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Lattice gauge theory and tensor networks

Introduction

This is an experiment in open science similar to my other project https://github.com/tobiasosborne/Continuous-Limits-of-Quantum-Lattice-Systems. What you see here is the current latex source of two papers I have been writing on constructing tensor network states for lattice gauge theory, an overview paper and a longer paper with detailed calculations. These papers are "somewhat finished", i.e., the basic idea and some constructions are worked out, however quite a lot remains to be done. These papers are meant to be rather self contained and should be readable by anyone with a background in quantum information theory, condensed matter theory, or quantum field theory. In particular, detailed knowledge of the representation theory of SU(2) and gauge theory is not assumed.

Objective

The purpose of this experiment is to determine whether github could provide a solid collaborative basis for open science. To this end, coauthors are warmly invited to join in at any time to contribute to fixing and finishing the papers and adding new results.

I will continue to edit and push commits. When the papers are ready, and after any pull requests and merges, the final version will be submitted to the arXiv and, eventually, a scientific journal for publication.

Guidelines

Please fork this repository if you are interested in contributing. If you fork this paper then please add yourself to the author list in your fork. If you make substantial contributions to the draft then I will merge your changes into the final version and include you on the final submission version author list.

What is a "substantial contribution"? At the moment I define this to be a nontrivial calculation, e.g., working out the details of an example, sorting out some of the unfinished calculations, or similar. Another form of "substantial contribution" is writing one or more paragraphs of new material. Also, nontrivial figures and diagrams, e.g., graphs of interesting quantities, will be considered. Spelling, grammar, and/or stylistic changes do not count as "substantial contributions" (but are still welcome!). This definition is subject to change as the experiment proceeds.

Note: the final author list will be in alphabetical order regardless of the number and form of contributions.

About

This is a project aimed at constructing gauge-invariant tensor networks for lattice gauge theory with a view to obtaining a continuous ground-state ansatz for pure Yang-Mills theory.

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