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Born-Jordan quantizationtheory and a...

Gosson, Maurice A. de.

Born-Jordan quantizationtheory and applications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Born-Jordan quantizationby Maurice A. de Gosson.
Reminder of title:	theory and applications /
Author:	Gosson, Maurice A. de.
Published:	Cham :Springer International Publishing :2016.
Description:	xiii, 226 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Mathematical physics.
Online resource:	http://dx.doi.org/10.1007/978-3-319-27902-2
ISBN:	9783319279022$q(electronic bk.)

Born-Jordan quantizationtheory and applications /
Gosson, Maurice A. de.

Born-Jordan quantizationtheory and applications /[electronic resource] :by Maurice A. de Gosson. - Cham :Springer International Publishing :2016. - xiii, 226 p. :ill., digital ;24 cm. - Fundamental theories of physics,v.1820168-1222 ;. - Fundamental theories of physics ;v.172..

Born-Jordan Quantization: Physical Motivation: On the Quantization Problem -- Quantization of Monomials -- Basic Hamiltonian Mechanics -- Wave Mechanics and the Schrodinger Equation -- Mathematical Aspects of Born-Jordan Quantization: The Weyl Correspondence -- The Cohen Class -- Born-Jordan Quantization -- Shubin's Pseudo-Differential Calculus -- Born-Jordan Pseudo-Differential Operators -- Weak Values and the Reconstruction Problem -- Some Advanced Topics: Metaplectic Operators -- Symplectic Covariance Properties -- Symbol Classes and Function Spaces.

This book presents a comprehensive mathematical study of the operators behind the Born-Jordan quantization scheme. The Schrodinger and Heisenberg pictures of quantum mechanics are equivalent only if the Born-Jordan scheme is used. Thus, Born-Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop Born-Jordan quantization from an operator-theoretical point of view, and analyze in depth the conceptual differences between the two schemes. We discuss various physically motivated approaches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero.

ISBN: 9783319279022$q(electronic bk.)

Standard No.: 10.1007/978-3-319-27902-2doiSubjects--Topical Terms:

190854
Mathematical physics.

LC Class. No.: QC20

Dewey Class. No.: 530.15

Born-Jordan quantizationtheory and applications /
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245 1 0 $a Born-Jordan quantization $h [electronic resource] : $b theory and applications / $c by Maurice A. de Gosson.
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490 1 $a Fundamental theories of physics, $x 0168-1222 ; $v v.182
505 0 $a Born-Jordan Quantization: Physical Motivation: On the Quantization Problem -- Quantization of Monomials -- Basic Hamiltonian Mechanics -- Wave Mechanics and the Schrodinger Equation -- Mathematical Aspects of Born-Jordan Quantization: The Weyl Correspondence -- The Cohen Class -- Born-Jordan Quantization -- Shubin's Pseudo-Differential Calculus -- Born-Jordan Pseudo-Differential Operators -- Weak Values and the Reconstruction Problem -- Some Advanced Topics: Metaplectic Operators -- Symplectic Covariance Properties -- Symbol Classes and Function Spaces.
520 $a This book presents a comprehensive mathematical study of the operators behind the Born-Jordan quantization scheme. The Schrodinger and Heisenberg pictures of quantum mechanics are equivalent only if the Born-Jordan scheme is used. Thus, Born-Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop Born-Jordan quantization from an operator-theoretical point of view, and analyze in depth the conceptual differences between the two schemes. We discuss various physically motivated approaches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero.
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