REALIZATIONS OF OBSERVABLES IN HAMILTONIAN SYSTEMS WITH FIRST CLASS CONSTRAINTS

2004/12/31 by A. V. Bratchikov, A. V. BRATCHIKOV · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Bracket #Class (philosophy) #First class constraint #Hamiltonian (control theory) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #Observable #Pointwise #Poisson algebra #Poisson bracket #Quotient #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1142/s0219887807002168

published as Int.J.Geom.Meth.Mod.Phys.4:517-522,2007 · 7 pages, misprints corrected

arxiv created 2005/04/23 · openalex publication_date 2007/06/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In a Hamiltonian system with first class constraints, observables can be defined as elements of a quotient Poisson bracket algebra. In the gauge fixing method, observables form a quotient Dirac bracket algebra. We show that these two algebras are isomorphic. A new realization of the observable algebras through the original Poisson bracket is found. Generators, brackets and pointwise products of the algebras under consideration are calculated.

Citations

• Fixation of Coordinates in the Hamiltonian Theory of Gravitation

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