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The Hamiltonian analysis for the linearized λ R gravity plus a Chern–Simons term is performed. The first-class and second-class constraints for arbitrary values of λ are presented, and one physical degree of freedom is reported. The second-class constraints are removed, and the corresponding generalized Dirac brackets are constructed; then, the difference between theories with different values of λ is remarked. [ABSTRACT FROM AUTHOR]

The Hamiltonian analysis for the linearized λ R gravity around the Minkowski background is performed. The first-class and second-class constraints for arbitrary values of λ are presented, and two physical degrees of freedom are reported. In addition, we remove the second-class constraints, and the generalized Dirac brackets are constructed; then, the equivalence between General Relativity and the λ R theory is shown. • The canonical analysis for the Horava-like theory is performed. • The constraints for λ = 1 3 and λ ≠ 1 3 were obtained. • The Dirac brackets are constructed. • The gauge fixing yields the same Dirac's brackets. • The equivalence between G R and λ R model is shown. [ABSTRACT FROM AUTHOR]

The Hamilton–Jacobi analysis for gravity without dynamics is performed. We report a detailed analysis where the complete set of Hamilton–Jacobi constraints, the characteristic equations and the gauge transformations of the theory are found. We compare our results with those reported in the literature where alternative approaches are used. In addition, we complete our work by performing the canonical covariant analysis by constructing a gauge invariant symplectic structure, and we find a full consistency between the results obtained from both approaches. • We report the HJ. analysis for three dimensional gravity without dynamics. • We report the complete set of Hamiltonians. • The characteristic equations are reported. • The canonical covariant method is performed. • A closed and gauge invariant symplectic structure is constructed. [ABSTRACT FROM AUTHOR]

The symplectic analysis for the four dimensional Pontryagin and Euler invariants is performed within the Faddeev–Jackiw context. The Faddeev–Jackiw constraints and the generalized Faddeev–Jackiw brackets are reported; we show that in spite of the Pontryagin and Euler classes give rise the same equations of motion, its respective symplectic structures are different to each other. In addition, a quantum state that solves the Faddeev–Jackiw constraints is found, and we show that the quantum states for these invariants are different to each other. Finally, we present some remarks and conclusions. [ABSTRACT FROM AUTHOR]

In this paper a detailed Hamiltonian analysis of three-dimensional gravity without dynamics proposed by V. Hussain is performed. We report the complete structure of the constraints and the Dirac brackets are explicitly computed. In addition, the Faddeev–Jackiw symplectic approach is developed; we report the complete set of Faddeev–Jackiw constraints and the generalized brackets, then we show that the Dirac and the generalized Faddeev–Jackiw brackets coincide to each other. Finally, the similarities and advantages between Faddeev–Jackiw and Dirac’s formalism are briefly discussed. [ABSTRACT FROM AUTHOR]

By using the Gitman–Lyakhovich–Tyutin canonical analysis for higher-order theories a four-dimensional Chern–Simons modification of general relativity is analyzed. The counting of physical degrees of freedom, the symmetries, and the fundamental Dirac brackets are reported. Additionally, we report the complete structure of the constraints and its Dirac algebra is developed. • We report the canonical analysis for higher-order modified gravity. • The complete structure of the constraints is reported. • The Dirac's brackets are constructed. • The gauge transformations are identified. • Second class constraints are used for removing Ostrogradski's instabilities. [ABSTRACT FROM AUTHOR]

The symplectic analysis of a four dimensional B F theory in the context of the Faddeev–Jackiw symplectic approach is performed. It is shown that this method is more economical than Dirac’s formalism. In particular, the complete set of Faddeev–Jackiw constraints and the generalized Faddeev–Jackiw brackets are reported. In addition, we show that the generalized Faddeev–Jackiw brackets and the Dirac ones coincide to each other. Finally, the similarities and advantages between Faddeev–Jackiw method and Dirac’s formalism are briefly discussed. [ABSTRACT FROM AUTHOR]

