Related papers: Professor C. N. Yang and Statistical Mechanics
The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is the first step towards this goal. This…
The Feynman path integral of ordinary quantum mechanics is complexified and it is shown that possible integration cycles for this complexified integral are associated with branes in a two-dimensional A-model. This provides a fairly direct…
Statistical mechanics describes interaction between particles of a physical system. Particle properties of the system can be modelled with a random field on a lattice and studied at different distance scales using renormalization group…
In the following paper, which is based on the authors PhD thesis submitted to Imperial College London, we explore the applicability of Yangian symmetry to various integrable models, in particular, in relation with S-matrices. One of the…
Supersymmetry plays prominent roles in the study of quantum field theory and in many proposals for potential new physics beyond the standard model. Lattice field theory provides a non-perturbative regularization suitable for strongly…
Supersymmetric gauge theories have played a central role in applications of quantum field theory to mathematics. Topologically twisted supersymmetric gauge theories often admit a rigorous mathematical description: for example, the Donaldson…
We introduce a class of new algebras, the shifted quiver Yangians, as the BPS algebras for type IIA string theory on general toric Calabi-Yau three-folds. We construct representations of the shifted quiver Yangian from general subcrystals…
I write about H\'ector, his contributions to the early work in the quark model, and a general discussion of quantum statistics
This dissertation reviews various aspects of the N=4 supersymmetric Yang--Mills theory in particular in relation with the AdS/CFT correspondence. The first two chapters are introductory. The first one contains a description of the general…
Supersymmetry plays prominent roles in the study of quantum field theory and in many proposals for potential new physics beyond the standard model, while lattice field theory provides a non-perturbative regularization suitable for strongly…
This is a survey paper on several aspects of differential geometry for the last 30 years, especially in those areas related to non-linear analysis. It grew from a talk I gave on the occasion of seventieth anniversary of Chinese Mathematical…
Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them. New inequalities for transcendental numbers are stated in Section 2 and…
The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
Supersymmetric gauge theories in four dimensions have taught us many important physics lessons. These can both inform and be informed by future work on the lattice. I focus on three issues: the properties of supersymmetric Yang-Mills theory…
Recently, there has been observed an interesting correspondence between supersymmetric quiver gauge theories with four supercharges and integrable lattice models of statistical mechanics such that the two-dimensional spin lattice is the…
In this article we establish the notion of classical Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory and for related planar gauge theories. After revisiting Yangian invariance for the equations of motion, we describe how…
In this paper, I give an overview of some selected results in quantum many body theory, lying at the interface between mathematical quantum statistical mechanics and condensed matter theory. In particular, I discuss some recent results on…
The field of neuroscience and the development of artificial neural networks (ANNs) have mutually influenced each other, drawing from and contributing to many concepts initially developed in statistical mechanics. Notably, Hopfield networks…