Dirac's Generalized Hamiltonian Dynamics Theory?

[rocdoc]

I wondered if anyone might know of any open access materials, possibly lecture notes, on the content of the following papers or books.

P.A.M Dirac, 1950, Can. J. Math. 2,147 "Generalized Hamiltonian Dynamics"

P.A.M Dirac, 1933, Proc. Camb. Phil. Soc., 29, 389 "Homogenous variables in classical dynamics"

S. Shanmugadhasan, 1963, Proc. Camb. Phil. Soc., 59, 743.

H.P.Kunzle, 1969, Ann. Inst. Henri Poincare, 40,107.

W. Kundt, 1965, Springer Tracts in Modern Physics, 40,107.

A.Mercier, 1963, Canonical Formalism in Classical Mechanics, New York, Dover.

P.A.M. Dirac, 1964, Lectures on Quantum Mechanics, Academic Press, London.I have access to the first article mentioned above but would still like lecture notes, problem sets with answers on it's content.

Does anyone have any comments on the importance of Dirac's theory?

I Googled "dirac generalized hamiltonian" and noted the following were mentioned in the searches returned content.

nambu

never regular

interconnected physical systems, port-hamiltonian

hamiltonian structures

Dirac solitons

Dirac operators

recursive properties of Dirac brakets

Dirac geometry

pontryagin
Does anyone have any comments on the importance of "these"?

 

[Dr Transport]

I'd bet that if you googled any of those papers or subjects you'd find what you are looking for online and free...

 

[rocdoc]

WOW.
It looks as if the following
P.A.M Dirac, 1950, Can. J. Math. 2,147 "Generalized Hamiltonian Dynamics"
is one of the most important papers in the history of physics!

 

[rocdoc]

It looks as if the paper is very important for "Classical Field Theory", "Quantum Field Theory", "Gauge Field Theory".

I did not know.

My origins in science are in chemistry. I was studying the Hamiltonian for the interaction of light with a molecule, when a reference to Dirac's work turned up. See the references mentioned in Chapter 5 of Loudon ( Reference 1 ).

Reference
1. R. Loudon, The quantum theory of light, 2nd Ed, Oxford University Press,1983.

 

[vanhees71]

It's not allowed to post links to illegal sources, although for this specific paper I consider it an act of self-defence since I've never been able to download this paper in a legal way from any institution I've ever visited around the world. I don't know, who has a subscription to the Can. J. Math ;-)).

There's a very good treatment of Dirac brackets and all that in

Weinberg, QT of Fields, vol. 1

and also

Weinberg, Lectures on Quantum Mechanics

 

[rocdoc]

Hi vanhees71. Any comment on the importance of Dirac brackets and all that?

 

[vanhees71]

It's important to understand the canonical quantization of gauge theories, including Abelian gauge theory (e.g., QED) in general gauges (particularly manifestly covariant ones like the Lorenz gauge). The non-Abelian case is pretty complicated in any gauge, and the path-integral formalism is much more intuitive in that case, although one understands a lot of the complicated aspects when also looking at the operator formalism. The seminal papers are by Kugo et al:

http://inspirehep.net/search?ln=en&...lls Field Theories&of=hb&sf=earliestdate&so=d

 

[rocdoc]

Anyone interested in "Generalized Hamiltonian Dynamics" might find the materials at the following web pages of interest.

See Appendix A Pgs 90-98 of

https://arxiv.org/abs/hep-th/0401185

See also

https://arxiv.org/abs/1702.07595

https://arxiv.org/abs/1702.07598

https://arxiv.org/abs/1107.4421

and possibly

https://arxiv.org/abs/hep-th/0611100

https://arxiv.org/abs/gr-qc/0402041

https://arxiv.org/abs/gr-qc/0608096

https://arxiv.org/abs/physics/0701299

https://arxiv.org/abs/physics/0608067

 

[dextercioby]

Amazing, thank you for your work :)