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Hamilton’s Principle and Noether’s Theorem

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/9780198567264.003.0013
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter presents extended forms of Hamilton’s principle and the phase space Hamilton’s principle based on the extended Lagrangian and Hamiltonian methods developed earlier. It also discusses ... More


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

Jennifer Coopersmith

Published in print:
2017
Published Online:
June 2017
ISBN:
9780198743040
eISBN:
9780191802966
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198743040.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

Action and the Principle of Least Action are explained: what Action is, why the Principle of Least Action works, why it underlies all physics, and what are the insights gained into energy, space, and ... More


Symmetries I: Continuous spacetime symmetry: why we need Lagrangians in field theory

Anthony Duncan

in The Conceptual Framework of Quantum Field Theory

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199573264
eISBN:
9780191743313
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573264.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter analyzes the peculiar and indispensable utility of the Lagrangian approach to dynamics in relativistic quantum field theories. It underscores the facility with which a Lagrangian ... More


Symmetries IV: Local symmetries in field theory

Anthony Duncan

in The Conceptual Framework of Quantum Field Theory

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199573264
eISBN:
9780191743313
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573264.003.0015
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter examines the additional rich structure introduced when a local quantum field theory displays a local gauge symmetry. It shows how such symmetries require a generalization of the ... More


Hamilton'S Principle and Noether's Theorem

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/9780191001628.003.0015
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter presents extended forms of Hamilton's Principle and the phase space Hamilton's principle based on the extended Lagrangian and Hamiltonian methods. Hamilton's Principle has already been ... More


The Divergence Equation

Philip Isett

in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0006
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter introduces the divergence equation. A key ingredient in the proof of the Main Lemma for continuous solutions is to find special solutions to this divergence equation, which includes a ... More


Symmetry

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/9780199699322.003.0011
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter describes Noether’s theorem in demonstrating the fundamental relationship between symmetry and conservation laws.


The Einstein field equations

Steven Carlip

in General Relativity: A Concise Introduction

Published in print:
2019
Published Online:
March 2019
ISBN:
9780198822158
eISBN:
9780191861215
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822158.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The Einstein field equations are the fundamental equations of general relativity. After a brief qualitative discussion of geodesic deviation and Newtonian gravity, this chapter derives the field ... More


Lagrangian 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/9780198743040.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

It is demonstrated how d’Alembert’s Principle can be used as the basis for a more general mechanics – Lagrangian Mechanics. How this leads to Hamilton’s Principle (the Principle of Least Action) is ... 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


Symmetries & Lagrangian-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/9780198822370.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses conservation laws in Lagrangian mechanics and shows that certain conservation laws are just particular examples of a more fundamental theory called ‘Noether’s theorem’, after ... More


Hamilton’s Equations & Routhian Reduction

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/9780198822370.003.0016
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this chapter, the Poisson bracket and angular momentum are investigated and first integrals are used to develop conservation laws as a canonical Noether’s theorem. The Poisson bracket was ... More


Classical Electromagnetism

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/9780198822370.003.0027
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this chapter, Noether’s theorem as a classical field theory is presented and the properties of variations are again discussed for fields (i.e. field variations, space variations, time variations, ... More


Symmetries and Explanatory Dependencies in Physics

Steven French and Juha Saatsi

in Explanation Beyond Causation: Philosophical Perspectives on Non-Causal Explanations

Published in print:
2018
Published Online:
June 2018
ISBN:
9780198777946
eISBN:
9780191823404
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198777946.003.0010
Subject:
Philosophy, Philosophy of Science, Metaphysics/Epistemology

Many important explanations in physics are based on ideas and assumptions about symmetries, but little has been said about the nature of such explanations. This chapter aims to fill this lacuna, ... More


Lagrange formalism in field theory

Iosif L. Buchbinder and Ilya L. Shapiro

in Introduction to Quantum Field Theory with Applications to Quantum Gravity

Published in print:
2021
Published Online:
April 2021
ISBN:
9780198838319
eISBN:
9780191874666
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198838319.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter is devoted to a general discussion of classical field theory. It presents the minimum information required about classical fields for the subsequent treatment of quantum theory in the ... More


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