Modern Mathematical Physics: what it should be?
英文摘要：
Personal view of author on goals and content of Mathematical Physics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
Adeles in Mathematical Physics
Application of adeles in modern mathematical physics is briefly reviewed. In particular, some adelic products are presented.
hep-thmath-phmath.MP
Methods of modern mathematical physics: Uncertainty and exclusion principles in quantum mechanics
These are lecture notes for a master-level course given at KTH, Stockholm, in the spring of 2017, with the primary aim of proving the stability of matter from first principles using modern mathematical methods in many-body quantum mechanics. General quantitative formulations of the uncertainty and the exclusion principles of quantum mechanics are introduced, such as the Hardy, Sobolev and Poincaré functional inequalities as well as the powerful Lieb-Thirring inequality that combines these two principles. The notes are aimed to be both fairly self-contained and at the same time complementary to…
math-phmath.FAmath.MP
Some beautiful equations of mathematical physics
The basic ideas and the important role of gauge principles in modern elementary particle physics are outlined. There are three theoretically consistent gauge principles in quantum field theory: the spin-1 gauge principle of electromagnetism and the standard model, the spin-2 gauge principle of general relativity, and the spin-3/2 gauge principle of supergravity. (Dirac Prize lecture, November 1993. Two figures are unavailable, but should not be essential.)
hep-thmath-phmath.MP
Introductive Backgrounds of Modern Quantum Mathematics with Application to Nonlinear Dynamical Systems
Introductive backgrounds of a new mathematical physics discipline - Quantum Mathematics - are discussed and analyzed both from historical and analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1932, are demonstrated, and an impressive application to the nonlinear dynamical systems theory is considered.
math-phmath.MP
Linear Response Theory: A Modern Analytic-Algebraic Approach
Linear response theory is a tool with which one can study systems that are driven out of equilibrium by external perturbations. This monograph presents a thoroughly modern framework to make linear response theory rigorous for a wide array of systems, that is suitable for novel applications such as periodic and random light conductors not yet covered in the literature. Our analytic-algebraic approach, based on von Neumann algebras and associated non-commutative $L^p$-spaces, can deal with discrete and continuous models alike, and include effects of disorder. First, we explain the mathematical s…
math-phmath.MP
$p$-Adic Mathematical Physics: The First 30 Years
$p$-Adic mathematical physics is a branch of modern mathematical physics based on the application of $p$-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale, but then was extended to many other areas including biology. This paper contains a brief review of main achievements in some selected topics of $p$-adic mathematical physics and its applications, especially in the last decade. Attention is mainly paid to developments with promising future …
hep-thmath-phmath.MP
更多相关论文收起更多论文
An appetizer to modern developments on the Kardar-Parisi-Zhang universality class
The Kardar-Parisi-Zhang (KPZ) universality class describes a broad range of non-equilibrium fluctuations, including those of growing interfaces, directed polymers and particle transport, to name but a few. Since the year 2000, our understanding of the one-dimensional KPZ class has been completely renewed by mathematical physics approaches based on exact solutions. Mathematical physics has played a central role since then, leading to a myriad of new developments, but their implications are clearly not limited to mathematics -- as a matter of fact, it can also be studied experimentally. The aim …
cond-mat.stat-mechmath-phmath.MP
What is geometry in quantum theory
In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.
gr-qchep-thmath-ph
一类随机共聚反应过程的数学分析
Mathematical Analysis for a Class of Stochastic Copolymerization Processes
本文通过严谨数学方法分析了一类共聚反应过程的随机模型，推导了转瞬即逝、零回归和正回归的判据，确定了瞬态情况下不同单体类型的极限比例及聚合物增长速度。
math-phmath.MPmath.PR
A Primer on Differential Forms
This primer is intended as an introduction to differential forms, a central object in modern mathematical physics, for scientists and engineers.
math-phmath.MP
关于 Fibonacci 镶嵌及其现代衍生
On the Fibonacci tiling and its modern ramifications
本文从著名的 Fibonacci 链出发，解释非周期序数学理论的新镶嵌与性质，并指出其各种推广及高维现象与结果，为该主题的现代文献提供切入点。
math-phmath.MGmath.MP
纪念路德维希·德米特里耶维奇·法捷耶夫——我们数理物理学研究的终身伙伴
Remembering Ludwig Dmitrievich Faddeev, our lifelong partner in mathematical physics
本文追忆作者与法捷耶夫自1966年相识以来跨越学派与家庭的终身友谊，并概述其科学影响及对数学物理本质的思考。
math-phmath.MPphysics.hist-ph
Geometry of turbulent dissipation and the Navier-Stokes regularity problem
The question of whether a singularity can form in an initially regular flow, described by the 3D incompressible Navier-Stokes (NS) equations, is a fundamental problem in mathematical physics. The NS regularity problem is super-critical, i.e., there is a 'scaling gap' between what can be established by mathematical analysis and what is needed to rule out a singularity. A recently introduced mathematical framework--based on a suitably defined `scale of sparseness' of the regions of intense vorticity--brought the first scaling reduction of the NS super-criticality since the 1960s. Here, we put th…
math-phmath.MPphysics.flu-dyn
