Attempts have been made to describe gauge theories in terms of extended objects such as Wilson loops and holonomies. The loop representation is a quantum hamiltonian representation of gauge theories in terms of loops. The aim of the loop representation in the context of Yang–Mills theories is to avoid the redundancy introduced by Gauss gauge symmetries allowing to work directly in the space of physical states (Gauss gauge invariant states). The idea is well known in the context of lattice Yang–Mills theory (see lattice gauge theory). Attempts to explore the continuous loop representation was made by Gambini and Trias for canonical Yang–Mills theory, however there were difficulties as they represented singular objects. As we shall see the loop formalism goes far beyond a simple gauge invariant description, in fact it is the natural geometrical framework to treat gauge theories and quantum gravity in terms of their fundamental physical excitations. The introduction by Ashtekar of a new set of variables (Ashtekar variables) cast general relativity in the same language as gauge theories and allowed one to apply loop techniques as a natural nonperturbative description of Einstein's theory. In canonical quantum gravity the difficulties in using the continuous loop representation are cured by the spatial diffeomorphism invariance of general relativity. The loop representation also provides a natural solution of the spatial diffeomorphism constraint, making a connection between canonical quantum gravity and knot theory. Surprisingly there were a class of loop states that provided exact (if only formal) solutions to Ashtekar's original (ill-defined) Wheeler–DeWitt equation. Hence an infinite set of exact (if only formal) solutions had been identified for all the equations of canonical quantum general gravity in this representation! This generated a lot of interest in the approach and eventually led to loop quantum gravity (LQG). The loop representation has found application in mathematics. If topological quantum field theories are formulated in terms of loops, the resulting quantities should be what are known as knot invariants. Topological field theories only involve a finite number of degrees of freedom and so are exactly solvable. As a result, they provide concrete computable expressions that are invariants of knots. This was precisely the insight of Edward Witten who noticed that computing loop dependent quantities in Chern–Simons and other three-dimensional topological quantum field theories one could come up with explicit, analytic expressions for knot invariants. For his work in this, in 1990 he was awarded the Fields Medal. He is the first and so far the only physicist to be awarded the Fields Medal, often viewed as the greatest honour in mathematics. (Wikipedia).
The inability of scientists to create a theory of quantum gravity arises from long-standing tensions between general relativity and quantum mechanics. There have been few approaches with any success. In this video, Fermilab’s Dr. Don Lincoln explains one of the few promising ideas, calle
From playlist Quantum Physics
Loop Quantum Gravity Explained
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From playlist The Map of Quantum Physics Expanded
Representation Theory as Gauge Theory - David Ben-Zvi [2016]
Slides for this talk: https://drive.google.com/file/d/1FHl_tIOjp26vuULi0gkSgoIN7PMnKLXK/view?usp=sharing Notes for this talk: https://drive.google.com/file/d/1BpP2Sz_zHWa_SQLM6DC6T8b4v_VKZs1A/view?usp=sharing David Ben-Zvi (University of Texas, Austin) Title: Representation Theory as G
From playlist Number Theory
The Interpretations of Quantum Mechanics
An introduction to the Interpretations of Quantum Mechanics. The first 500 people to sign up via my link will get two FREE months of Skillshare Premium: https://skl.sh/domainofscience The interpretations of quantum physics are a collection of attempts of many physicists to try and make qua
From playlist The Map of Quantum Physics Expanded
Why Space Itself May Be Quantum in Nature - with Jim Baggott
Loop quantum gravity aims to unify the theories of general relativity and quantum mechanics, as explained by Jim Baggott. Subscribe for regular science videos: http://bit.ly/RiSubscRibe Buy Jim's book "Quantum Space": https://geni.us/7cLy Quantum gravity is the holy grail for modern theo
From playlist Ri Talks
Quantum Mechanics Concepts: 1 Dirac Notation and Photon Polarisation
Part 1 of a series: covering Dirac Notation, the measurable Hermitian matrix, the eigenvector states and the eigenvalue measured outcomes and application to photon polarisation
From playlist Quantum Mechanics
The Map of Particle Physics | The Standard Model Explained
In this video I explain all the basics of particle physics and the standard model of particle physics. Check out Brilliant here: https://brilliant.org/DOS/ Buy the poster here: https://store.dftba.com/collections/domain-of-science/products/map-of-fundamental-particles Digital version here:
From playlist Quantum Physics Videos - Domain of Science
Here's What a Quantum Wave Function REALLY Represents
The quantum mechanical wave function can seem a little bit mysterious, but here's what it really represents. We begin by looking at a particle that can only move along a single direction, between two fixed points. These restrictions are absolutely not necessary in order to understand the
From playlist Quantum Physics by Parth G
Loop-String-Hadron Dynamics in a SU(3) Lattice Gauge Theory by Indrakshi Raychowdhury
PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II
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If You Don't Understand Quantum Physics, Try This!
A simple and clear explanation of all the important features of quantum physics that you need to know. Check out this video's sponsor https://brilliant.org/dos I have spent a lot of time thinking about how best to explain quantum physics and this is the result of all my hours of pondering
From playlist The Map of Quantum Physics Expanded
Nikita Nekrasov - Non-perturbative Dyson-Schwinger equations...
Nikita NEKRASOV (Simons Center for Geometry and Physics, Stony Brook, USA)
From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur
Yang-Mills for mathematicians (Lecture - 01) by Sourav Chatterjee
INFOSYS-ICTS RAMANUJAN LECTURES SOME OPEN QUESTIONS ABOUT SCALING LIMITS IN PROBABILITY THEORY SPEAKER Sourav Chatterjee (Stanford University, California, USA) DATE & TIME 14 January 2019 to 18 January 2019 VENUE Madhava Lecture Hall, ICTS campus GALLERY Lecture 1: Yang-Mills for mathemat
From playlist Infosys-ICTS Ramanujan Lectures
A New Poisson Bracket Identity for Gravity by Madhavan Varadarajan
Bangalore Area String Meeting URL: http://www.icts.res.in/discussion_meeting/BASM2016/ DATES: Monday 25 Jul, 2016 - Wednesday 27 Jul, 2016 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore DESCRIPTION: This meeting is designed to bring together string theorists working in the Bangalore
From playlist Bangalore Area String Meeting
The Mystery of Chiral Gauge Theories (Lecture - 03) by David B Kaplan
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
Quantum Inequivalence, Evanescent Operators and Gravity Divergences: Zvi Bern
https://strings2015.icts.res.in/talkTitles.php
From playlist Strings 2015 conference
Counting and Constraining Gravitational Scattering matrices (Lecture 1) by Shiraz Minwalla
RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE:Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through online lectures
From playlist Recent Developments in S-matrix Theory (Online)
Harold Steinacker - Covariant Cosmological Quantum Space-Time
Covariant Cosmological Quantum Space-Time: Higher-spin and Gravity in the IKKT Matrix Model https://indico.math.cnrs.fr/event/4272/attachments/2260/2717/IHESConference_Harold_STEINACKER.pdf
From playlist Space Time Matrices
Spin in quantum mechanics is an incredibly interesting property. However, it can be very difficult to understand what exactly it is. In this video, we dispel some misconceptions about spin as well as answer some of the more frequently asked questions about spin. #physics #quantum
From playlist Quantum Mechanics
An Introduction to Tensor Renormalization Group (Lecture 2) by Daisuke Kadoh
PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II
From playlist NUMSTRING 2022