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## Analytical Mechanics for Relativity and Quantum Mechanics

*Oliver Johns*

- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567264
- eISBN:
- 9780191717987
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567264.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics

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

## Knowing: The Nature of Physical Law

*Michael Munowitz*

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780195167375
- eISBN:
- 9780199787104
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195167375.001.0001
- Subject:
- Physics, History of Physics

This book interprets the book of nature for curious readers of all sorts, but especially for those looking to appreciate the power and beauty of physics without having to grapple with the ... More

## Intertheoretic Relations—Mechanics

*Robert W. Batterman*

### in The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780195146479
- eISBN:
- 9780199833078
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195146476.003.0007
- Subject:
- Philosophy, Philosophy of Science

This chapter discusses limiting correspondence relations between quantum mechanics and classical mechanics. The semiclassical limit is singular and no reductive relation obtains between these two ... 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

## Three-Part Invention

*Michael Munowitz*

### in Knowing: The Nature of Physical Law

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780195167375
- eISBN:
- 9780199787104
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195167375.003.0004
- Subject:
- Physics, History of Physics

The Moon — caught in an exact balance of attractive and repulsive forces — orbits the Earth with flawless regularity, never faltering. A ball rolls predictably down a slope of a certain grade, always ... More

## Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

*Alfonso Sorrentino*

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164502
- eISBN:
- 9781400866618
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164502.001.0001
- Subject:
- Mathematics, Applied Mathematics

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical ... More

## PATH INTEGRALS IN PHASE SPACE

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0010
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter contains a few additional results such as a definition of path integrals over phase space trajectories, and the problems generated by the quantization of lagrangians with potentials ... More

## The problem of polyatomic molecules

*CARLO CERCIGNANI*

### in Ludwig Boltzmann: The Man Who Trusted Atoms

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198570646
- eISBN:
- 9780191717949
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570646.003.0008
- Subject:
- Physics, History of Physics

Polyatomic molecules created difficulties in kinetic theory from the start, with the problem of thermal capacities or specific heats. If the problem of specific heats was initially solved with the ... 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

## Lagrangian and Hamiltonian Dynamics

*Peter Mann*

- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198822370
- eISBN:
- 9780191861253
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198822370.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This book explores the fascinating subject of classical mechanics, which is the pinnacle of nineteenth-century physics, from a fresh and exciting viewpoint. With its foundations laid down in ancient ... More

## Newton, Laplace, and Determinism

*David P. Feldman*

### in Chaos and Fractals: An Elementary Introduction

- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199566433
- eISBN:
- 9780191774966
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199566433.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses a few of the central, but sometimes unspoken, scientific ideas or assumptions about the world. It first looks at the character of Newtonian physics and classical mechanics by ... More

## The Classical Connection

*John A. Adam*

### in Rays, Waves, and Scattering: Topics in Classical Mathematical Physics

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691148373
- eISBN:
- 9781400885404
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691148373.003.0015
- Subject:
- Mathematics, Applied Mathematics

This chapter discusses the relationship between the elegance of the classical Lagrangian and Hamiltonian formulations of mechanics and optics. In physics, action is a mathematical functional which ... More

## Complexity and Emergence

*A. R. P. Rau*

### in The Beauty of Physics: Patterns, Principles, and Perspectives

- Published in print:
- 2014
- Published Online:
- December 2014
- ISBN:
- 9780198709916
- eISBN:
- 9780191780189
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198709916.003.0008
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

At each level of hierarchy, especially in the relevant energies for the phenomena under study, various concepts and entities of physics emerge. While reducible to other levels that are smaller in ... More

## Hamilton-Jacobi Theory

*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/9780198822370.003.0019
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an ... More

## Applied Computational Physics

*Joseph F. Boudreau and Eric. S. Swanson*

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198708636
- eISBN:
- 9780191858598
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198708636.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Applied Computational Physics describes methods for solving a vast array of classical and quantum mechanical scientific problems while stressing modern computational paradigms for achieving these ... More

## Lagrangians

*Tom Lancaster and Stephen J. Blundell*

### in Quantum Field Theory for the Gifted Amateur

- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199699322
- eISBN:
- 9780191779435
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199699322.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter provides a formulation of classical mechanics, which is suitable for a quantum upgrade. The chapter then talks about functionals and Lagrangians.

## Spin liquids and frustrated magnetism

*John T. Chalker*

### in Topological Aspects of Condensed Matter Physics: Lecture Notes of the Les Houches Summer School: Volume 103, August 2014

- Published in print:
- 2017
- Published Online:
- March 2017
- ISBN:
- 9780198785781
- eISBN:
- 9780191827600
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198785781.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials

Two important markers in the history of research on spin liquids and frustrated magnetism are Anderson’s suggestion, over 40 years ago, of the resonating valence bond state as an alternative to Néel ... More

## Introduction

*Laurent Baulieu, John Iliopoulos, and Roland Sénéor*

### in From Classical to Quantum Fields

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198788393
- eISBN:
- 9780191830310
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788393.003.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

General introduction with a review of the principles of Hamiltonian and Lagrangian mechanics. The connection between symmetries and conservation laws, with a presentation of Noether’s theorem, is ... More

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