In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries, of the classical theory, to the greatest extent possible. Historically, this was not quite Werner Heisenberg's route to obtaining quantum mechanics, but Paul Dirac introduced it in his 1926 doctoral thesis, the "method of classical analogy" for quantization, and detailed it in his classic text. The word canonical arises from the Hamiltonian approach to classical mechanics, in which a system's dynamics is generated via canonical Poisson brackets, a structure which is only partially preserved in canonical quantization. This method was further used in the context of quantum field theory by Paul Dirac, in his construction of quantum electrodynamics. In the field theory context, it is also called the second quantization of fields, in contrast to the semi-classical first quantization of single particles. (Wikipedia).
The Symmetry at the Heart of the Canonical Commutation Relation
The canonical commutator is one of the most fundamental equations of quantum mechanics. But where does it come from? I'll show you how symmetry leads straight to it! Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up The canonical commutation relation between
From playlist Hamiltonian Mechanics Sequence
Lecturer: Dr. Erin M. Buchanan Missouri State University Spring 2015 This video covers how to run a canonical correlation in SPSS using the syntax provided on IBM's website, along with data screening. Lecture materials and assignments available at statisticsofdoom.com. https://statisti
From playlist Advanced Statistics Videos
Canonical Commutation Relation
We discuss the canonical commutation relation between position and momentum operators in quantum mechanics.
From playlist Quantum Mechanics Uploads
Diagonalizing a symmetric matrix. Orthogonal diagonalization. Finding D and P such that A = PDPT. Finding the spectral decomposition of a matrix. Featuring the Spectral Theorem Check out my Symmetric Matrices playlist: https://www.youtube.com/watch?v=MyziVYheXf8&list=PLJb1qAQIrmmD8boOz9a8
From playlist Symmetric Matrices
Example of Rational Canonical Form 2: Several Blocks
Matrix Theory: Let A be a 12x12 real matrix with characteristic polynomial (x^2+1)^6, minimal polynomial (x^2 + 1)^3, and dim(Null(A^2 + I)) = 6. Find all possible rational canonical forms for A.
From playlist Matrix Theory
Quantization in modular setting, and its applications - Roman Travkin
Short Talks by Postdoctoral Members Roman Travkin - September 30, 2015 http://www.math.ias.edu/calendar/event/88334/1443637800/1443638700 More videos on http://video.ias.edu
From playlist Short Talks by Postdoctoral Members
Alexander Soibelman - Quantizations of Complex Lagrangian Fibrations, Normal Forms, and Spectra
Under certain conditions, it is possible to compute the spectrum of a polynomial differential operator via its Birkhoff normal form. In this talk, I will explain a geometric approach for obtaining the Birkhoff normal form of a quantized Hamiltonian using the variation of Hodge structure fo
From playlist Workshop on Quantum Geometry
Differential Equations | e^{tA}: A different strategy.
We present one more strategy for finding the matrix exponential e^{tA} that does not require diagonalization or finding the Jordan canonical form. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Systems of Differential Equations
Elmar Schrohe: Index theory for Fourier integral operators and Connes-Moscovici local index formulae
Talk by Elmar Schrohe in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on January 12, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Quantization by Branes and Geometric Langlands (Lecture 4) by Edward Witten
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 Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Quantization, Gauge Theory, And The Analytic Approach To Geometric... (Lecture 1) by Edward Witten
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)
Jerzy Lewandowski: The quantum states and operators of the canonical LQG
Recording during the meeting "Twistors and Loops Meeting in Marseille" the September 02, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisua
From playlist Mathematical Physics
Maxim Kontsevich - 2/6 Resurgence and Quantization
There are two canonical ``quantizations'' of symplectic manifolds: \begin{itemize} \item Deformation quantization, associating with any ($C^\infty$, analytic, algebraic over field of characteristic zero) symplectic manifold $(M,\omega)$ a sheaf of catgeories, which is locally equivalent
From playlist Maxim Kontsevich - Resurgence and Quantization
Stochastic GW Background From the Early Universe (Lecture 4) by Shi Pi
PROGRAM ICTS SUMMER SCHOOL ON GRAVITATIONAL-WAVE ASTRONOMY (ONLINE) ORGANIZERS: Parameswaran Ajith (ICTS-TIFR, India), K. G. Arun (CMI, India), Bala R. Iyer (ICTS-TIFR, India) and Prayush Kumar (ICTS-TIFR, India) DATE : 05 July 2021 to 16 July 2021 VENUE : Online This school is part
From playlist ICTS Summer School on Gravitational-Wave Astronomy (ONLINE)
In this video, I define a cool operation called the symmetrization, which turns any matrix into a symmetric matrix. Along the way, I also explain how to show that an (abstract) linear transformation is one-to-one and onto. Finally, I show how to decompose and matrix in a nice way, sort of
From playlist Linear Transformations