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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

## 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

## 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

## 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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