Abstract
The natural constraints for the weak-field approximation to composite gravity, which is obtained by expressing the gauge vector fields of the Yang-Mills theory based on the Lorentz group in terms of tetrad variables and their derivatives, are analyzed in detail within a canonical Hamiltonian approach. Although this higher derivative theory involves a large number of fields, only few degrees of freedom are left, which are recognized as selected stable solutions of the underlying Yang-Mills theory. The constraint structure suggests a consistent double coupling of matter to both Yang-Mills and tetrad fields, which results in a selection among the solutions of the Yang-Mills theory in the presence of properly chosen conserved currents. Scalar and tensorial coupling mechanisms are proposed, where the latter mechanism essentially reproduces linearized general relativity. In the weak-field approximation, geodesic particle motion in static isotropic gravitational fields is found for both coupling mechanisms. An important issue is the proper Lorentz covariant criterion for choosing a background Minkowski system for the composite theory of gravity.
Highlights
Einstein’s general theory of relativity may not be the final word on gravity
The occurrence of time derivatives in the “composition rule” leads to a higher derivative theory, which is naturally tamed by the constraints resulting from the composition rule
For the composite theory of gravity proposed in [2], the underlying workhorse theory is the Yang-Mills theory [5] based on the Lorentz group, and the
Summary
Einstein’s general theory of relativity may not be the final word on gravity. As beautiful and successful as it is, it seems to have serious problems both on very small and on very large length scales. The Hamiltonian approach provides the natural starting point for a generalization to dissipative systems This approach allows us to formulate quantum master equations [16,17,18,19] and to make gravity accessible to the robust framework of dissipative quantum field theory [20]. A key task of the present paper is to elaborate in detail in the context of the linearized theory that the constraints from the composition rule, together with the gauge constraints, reduce this enormous number of fields to just a few degrees of freedom, as expected for a theory of gravity. The relation between the Lagrangian and Hamiltonian approaches and some intermediate and additional results are provided in three appendixes
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