Related papers: Geometric renormalization below the ground state
We establish global well-posedness and scattering for wave maps from $d$-dimensional hyperbolic space into Riemannian manifolds of bounded geometry for initial data that is small in the critical Sobolev space for $d \geq 4$. The main…
There has been much progress in recent years in understanding the existence problem for wave maps with small critical Sobolev norm (in particular for two-dimensional wave maps with small energy); a key aspect in that theory has been a…
In the monograph Renormalization and Effective Field Theory, Costello made two major advances towards the mathematical formulation of quantum field theory. Firstly, he developed an inductive position space renormalization procedure for…
Calorimetry has been a traditional tool for obtaining invaluable thermodynamic information of matter, the free energy. We describe recent efforts to go beyond this traditional calorimetry: After introducing dynamic heat capacity, we present…
The thermodynamic geometry formalism is applied to strongly interacting matter to estimate the deconfinement temperature. The curved thermodynamic metric for Quantum Chromodynamics (QCD) is evaluated on the basis of lattice data, whereas…
Universality of classical thermodynamics rests on the central limit theorem, due to which, measurements of thermal fluctuations are unable to reveal detailed information regarding the microscopic structure of a macroscopic body. When small…
The recently introduced concept of generalized thermodynamics is explored here in the context of 1d, 2d and 3d data analysis, performed on samples drawn from a 3d X-ray soil sample image. Different threshold levels are used to binarize the…
H. Weyl's proposal of 1918 for generalizing Riemannian geometry by local scale gauge (later called {\em Weyl geometry}) was motivated by mathematical, philosophical and physical considerations. It was the starting point of his unified field…
We investigate the time evolution of a generic and finite isolated quantum many-body system starting from a pure quantum state. We find the kinematical general canonical principle proposed by Popescu-Short-Winter for statistical mechanics…
Data from a number of different experimental measurements have been used to construct caloric curves for five different regions of nuclear mass. These curves are qualitatively similar and exhibit plateaus at the higher excitation energies.…
We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as the limit of integrals over the approximating spaces. This…
We consider Wave Maps with smooth compactly supported initial data of small H^{{3/2}}-norm from R^{3+1} to the hyperbolic plane and show that they stay smooth globally in time. Our methods are based on the introduction of a global Coulomb…
The application of Riemannian geometry to the analysis of the equilibrium thermodynamics in Quantum Chromodynamics (QCD) at finite temperature and baryon density gives a new method to evaluate the critical temperature, $T_c$, of the…
We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…
While the geometry of equilibrium states and driven non-equilibrium processes is clearly understood, a geometric description for relaxation towards equilibrium is still lacking. Here, we propose a thermo-geometric measure based on the…
In this paper, we prove that the Schr\"odinger map flows from $\Bbb R^d$ with $d\ge 3$ to compact K\"ahler manifolds with small initial data in critical Sobolev spaces are global. This is a companion work of our previous paper [23] where…
We consider a gauge symmetry in a quantum Hilbert space. The symmetry leads to that of the heat-kernel and of the anomaly formulae which were previously obtained by the authors. This greatly simplifies and clarifies the structure of the…
Thermalization of isolated many-body systems is demonstrated by generalizing an approach originally due to von Neumann: For arbitrary initial states with a macroscopically well-defined energy, quantum mechanical expectation values become…
We provide a natural generalization of a Riemannian structure, i.e., a metric, recently introduced by Sj\"{o}qvist for the space of non degenerate density matrices, to the degenerate case, i.e., the case in which the eigenspaces have…
Early developments leading to renormalizable non-Abelian gauge theories for the weak, electromagnetic and strong interactions, are discussed from a personal viewpoint. They drastically improved our view of the role of field theory, symmetry…