Symmetry | Differential topology
A gauge theory is a type of theory in physics. The word gauge means a measurement, a thickness, an in-between distance (as in railroad tracks), or a resulting number of units per certain parameter (a number of loops in an inch of fabric or a number of lead balls in a pound of ammunition). Modern theories describe physical forces in terms of fields, e.g., the electromagnetic field, the gravitational field, and fields that describe forces between the elementary particles. A general feature of these field theories is that the fundamental fields cannot be directly measured; however, some associated quantities can be measured, such as charges, energies, and velocities. For example, say you cannot measure the diameter of a lead ball, but you can determine how many lead balls, which are equal in every way, are required to make a pound. Using the number of balls, the density of lead, and the formula for calculating the volume of a sphere from its diameter, one could indirectly determine the diameter of a single lead ball. In field theories, different configurations of the unobservable fields can result in identical observable quantities. A transformation from one such field configuration to another is called a gauge transformation; the lack of change in the measurable quantities, despite the field being transformed, is a property called gauge invariance. For example, if you could measure the color of lead balls and discover that when you change the color, you still fit the same number of balls in a pound, the property of "color" would show gauge invariance. Since any kind of invariance under a field transformation is considered a symmetry, gauge invariance is sometimes called gauge symmetry. Generally, any theory that has the property of gauge invariance is considered a gauge theory. For example, in electromagnetism the electric field E and the magnetic field B are observable, while the potentials V ("voltage") and A (the vector potential) are not. Under a gauge transformation in which a constant is added to V, no observable change occurs in E or B. With the advent of quantum mechanics in the 1920s, and with successive advances in quantum field theory, the importance of gauge transformations has steadily grown. Gauge theories constrain the laws of physics, because all the changes induced by a gauge transformation have to cancel each other out when written in terms of observable quantities. Over the course of the 20th century, physicists gradually realized that all forces (fundamental interactions) arise from the constraints imposed by local gauge symmetries, in which case the transformations vary from point to point in space and time. Perturbative quantum field theory (usually employed for scattering theory) describes forces in terms of force-mediating particles called gauge bosons. The nature of these particles is determined by the nature of the gauge transformations. The culmination of these efforts is the Standard Model, a quantum field theory that accurately predicts all of the fundamental interactions except gravity. (Wikipedia).
An introduction to this first course in differential equations.
From playlist Differential Equations
QED Prerequisites: The basics of gauge transformations
In this lesson we study the basic ideas behind gauge transformation in classical electromagnetic theory. We convert Maxwell's equations into their potential-based form and then discuss why we can "choose a gauge" to simplify the resulting equations. We introduce the elementary ontology use
From playlist QED- Prerequisite Topics
Category Theory: The Beginner's Introduction (Lesson 1 Explorations)
These are the explorations for Lesson 1 of my Category Theory: The Beginner's Introduction. These cover the material from Lesson 1 as well as prepare you for the material of Lesson 2. A pdf is available here; http://is.gd/Ffukld Follow me on Twitter: @mjmcodrington g+: google.com/+MJMCodr
From playlist Category Theory: The Beginner’s Introduction
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
Category Theory: The Beginner’s Introduction (Lesson 1 Video 2)
Lesson 1 is concerned with defining the category of Abstract Sets and Arbitrary Mappings. We also define our first Limit and Co-Limit: The Terminal Object, and the Initial Object. Other topics discussed include Duality and the Opposite (or Mirror) Category. Follow me on Twitter: @mjmcodr
From playlist Category Theory: The Beginner’s Introduction
A01 Introduction to linear systems
An introduction to linear sets of ordinary differential equations.
From playlist A Second Course in Differential Equations
A Mathematical Introduction to 3d N = 4 Gauge Theories (Lecture 1) by Mathew Bullimore
PROGRAM : QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS : Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
B01 An introduction to separable variables
In this first lecture I explain the concept of using the separation of variables to solve a differential equation.
From playlist Differential Equations
Particle Physics is Founded on This Principle!
Take your first steps toward understanding gauge field theory, which underlies everything we know about particle physics! Sponsored by Blinkist: Start your free trial and get 25% off! https://www.blinkist.com/elliot Get the notes for free here: https://courses.physicswithelliot.com/notes-
From playlist Field Theory Sequence
Quantum Simulating Gauge Theories: from Tensor field theory to Rydberg Atom.... by Yannick Meurice
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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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
Introduction to Lattice Field Theory by Anna Hasenfratz
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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Target Space Entanglement and Space-Time Geometry by Sandip Trivedi
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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Entanglement Entropy in Gauge Theories by Sandip Trivedi
New questions in quantum field theory from condensed matter theory URL: http://www.icts.res.in/discussion_meeting/qft2015/ Description:- The last couple of decades have seen a major revolution in the field of condensed matter physics, where the severe limitations of conventional paradigm
From playlist New questions in quantum field theory from condensed matter theory
Lattice realization of integer QHE of bosons by Subhro Bhattacharjee
New questions in quantum field theory from condensed matter theory URL: http://www.icts.res.in/discussion_meeting/qft2015/ Description:- The last couple of decades have seen a major revolution in the field of condensed matter physics, where the severe limitations of conventional paradigm
From playlist New questions in quantum field theory from condensed matter theory
Partial deconfinement in large N gauge theory by Hiromasa Watanabe
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
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Quantum simulation of lattice gauge theories - requirements, challenges and methods by Erez Zohar
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
Category Theory: The Beginner’s Introduction (Lesson 1 Video 1)
Lesson 1 is concerned with defining the category of Abstract Sets and Arbitrary Mappings. We also define our first Limit and Co-Limit: The Terminal Object, and the Initial Object. Other topics discussed include Duality and the Opposite (or Mirror) Category. These videos will be discussed
From playlist Category Theory: The Beginner’s Introduction
A simple Qubit Regularization Scheme for SU(N) Lattice Gauge Theories by Shailesh Chandrasekharan
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