In this paper the Dirac and Faddeev–Jackiw formulation for Einstein’s theory in the G → 0 limit is performed; the fundamental Dirac’s and Faddeev–Jackiw brackets for the theory are obtained. First, the Dirac brackets are constructed by eliminating the second class constraints remaining the first class ones, then we fix the gauge and we convert the first class constraints into second class constraints and the new fundamental Dirac’s brackets are computed. Alternatively, we reproduce all relevant Dirac’s results by means of the symplectic method. We identify the Faddeev–Jackiw constraints and we prove that the Dirac and the Faddeev–Jackiw brackets coincide to each other. [ABSTRACT FROM AUTHOR]

A detailed Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions is performed. We obtain for the theories under study the constraints, the gauge transformations, the generalized Faddeev–Jackiw brackets and we perform the counting of physical degrees of freedom. In addition, we compare our results with those found in the literature where the canonical analysis is developed, in particular, we show that both the generalized Faddeev–Jackiw brackets and Dirac’s brackets coincide to each other. Finally we discuss some remarks and prospects. [ABSTRACT FROM AUTHOR]

A detailed Hamiltonian analysis for a five-dimensional Stüeckelberg theory with a compact dimension is performed. First, we develop a pure Dirac’s analysis of the theory; we show that after performing the compactification, the theory is reduced to four-dimensional Stüeckelberg theory plus a tower of Kaluza–Klein modes. We develop a complete analysis of the constraints, we fix the gauge and we show that there are present pseudo-Goldstone bosons. Then we quantize the theory by constructing the Dirac brackets. As complementary work, we perform the Faddeev–Jackiw quantization for the theory under study, and we calculate the generalized Faddeev–Jackiw brackets, we show that both the Faddeev–Jackiw and Dirac’s brackets are the same. Finally we discuss some remarks and prospects. [ABSTRACT FROM AUTHOR]

Abstract: The Hamiltonian dynamics and the canonical covariant formalism for an exotic action in three dimensions are performed. By working with the complete phase space, we report a complete Hamiltonian description of the theory such as the extended action, the extended Hamiltonian, the algebra among the constraints, the Dirac’s brackets and the correct gauge transformations. In addition, we show that in spite of exotic action and tetrad gravity with a cosmological constant give rise to the same equations of motion, they are not equivalent, in fact, we show that their corresponding Dirac’s brackets are quite different. Finally, we construct a gauge invariant symplectic form which in turn represents a complete Hamiltonian description of the covariant phase space. [Copyright &y& Elsevier]

Abstract: The Hamiltonian analysis for the Chern-Simons theory and Pontryagin invariant, which depends of a connection valued in the Lie algebra of SO(3,1), is performed. By applying a pure Dirac’s method we find for both theories the extended Hamiltonian, the extended action, the constraint algebra, the gauge transformations and we carry out the counting of degrees of freedom. From the results obtained in the present analysis, we will conclude that the theories under study have a closed relation among its constraints and defines a topological field theory. In addition, we extends the configuration space for the Pontryagin theory and we develop the Hamiltonian analysis for this modified version, finding a best description of the results previously obtained. [Copyright &y& Elsevier]

By using the Hamilton–Jacobi [HJ] framework the topological theories associated with Euler and Pontryagin classes are analyzed. We report the construction of a fundamental H J differential where the characteristic equations and the symmetries of the theory are identified. Moreover, we work in both theories with the same phase space variables and we show that in spite of Pontryagin and Euler classes share the same equations of motion their symmetries are different. In addition, we report all HJ Hamiltonians and we compare our results with other formulations reported in the literature. • We report the Hamilton–Jacobi [HJ] analysis for Pontryagin and Euler classes. • We report a fundamental HJ differential. • The characteristic equations are reported. • The symmetries of both theories are compared. • The generalized HJ brackets are constructed. [ABSTRACT FROM AUTHOR]