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第七届辛几何和拓扑场论高级研讨会（The Seventh Advanced Seminar in Symplectic Geometry and Topological Field Theory）
第七届 辛几何和拓扑场论 高级研讨会
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2017/4/24
Beijing International Center for Mathematical Research (BICMR) locates on the north Shore of Weiming Lake on the campus of Peking University. Sponsored by the national government of China, BICMR is de...
The Seventh Advanced Seminar in Symplectic Geometry and Topological Field Theory
The Seventh Advanced Seminar Symplectic Geometry and Topological Field Theory
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2017/3/28
The topics of the 7th Advanced Seminar in Symplectic Geometry and Topological Field Theory are 1) Givental's quantization formula and Teleman's classification of semisimple cohomological field theory;...
EXPLICIT CLASS FIELD THEORY FOR GLOBAL FUNCTION FIELDS
EXPLICIT CLASS FIELD THEORY GLOBAL FUNCTION FIELDS
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2015/8/26
Let F be a global function field and let F ab be its maximal abelian extension. Following an approach of D. Hayes, we shall construct a continuous homomorphism ρ: Gal(F ab/F) → CF , where CF is the id...
Conformal field theory and a new geometry
Conformal field theory D-branes vertex operator algebra stringy algebraic geometry
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2011/9/14
Abstract: This paper is a review of open-closed rational conformal field theory (CFT) via the theory of vertex operator algebras (VOAs), together with a proposal of a new geometry based on CFTs and D-...
Noninteraction of waves in two-dimensional conformal field theory
Noninteraction of waves two-dimensional conformal field theory Operator Algebras
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2011/9/6
Abstract: In higher dimensional quantum field theory, irreducible representations of the Poincare group are associated with particles. Their counterpart in two-dimensional massless models are "waves" ...
Class field theory as a dynamical system
Class field theory dynamical system Number Theory
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2011/9/1
Abstract: This is the text from a talk at the Arbeitstagung 2011, which can serve as an introduction to arxiv:1009.0736 and arXiv:1007.0907. I first discuss how a global field is determined by a certa...
Reconstruction in quantum field theory with a fundamental length
Reconstruction quantum field theory fundamental length
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2011/2/21
In this paper, we establish an analog of Wightman’s reconstruction theorem for nonlocal
quantum field theory with a fundamental length. In our setting, the Wightman generalized functions are defined ...
Integrable defects in affine Toda field theory and infinite dimensional representations of quantum groups
Integrable defects affine Toda field theory infinite dimensional representations quantum groups
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2011/3/3
Transmission matrices for two types of integrable defect are calculated explicitly, first by solving directly the nonlinear transmission Yang-Baxter equations.
Fuzzy Scalar Field Theory as Matrix Quantum Mechanics
Fuzzy Scalar Field Theory Matrix Quantum Mechanics
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2011/3/3
We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix mo...
From constructive field theory to fractional stochastic calculus. (I) An introduction: rough path theory and perturbative heuristics
fractional Brownian motion stochastic integrals rough paths
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2011/2/22
Let B = (B1(t), . . . ,Bd(t)) be a d-dimensional fractional Brownian motion with Hurst index ≤ 1/4, or more generally a Gaussian process whose paths have the same local regularity. Defining properly...
Modal Hamiltonian interpretation of quantum mechanics and Casimir operators: the road towards quantum field theory
Modal Hamiltonian interpretation of quantum mechanics Casimir operators quantum field theory
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2011/3/2
The general aim of this paper is to extend the Modal-Hamiltonian interpretation of quantum mechanics to the case of relativistic quantum mechanics with gauge U(1) fields.
Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory
Surface operators 3d Topological Field Theory 2d Rational Conformal Field Theory
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2011/3/2
We study surface operators in 3d Topological Field Theory and their relations with 2d Rational Conformal Field Theory.
Proof of the Borwein-Broadhurst conjecture for a dilogarithmic integral arising in quantum field theory
the Borwein-Broadhurst conjecture dilogarithmic integral arising quantum field theory
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2010/11/8
Borwein and Broadhurst, using experimental-mathematics techniques, in 1998 identified numerous hyperbolic 3-manifolds whose volumes are rationally related to values of various Dirichlet L series $\te...
From Quantum Mechanics to Quantum Field Theory: The Hopf route
Quantum Mechanics Quantum Field Theory
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2010/11/9
We show that the combinatorial numbers known as {\em Bell numbers} are generic in quantum physics. This is because they arise in the procedure known as {\em Normal ordering} of bosons, a procedure wh...
Symmetric Criticality in Classical Field Theory
Symmetric Criticality Classical Field Theory
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2010/11/22
This is a brief overview of work done by Ian Anderson, Mark Fels, and myself on symmetry reduction of Lagrangians and Euler-Lagrange equations, a subject closely related to Palais' Principle of Symme...