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Canonical Transformations

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0017
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter considers a broader class of transformations known as canonical transformations, which transform the whole of the extended phase space in a more general way. Each new canonical ... More


Generating Functions

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0018
Subject:
Physics, Atomic, Laser, and Optical Physics

In the previous chapter, several conditions were given that could be used for testing transformations to see whether they were canonical or not. But no methods, other than trial and error, were given ... More


Canonical Transformations

Oliver Davis Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2011
Published Online:
December 2013
ISBN:
9780191001628
eISBN:
9780191775161
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780191001628.003.0019
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter describes canonical transformations as the most general phase-space transformations that preserve the extended Hamilton equations. There are several equivalent definitions of canonical ... More


Generating Functions

Oliver Davis Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2011
Published Online:
December 2013
ISBN:
9780191001628
eISBN:
9780191775161
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780191001628.003.0020
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter proposes methods for creating transformations that will automatically be canonical. Canonical transformations can be created by first choosing what are called generating functions. Using ... More


Hamilton–Jacobi Theory

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0019
Subject:
Physics, Atomic, Laser, and Optical Physics

The Hamilton-Jacobi theory is the apotheosis of Lagrangian and Hamiltonian mechanics: action functions encode all of the possible trajectories of a mechanical system satisfying certain criteria. ... More


Schwinger, Tomonaga, Feynman, and Dyson: the triumph of renormalization

JAGDISH MEHRA and KIMBALL A. MILTON

in Climbing the Mountain: The Scientific Biography of Julian Schwinger

Published in print:
2003
Published Online:
February 2010
ISBN:
9780198527459
eISBN:
9780191709593
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527459.003.0008
Subject:
Physics, History of Physics

Barely six months after the Shelter Island Conference, which reawakened his interest in quantum electrodynamics (QED), and just three months after returning to Harvard University from his extended ... More


Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Johns

Published in print:
2011
Published Online:
December 2013
ISBN:
9780191001628
eISBN:
9780191775161
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780191001628.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics, and of the relation of classical mechanics to relativity and quantum theory. A ... More


Canonical Transformations

Bryan J. Dalton, John Jeffers, and Stephen M. Barnett

in Phase Space Methods for Degenerate Quantum Gases

Published in print:
2014
Published Online:
April 2015
ISBN:
9780199562749
eISBN:
9780191747311
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562749.003.0006
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter focuses on linear canonical unitary transformations of mode annihilation and creation operators, both for bosons and for fermions. The generators of such transformations (which form a ... More


Hamiltonian Mechanics

Jennifer Coopersmith

in The Lazy Universe: An Introduction to the Principle of Least Action

Published in print:
2017
Published Online:
June 2017
ISBN:
9780198743040
eISBN:
9780191802966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198743040.003.0007
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

Hamilton’s genius was to understand what were the true variables of mechanics (the “p − q,” conjugate coordinates, or canonical variables), and this led to Hamilton’s Mechanics which could obtain ... More


Poisson Brackets & Angular Momentum

Peter Mann

in Lagrangian and Hamiltonian Dynamics

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.003.0017
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses canonical transformations and gauge transformations and is divided into three sections. In the first section, canonical coordinate transformations are introduced to the reader ... More


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