Related papers: Random systems and replica field theory
A tutorial review is given of some developments and applications of stochastic processes from the point of view of the practicioner physicist. The index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient Stochastic…
The first free comprehensive textbook on quantum (and classical) field theory. The approach is pragmatic, rather than traditional or artistic: It includes practical techniques, such as the 1/N expansion (color ordering) and spacecone…
This review article provides the basics and discusses some important applications of thermal field theory, namely the combination of statistical mechanics and relativistic quantum field theory. In a first part the fundamentals are covered:…
We provide an overview of basic concepts, tools, and results of quantum field theoretical scattering theory. This article is prepared for the second edition of the Encyclopedia of Mathematical Physics, edited by M. Bojowald and R.J. Szabo,…
We present a quick introduction to quantum field theory and Wilson's theory of the renormalization group from the point of view of mathematical analysis. The presentation is geared primarily towards a probability theory, harmonic analysis…
1 Introduction 2 Multipole Decomposition 3 Source Multipole Moments 4 Post-Minkowskian Approximation 5 Radiative Multipole Moments 6 Post-Newtonian Approximation 7 Point-Particles 8 Conclusion
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
The paper investigates random fields in the ball. It studies three types of such fields: restrictions of scalar random fields in the ball to the sphere, spin, and vector random fields. The review of the existing results and new spectral…
In these 4 lectures, I give a brief introduction to the principles of effective field theory and discuss their application via 3 examples: (i) the Standard Model as an effective theory; (ii) non-linear sigma models and the composite Higgs;…
While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium…
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…
For Encyclopedia of Complexist and System Science No abstract given I. Definition and Introduction II. Ising Model III. Fractals IV. Diffusion on Fractals V. Ising Model on Fractals VI. Other Subjects ? VII. Networks VIII. Future Directions
The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric…
These lectures review phases and phase transitions of the Standard Model, with emphasis on those aspects which are amenable to a first principle study. Model calculations and theoretical ideas of practical applicability are discussed as…
This is a cursory overview of applications of concepts from random matrix theory (RMT) to quantum electronics and classical & quantum optics. The emphasis is on phenomena, predicted or explained by RMT, that have actually been observed in…
A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.
Contents: Generalities, Chiral supermultiplets, Super Yang-Mills theory, Superspace Feynman graphs, Renormalization, Supercurrent, Finite theories.
This paper focuses on rotational phenomena of rigid body kinematics. It discusses them in a group-theoretic approach as completely as possible, using methods and notations as intuitive as possible. With a review of current literature, this…