Differential equations | Fiber bundles | Differential topology

Covariant classical field theory

In mathematical physics, covariant classical field theory represents classical fields by sections of fiber bundles, and their dynamics is phrased in the context of a finite-dimensional space of fields. Nowadays, it is well known that jet bundles and the variational bicomplex are the correct domain for such a description. The Hamiltonian variant of covariant classical field theory is the covariant Hamiltonian field theory where momenta correspond to derivatives of field variables with respect to all world coordinates. Non-autonomous mechanics is formulated as covariant classical field theory on fiber bundles over the time axis ℝ. (Wikipedia).

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Quantum Field Theory 5c - Classical Electrodynamics III

We end with a derivation of the classical interaction Hamiltonian for a charged particle moving in an electromagnetic field. There is a lot of "turn the crank" math in this installment, but the final result will be key to our continued development of quantum field theory.

From playlist Quantum Field Theory

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Galilean group cohomology in classical mechanics

In this video we discuss how the second group cohomology relates to classical mechanics. We discuss Galilean invariance in the Lagrangian formalism and its quantum mechanics analog. You find the used text and all the links mentioned here: https://gist.github.com/Nikolaj-K/deb54c9127b6f0f3f

From playlist Algebra

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Quantum field theory, Lecture 2

This winter semester (2016-2017) I am giving a course on quantum field theory. This course is intended for theorists with familiarity with advanced quantum mechanics and statistical physics. The main objective is introduce the building blocks of quantum electrodynamics. Here in Lecture 2

From playlist Quantum Field Theory

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Quantum Field Theory 3a - Photons I

In this video we apply the theory we developed in videos 1 & 2, along with some ideas from electromagnetic theory, to develop a rigorous theory of photons.

From playlist Quantum Field Theory

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What are Quantum Fields? | Introduction to Quantum Field Theory

In this video, we will discuss what makes a quantum field "quantum" and give a soft introduction to quantum field theory. Contents: 00:00 Introduction 03:00 Quantization 05:36 Appendix Follow us on Instagram: https://www.instagram.com/prettymuchvideo/ If you want to help us get rid of

From playlist Quantum Mechanics, Quantum Field Theory

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Quantum field theory, Lecture 1

*UPDATE* Lecture notes available! https://github.com/avstjohn/qft Many thanks to Dr. Alexander St. John! This winter semester (2016-2017) I am giving a course on quantum field theory. This course is intended for theorists with familiarity with advanced quantum mechanics and statistical p

From playlist Quantum Field Theory

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Quantum Field Theory 5a - Classical Electrodynamics I

In this video we look at two important results from classical electrodynamics that we will need in order to continue with our development of quantum electrodynamics. First is the problem of the electron "self-force." The pieces of a finite distribution of electric charge exert forces on

From playlist Quantum Field Theory

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Quantum Field Theory 2a - Field Quantization I

In the previous video we saw how the quantum harmonic oscillator provides a model system in which we can describe the creation and destruction of energy quanta. In 1925 Born, Heisenberg and Jordan presented a way to apply these ideas to a continuous field. (Note: My voice is lower and slow

From playlist Quantum Field Theory

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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

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Inflation, geometry and stochasticity - S. Renaux-Petel - Workshop 1 - CEB T3 2018

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From playlist 2018 - T3 - Analytics, Inference, and Computation in Cosmology

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What IS Quantum Field Theory? (For Dummies?)

The framework in which quantum mechanics and special relativity are successfully reconciled is called quantum field theory. Heres how you can easily understand Quantum Field Theory. Support me on patreon so that i can keep on making videos! https://www.patreon.com/quantasy In theoretical

From playlist Quantum Field Theory

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QED Prerequisites: Field Equations - Conventions

In this lesson we lay down the notation conventions used for our introduction to the two key field equations used in elementary QED: the Klein-Gordon Equation and the Dirac Equation. These subjects are often taught at the beginning of a QED course, but we will treat them as pre-requisite c

From playlist QED- Prerequisite Topics

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Stilian Stoev: Function valued random fields: tangents, intrinsic stationarity, self-similarity

We study random fields taking values in a separable Hilbert space H. First, we focus on their local structure and establish a counterpart to Falconer's characterization of tangent fields. That is, we show (under general conditions) that the tangent fields to a H-valued process are self-sim

From playlist Probability and Statistics

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Is geophysical fluid motion Newtonian? - Dubos - Workshop 1 - CEB T3 2019

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From playlist 2019 - T3 - The Mathematics of Climate and the Environment

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Consistent quantum histories and the probability for singularity resolution by Parampreet Singh

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From playlist Fundamental Problems of Quantum Physics

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Lec 20. Einstein's General Relativity and Gravitation: Gravitation and Quantum Mechanics

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From playlist Einstein's General Relativity and Gravitation

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G actions in SUSY QM; or, the Fukaya category of point/G by Tudor Dimofte

Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries

From playlist Quantum Fields, Geometry and Representation Theory

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Categorical aspects of vortices (Lecture 3)  by Niklas Garner

PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie

From playlist Vortex Moduli - 2023

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(PP 6.2) Multivariate Gaussian - examples and independence

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From playlist Probability Theory

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Line operators and geometry in 3d N=4 gauge theory by Tudor Dimofte

Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries

From playlist Quantum Fields, Geometry and Representation Theory

Related pages

Poincaré group | Covariant derivative | Lie group | Fiber bundle | Scalar field theory | Yang–Mills theory | Frame bundle | Algebraic topology | Dirac equation | Lagrangian system | Jet bundle | Levi-Civita connection | Pseudo-Euclidean space | Lie group–Lie algebra correspondence | Section (fiber bundle) | Euclidean space | Lie algebra | Variational bicomplex | Exterior algebra | Principal homogeneous space | Klein–Gordon equation | Higgs field (classical) | Non-autonomous mechanics | Majorana equation