相关论文: Markov paths, loops and fields

Fifteen years after their discovery, ample fields now stand at the center of research in contemporary Galois theory and attract more and more attention also from other areas of mathematics. This survey gives an introduction to the theory of…

We summarize recent developments of the semiclassical description of shell effects in finite fermion systems with explicit inclusion of spin degrees of freedom, in particluar in the presence of spin-orbit interactions. We present a new…

We sketch the construction of a derived enhancement of the reciprocity isomorphism of class field theory. Details will appear in a forthcoming joint paper of the authors with A. Raksit.

These lecture notes give an exposition of microlocal analysis methods in the study of Quantum Field Theory on curved spacetimes. We concentrate on free fields and the corresponding quasi-free states and mainly on Klein-Gordon fields.Updated…

We develop a coarse-graining procedure for two-dimensional models of fluctuating loops by mapping them to interface models. The result is an effective field theory for the scaling limit of loop models, which is found to be a Liouville…

This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.

Markov processes are popular mathematical models, studied by theoreticians for their intriguing properties, and applied by practitioners for their flexible structure. With this book we teach how to model and analyze Markov processes. We…

We provide a systematic study of the notion of duality of Markov processes with respect to a function. We discuss the relation of this notion with duality with respect to a measure as studied in Markov process theory and potential theory…

We study a notion of operator growth known as Krylov complexity in free and interacting massive scalar quantum field theories in $d$-dimensions at finite temperature. We consider the effects of mass, one-loop self-energy due to perturbative…

In this short review we describe some aspects of $\kappa$-deformation. After discussing the algebraic and geometric approaches to $\kappa$-Poincar\'e algebra we construct the free scalar field theory, both on non-commutative…

The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a…

We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by…

The Gaussian Free Field (GFF) in the continuum appears to be the natural generalisation of Brownian motion, when one replaces time by a multidimensional continuous parameter. The goal of these lecture notes is to describe some aspects of…

It is well known that any higher order Markov chain can be associated with a first order Markov chain. In this primarily expository article, we present the first fairly comprehensive analysis of the relationship between higher order and…

We build a bridge between Floer theory on open symplectic manifolds and the enumerative geometry of holomorphic disks inside their Fano compactifications, by detecting elements in symplectic cohomology which are mirror to Landau-Ginzburg…

We review main features and problems of higher spin field theory and flash some ways along which it has been developed over last decades.

We relate the author's Lie cobracket in the module additively generated by loops on a surface with the Connes-Kreimer Lie bracket in the module additively generated by trees. To this end we introduce a pre-Lie coalgebra and a (commutative)…

I outline the theory of relativistic charged-particle motion in the magnetosphere in a way suitable for undergraduate courses. I discuss particle and guiding center motion, derive the three adiabatic invariants associated with them, and…

This work is intended as an introduction to the statement and the construction of the local Langlands correspondence for GL(n) over p-adic fields. The emphasis lies on the statement and the explanation of the correspondence.

Having previously identified the photon field with a (special) linear Complex, we give a brief account on identifications and reasoning so far. Then, in order to include spinorial degrees of freedom into the Lagrangean description, we…