal here is to present a detailed analysis connecting the anomalous scaling properties of 2D... more Our goal here is to present a detailed analysis connecting the anomalous scaling properties of 2D simplicial quantum gravity to the geometry of the moduli space M g , N0 of genus g Riemann surfaces with N 0 punctures. In the case of pure gravity we prove that the scaling properties of the set of dynamical triangulations with N 0 vertices are directly provided by the large N 0 asymptotics of the Weil-Petersson volume of M g , N0 , recently discussed by Manin and Zograf. Such a geometrical characterization explains why dynamical triangulations automatically take into account the anomalous scaling properties of Liouville theory. In the case of coupling with conformal matter we briefly argue that the anomalous scaling of the resulting discretized theory should be related to the Gromov-Witten invariants of the moduli space M g , N0 (X, β) of stable maps from (punctured Riemann surfaces associated with) dynamical triangulations to a (smooth projective) manifold X parameterizing the conformal matter configurations.
We will show how the study of randomly triangulated surfaces merges with the study of open/closed... more We will show how the study of randomly triangulated surfaces merges with the study of open/closed string dualities. In particular we will discuss the Conformal Field Theory which arises in the open string sector and its implications.
We investigate the scale-dependence of Eulerian volume averages of scalar functions on Riemannian... more We investigate the scale-dependence of Eulerian volume averages of scalar functions on Riemannian three-manifolds. We propose a complementary view of a Lagrangian scaling of variables as opposed to their Eulerian averaging on spatial domains. This program explains rigorously the origin of the Ricci deformation flow for the metric, a flow which, on heuristic grounds, has been already suggested as a possible candidate for averaging the initial data set for cosmological spacetimes.
ABSTRACT This book contains papers presented at a conference on general relativity and gravitatio... more ABSTRACT This book contains papers presented at a conference on general relativity and gravitational physics. Topics covered include non-perturbative quantum gravity: a status report and stochastic quantization in curved space time.
By exploiting a correspondence between Random Regge triangula- tions (i.e., Regge triangulations ... more By exploiting a correspondence between Random Regge triangula- tions (i.e., Regge triangulations with variable connectivity) and punc- tured Riemann surfaces, we propose a possible characterization of the SU(2) Wess-Zumino-Witten model on a triangulated surface of genus g. Techniques of boundary CFT are used for the analysis of the quantum amplitudes of the model at level � = 1. These techniques
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Papers by Mauro Carfora