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Branes on Poisson Varieties

Marco Gualtieri

in The Many Facets of Geometry: A Tribute to Nigel Hitchin

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199534920
eISBN:
9780191716010
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534920.003.0018
Subject:
Mathematics, Geometry / Topology

This chapter takes a second look at a classical structure in differential and algebraic geometry — that of a holomorphic Poisson structure — which is a complex manifold with a holomorphic Poisson ... More


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


Hamiltonian Mechanics with Time as a Coordinate

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/9780198567264.003.0012
Subject:
Physics, Atomic, Laser, and Optical Physics

In the previous chapter, the traditional Lagrange equations were used as the basis for an extended Lagrangian theory in which time is treated as a coordinate. This extended theory combined the ... 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


Introduction To Hamiltonian Mechanics

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/9780198567264.003.0004
Subject:
Physics, Atomic, Laser, and Optical Physics

The power of Lagrangian mechanics has caused generations of students to wonder why it is necessary or even desirable, to recast mechanics in Hamiltonian form. The answer is that the Hamiltonian ... More


Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

S. G. Rajeev

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199670857
eISBN:
9780191775154
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199670857.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book begins with the ancient parts of classical mechanics: the variational principle, Lagrangian and Hamiltonian formalisms, and Poisson brackets. The simple pendulum provides a glimpse of the ... More


Hamilton’s principle

S. G. Rajeev

in Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199670857
eISBN:
9780191775154
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199670857.003.0007
Subject:
Physics, Atomic, Laser, and Optical Physics

The variational principle is formulated in first order form, deriving Hamilton's equations. Poisson brackets are found as generating infinitesimal canonical transformations. Symmetries are found to ... More


Hamiltonian mechanics including constraints and fields

Rodolfo Gambini and Jorge Pullin

in A First Course in Loop Quantum Gravity

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199590759
eISBN:
9780191774980
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199590759.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses the formulation of mechanical systems in Hamiltonian form, and briefly describes the role that constraints among the canonical variables play as generators of gauge symmetries. ... More


Continuous systems

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/9780199699322.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter describes how the arguments in the previous part, which worked on discrete systems, can be generalized to the continuum limit. After reviewing Hamilton’s formulation of classical ... More


Absolute time

George Jaroszkiewicz

in Images of Time: Mind, Science, Reality

Published in print:
2016
Published Online:
January 2016
ISBN:
9780198718062
eISBN:
9780191787553
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198718062.003.0014
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses Newton’s concept of absolute time and its use in classical mechanics. It defines clocks and our freedom to change them, that is, reparametrization of time. The chapter goes on ... More


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