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We describe three perspectives on higher quantization, using the example of magnetic Poisson structures which embody recent discussions of n

#arxiv #hep-th #math-ph

We give a pedagogical introduction to the nonassociative structures arising from recent developments in quantum mechanics with magnetic mono

#arxiv #hep-th #math-ph

Seven Myths in Machine Learning Research · Oscar Chang

Here is a conversation I had with Scott Aaronson. It started on his blog, in a discussion about ‘fine-tuning’. Some say the Standard Mod

Damien Calaque has invited me to speak at FGSI 2019, a conference on the Foundations of Geometric Structures of Information. It will focus o

Check out the video of my talk, the first in the Applied Category Theory Seminar here at U. C. Riverside. It was nicely edited by Paola F

We’re going to have a seminar on applied category theory here at U. C. Riverside! My students have been thinking hard about category theor

I can’t help thinking about geometric quantization. I feel it holds some lessons about the relation between classical and quantum mecha

I’m teaching a course on category theory at U.C. Riverside, and since my website is still suffering from reduced functionality I’ll put

Tai-Danae Bradley has a new free “booklet” on applied category theory. It was inspired by the workshop Applied Category Theory 2018, whi

I’ve been spending the last month at the Centre of Quantum Technologies, getting lots of work done. This Friday I’m giving a talk, an

These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich

#arxiv #math-ph

Direct numerical evaluation of the real-time path integral has a well-known sign problem that makes convergence exponentially slow. One prom

#arxiv #hep lat

T he postcard contained only two words: “Hurry up.”John Archibald Wheeler, a 33-year-old physicist, was in Hanford, Wash., working…

Accounts of Wheeler's life are always fascinating… this one is also poetic. Worth reading.

#wheeler #time #physics #nautilus

We introduce a "web-based formalism" for describing the category of half-supersymmetric boundary conditions in 1+1 dimensional massive field theories with N=(2,2) supersymmetry and unbroken U(1)R symmetry. We show that the category can be completely constructed from data available in the far infrared, namely, the vacua, the central charges of soliton sectors, and the spaces of soliton states on R, together with certain "interaction and boundary emission amplitudes". These amplitudes are shown to satisfy a system of algebraic constraints related to the theory of A∞ and L∞ algebras. The web-based formalism also gives a method of finding the BPS states for the theory on a half-line and on an interval. We investigate half-supersymmetric interfaces between theories and show that they have, in a certain sense, an associative "operator product." We derive a categorification of wall-crossing formulae. The example of Landau-Ginzburg theories is described in depth drawing on ideas from Morse theory, and its interpretation in terms of supersymmetric quantum mechanics. In this context we show that the web-based category is equivalent to a version of the Fukaya-Seidel A∞-category associated to a holomorphic Lefschetz fibration, and we describe unusual local operators that appear in massive Landau-Ginzburg theories. We indicate potential applications to the theory of surface defects in theories of class S and to the gauge-theoretic approach to knot homology.

#arXiv #hep-th #math.AG #math.SG

This paper summarizes our rather lengthy paper, "Algebra of the Infrared: String Field Theoretic Structures in Massive N=(2,2) Field Theory In Two Dimensions," and is meant to be an informal, yet detailed, introduction and summary of that larger work.

#arXiv #hep-th #math.AG #math.SG

All truths are easy to understand once they are discovered; the point is to discover them.

Galileo Galilei, astronomer.

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