Related papers: Lectures on Topos Quantum Theory
A preliminary investigation is made of possible applications in quantum theory of the topos formed by the collection of all $M$-sets, where $M$ is a monoid. Earlier results on topos aspects of quantum theory can be rederived in this way.…
These notes are an introduction to General Relativity as a Quantum Effective Field Theory, following the material given in a short course on the subject at EPFL. The intent is to develop General Relativity starting from a quantum field…
The basic concepts of neutrino physics are presented at a level appropriate for integration into elementary courses on quantum mechanics and/or modern physics.
A quantum scattering theory is developed for Fock states scattered by two-level systems in the free space. Compared to existing scattering theories that treat incident light semi-classically, the theory fully quantizes the incident light as…
In these lectures we discuss some elementary concepts in connection with the theory of symmetric spaces applied to ensembles of random matrices. We review how the relationship between random matrix theory and symmetric spaces can be used in…
These lecture notes, suitable for a two-semester introductory course or self-study, offer an elementary and self-contained exposition of the basic tools and concepts that are encountered in practical computations in perturbative thermal…
This is the first of three PiTP lectures on complexity and its role in black hole physics.
Quantum Physics and Logic is an annual conference that brings together researchers working on mathematical foundations of quantum physics, quantum computing, and related areas, with a focus on structural perspectives and the use of logical…
In topological quantum computing, information is encoded in "knotted" quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been confirmed in quantum Hall liquids by…
Brief lecture notes for a course about random matrices given at the University of Cambridge.
This is the logical foundation for for Relativity Theory, Probability Theory, and for Quantum Theory. Contents is the following: 1 Introduction. 2 Classical logic. 3 Time and space. 3.1 Recorders. 3.2 Time. 3.3 Space. 3.4 Relativity. 4.…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards…
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
A brief synopsis of recent conceptions and results, the current status and future outlook of our research program of applying sheaf and topos-theoretic ideas to quantum gravity and quantum logic is presented.
This paper introduces the Quantum Contextual Topos (QCT), a novel framework that extends traditional quantum logic by embedding contextual elements within a topos-theoretic structure. This framework seeks to provide a classically-obedient…
The lecture notes cover the basics of quantum computing methods for quantum field theory applications. No detailed knowledge of either quantum computing or quantum field theory is assumed and we have attempted to keep the material at a…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological…