Presymplectic manifolds and the Dirac–Bergmann theory of constraints

Gotay, Mark J.; Nester, James M.; Hinds, George

doi:10.1063/1.523597

Presymplectic manifolds and the Dirac–Bergmann theory of constraints

Nov 1, 1978

Published in:

J.Math.Phys. 19 (1978) 11, 2388

Published: Nov 1, 1978

DOI:

10.1063/1.523597

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Abstract: (AIP)

We present an algorithm which enables us to state necessary and sufficient conditions for the solvability of generalized Hamilton‐type equations of the form ι (X) ω=α on a presymplectic manifold (M,ω) where α is a closed 1‐form. The algorithm is phrased in the context of global infinite‐dimensional symplectic geometry, and generalizes as well as improves upon the local Dirac–Bergmann theory of constraints. The relation between our algorithm and the geometric constraint theory of Śniatycki, Tulczyjew, and Lichnerowicz is discussed.

References(59)

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[1]

Foundations of Mechanics

R. Abraham
,
J. Marsden

[2]

Structures des Systemes Dynamiques (Dunod, Paris,)

J.M. Souriau

[3]

Lectures on Geometric Quantization, unpublished notes from a course given at Oxford University

N.M.J. Woodhouse

[4]

Géométrie Différentielle et Méchanique Analytique (Hermann, Paris,)

C. Godbillon

[5]

and references contained therein

P.G. Bergmann

- Helv.Phys.Acta Suppl. 4 (1956) 79

[5]

P.G. Bergmann

Generalized Hamiltonian dynamics

Paul A.M. Dirac
(
- Cambridge U.
)

- Can.J.Math. 2 (1950) 129-148
•
DOI:
- 10.4153/CJM-1950-012-1

OpenURL

P.A.M. Dirac

P.A.M. Dirac

- Proc.Roy.Soc.Lond.A A 246 (1958) 326

[6]

New York,)

E.C.G. Sudarshan
,
N. Mukunda

[6]

Classical Dynamics:

A. Modern Perspective

Accademia Nazionale dei Lincei, Rome, ♯22

A. Hanson
,
T. Regge
,
C. Teitelboim

[7]

Lectures on Quantum Mechanics, Belfer Graduate School of Science Monograph Series ♯2 . The Dirac‐Bergmann theory of constraints will be briefly reviewed at the beginning of Section V

P.A.M. Dirac

[8]

The Theory of gravitation in Hamiltonian form

Paul A.M. Dirac
(
- Cambridge U.
)

- Proc.Roy.Soc.Lond.A 246 (1958) 333-343
•
DOI:
- 10.1098/rspa.1958.0142

Fixation of coordinates in the Hamiltonian theory of gravitation

P.A.M. Dirac
(
- Princeton, Inst. Advanced Study
)

- Phys.Rev. 114 (1959) 924-930,
•
DOI:
- 10.1103/PhysRev.114.924

[9]

Topics in Canonical Dynamics I: Geometric Theory of Constraints

J. Śniatycki

[9]

Journées Relativistes 1970

J. Śniatycki

[9]

J. Śniatycki

Ann

Inst. H.

[10]

Symposia Math. 14, 247

W.M. Tulczyjew

[11]

A. Lichnerowicz

- Compt.Rend.Hebd.Seances Acad.Sci.A 280 (1975) 523

[12]

Ref. 7, pp. 23-4

[13]

append

[14]

The Definition of a Physical State and the Problem of First‐Class Secondary Constraints

J.M. Nester
,
M.J. Gotay

[15]

Applications of Global Analysis in Mathematical Physics, Lecture Notes ♯3 (Publish or Perish, Boston,)

J. Marsden

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