Hamiltonian formulation of a class of constrained fourth-order differential equations in the Ostrogradsky framework

We consider a class of Lagrangians that depend not only on some configurational variables and their first time derivatives, but also on second time derivatives, thereby leading to fourth-order evolution equations. The proposed higher-order Lagrangians are obtained by expressing the variables of standard Lagrangians in terms of more basic variables and their time derivatives. The Hamiltonian formulation of the proposed class of models is obtained by means of the Ostrogradsky formalism. The structure of the Hamiltonians for this particular class of models is such that constraints can be introduced in a natural way, thus eliminating expected instabilities of the fourth-order evolution equations. Moreover, canonical quantization of the constrained equations can be achieved by means of Dirac's approach to generalized Hamiltonian dynamics.Comment: 8 page

Mathematical structure and physical content of composite gravity in weak-field approximation

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.Comment: This paper elaborates the "Composite higher derivative theory of gravity" proposed in Phys. Rev. Research 2, 013190 (2020) [which is an expanded version of arXiv:1806.02765] for the weak field approximation in greatest detail; 17 page

Conserved Currents for the Gauge-Field Theory with Lorentz Symmetry Group

For the Yang-Mills-type gauge-field theory with Lorentz symmetry group, we propose and verify an explicit expression for the conserved currents in terms of the energy-momentum tensor. A crucial ingredient is the assumption that the gauge symmetry arises from the decomposition of a metric in terms of tetrad variables. The currents exist under the weak condition that the energy-momentum tensor and the Ricci tensor commute. We show how the conserved currents can be used to obtain a composite theory of gravity and discuss the static isotropic field around a point mass at rest.Comment: 5 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:2110.0252