Mathematical quantization

Canonical quantization

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).

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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

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SPSS - Canonical Correlation

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

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Canonical Commutation Relation

We discuss the canonical commutation relation between position and momentum operators in quantum mechanics.

From playlist Quantum Mechanics Uploads

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Symmetric Matrix

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

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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

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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

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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

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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

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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)

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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)

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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)

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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

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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

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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)

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Symmetrization

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

Related pages

Path integral formulation | Second quantization | Commutator | Segal–Bargmann space | Quantum harmonic oscillator | Geometric quantization | Poisson algebra | Hamiltonian mechanics | Normal mode | Poisson manifold | Scalar field theory | Dirac bracket | Identical particles | Symplectomorphism | Moyal bracket | Electric charge | Higgs mechanism | Pauli exclusion principle | Hamiltonian (quantum mechanics) | Constructive quantum field theory | Spin (physics) | Poisson bracket | Spontaneous symmetry breaking | Unitary transformation | Uncertainty principle | Symplectic geometry | Energy | Poisson supermanifold | Canonical transformation | Linear combination | Legendre transformation | Functor | Lagrangian (field theory) | Slater determinant | Hilbert space | Klein–Gordon equation | Symplectic manifold | Unitary representation | Foliation | Fourier transform | Symmetry (physics) | Quantization (physics)