Related papers: The Eightfold Way
This is the revised version of a Comment on a paper by C. Escudero (Phys. Rev. Lett. 100, 116101, 2008; arXiv:0804.1898).
This is lecture notes for a course given at the PCMI Summer School "Quantum Field Theory and Manifold Invariants" (July 1 -- July 5, 2019). I describe basics of gauge-theoretic approach to construction of invariants of manifolds. The main…
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in $D$ dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action…
We present some plausible definitions for the tangent grupoid of a manifold M, as well as some of the known applications of the structure. This is a kind of introductory note.
This article gives a conceptual introduction to the topos approach to the formulation of physical theories.
This article (which appeared with illustrations) was the astrophysics/cosmology contribution to the historical series ``Pathways of Discovery'' which appeared in ``Science'' during last year.
These lecture notes are based on [arXiv: math/0702714, 0907.4469, 0907.4470]. We introduce and study basic aspects of non-Euclidean geometries from a coordinate-free viewpoint.
The object of this contribution is twofold. On one hand, it rises some general questions concerning the definition of the electromagnetic field and its intrinsic properties, and it proposes concepts and ways to answer them. On the other…
In this article we present an elementary introduction to the theory of minimal surfaces in Euclidean spaces $\mathbb R^n$ for $n\ge 3$ by using only elementary calculus of functions of several variables at the level of a typical second-year…
We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…
Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM
In this paper, a class of fractals, called quadrilateral labyrinth fractals, are introduced and studied. They are a special kind of fractals on any quadrilateral on the plane. This type of fractal is motivated by labyrinth fractal on the…
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,…
In this letter we study the classical motion of an electric dipole in the presence of a uniform magnetic field in the approximation of small oscillations. The normal modes of oscillations are obtained and propose a criterion of…
Proposal for contribution to the quantum field theory section in "Encyclopedia of Mathematical Physics".
This work thoroughly examines several analytical tools, each possessing a different level of mathematical intricacy, for the purpose of characterizing the orientation distribution function of elongated objects under flow. Our investigation…
This article is a draft of a book chapter of the book entitled "Quantum Percolation and Breakdown", to appear 2008.
Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of…
Three approaches to the derivation of the classical electromagnetic modes of a rectangular cavity are described. In so doing, some apparent errors in a widely-used physics text are pointed out.
We give a rather informal introduction to the theory of mixed Hodge modules for young mathematicians.