گرانش در فرمول‌بندي ويل‌بينِ ADM

General Relativity in the Vielbein-ADM Formalism is formulated with 16 independent variables, whereas the stan‎dard metric formalism involves only 10 variables. This increase in degrees of freedom arises from the presence of the additional local Lorentz symmetry in the vielbein formalism, a symmetry that remains implicit in the metric description. According to the principles of gauge theories, this symmetry is expected to appear in the Hamiltonian approach as a set of first-class constraints. In this study, the full form of these constraints is derived an‎d shown to generate local Lorentz transformations in the configuration space, with their Poisson bracket algebra being fully consistent with the Lorentz group algebra. In a more comprehensive approach, utilizing the Hamiltonian formulation within the vielbein framework, the momentum constraints an‎d the Hamiltonian constraint are also derived an‎d determined, an‎d the Poincaré algebra for the complete set of these constraints is carefully examined an‎d analyzed. The results demonstrate that the ADM-vielbein formulation not only provides a precise an‎d coherent geometric description of general relativity but also offers an efficient an‎d reliable framework for studying, analyzing, an‎d extending gravitational theories based on gauge symmetries. This framework further allows for the independent investigation of local Lorentz symmetries an‎d the analysis of the additional degrees of freedom arising from the vielbein formulation, serving as a solid foundation for the development of more advanced gravitational models.

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بهروز ميرزا

علي مهدي فر , مجيد منعم زاده , سروش شاكري