The ordinary Poisson brackets in field theory do not fulfill the Jacobi identity if boundary values are reasonably fixed by special conditions. It is shown that these can be modified adding some surface terms to lift this restriction. new generalize a canonical bracket considered Lewis, Marsden, Montgomery, and Ratiu for free problem hydrodynamics. definition of used herein permits treating treat on equal footing with its internal direct estimation estimate between both volume integrals....

It is proved that, in order to avoid the ghost mode bigravity theory, it sufficient impose four conditions on potential of interaction two metrics. First, should allow its expression as a function components metrics' $3+1$ decomposition. Second, must satisfy first linear differential equations which are necessary for presence class constraints bigravity. Third, be solution Monge-Amp\`ere equation, where lapse and shift considered variables. Fourth, have nondegenerate Hessian The proof based...

In Friedmann–Lobachevsky space-time with a radius of curvature slowly varying over time, we study numerically the problem motion particle moving in Cornell potential. The mass is taken to be reduced charmonium system. contrast similar flat space, Lobachevsky space potential has finite depth and, as consequence, number bound states system and continuum energy spectrum also possible. this paper, well scattering

The tetrad approach is used to resolve the matrix square root appearing in dRGT potential. Constraints and their algebra are derived for minimal case. It shown that number of gravitational degrees freedom corresponds one massless massive fields when two sorts matter separately interact with metric tensors. Boulware-Deser ghost then excluded by second class constraints. In other case couples a linear combination tetrads this re-appears.

Recently it has been suggested by S. Carlip that black hole entropy can be derived from a central charge of the Virasoro algebra arising as subalgebra in surface deformations General Relativity any dimension. Here is shown argumentation given Section 2 hep-th/9812013 and based on Regge-Teitelboim approach unsatisfactory. The functionals used are really ``non-differentiable'' under required variations also standard Poisson brackets for these exactly zero so being unable to get with charge....

It is shown that the Poisson bracket with boundary terms recently proposed by Bering (hep-th/9806249) can be deduced from present author (hep-th/9305133) if one omits free of Euler-Lagrange derivatives ("annihilation principle"). This corresponds to another definition formal product distributions (or, saying it in other words, pairing between 1-forms and 1-vectors variational calculus). We extend formula (initially suggested only for ultralocal case constant coefficients) onto general...

In the Hamiltonian language we provide a study of flat-space cosmology in bigravity and massive gravity constructed mostly with de Rham, Gabadadze, Tolley (dRGT) potential. It is demonstrated that methods are powerful not only proving absence Boulware-Deser ghost, but also solving other problems. The purpose this work to give an introduction both formalism bigravity. We sketch three roads dRGT potential: metric, tetrad minisuperspace approaches.

We provide a space-time covariant Hamiltonian treatment for finite-range gravitational theory. The Kuchar approach is used to demonstrate the bimetric picture of in its most transparent form. This formalism applied straightforward realization Poincaré algebra Dirac brackets. It uncovers simplest form generators expressed as spatial integrals ultralocal quantities constructed pure algebraically by means two metrics.

The constraint algebra is derived in the second order tetrad Hamiltonian formalism of bigravity. This done by a straightforward calculation without involving any insights, implicit functions, and Dirac brackets. approach only way to present bigravity action as linear functional lapses shifts, Hassan-Rosen transform (characterized "a complicated redefinition shift variable" according authors) appears here not an ansatz but fixing Lagrange multiplier. A comparison this with other ones provided.

Nearly 2300 years ago, the Greek mathematician Euclid of Alexandria laid down basis geometry now known from textbooks and used in everyday life [...]

An application of the approach to Hamiltonian treatment boundary terms proposed in previous articles this series is considered. Here formalism constructed and role standard conditions revealed for a inviscid compressible fluid with surface tension which moves field Newtonian gravitational potential. It shown that these guarantee absence singular contributions equations motion, i.e., vector field. From other side variation contains nonzero term. Such Hamiltonians are usually treated as...

Bigravity is one of the most natural modifications General Relativity (GR), as it based on equivalence principle. However, its canonical structure appears rather complicated because unusual form interaction between two metrics. As a consequence, there are different approaches that difficult to compare in detail. This work first attempt obtain synthetic picture Hamiltonian formalism for bigravity. Here, we trying combine gain binocular view theory. The publications subject were metric...

We discuss the most interesting approaches to derivation of Bekenstein-Hawking entropy formula from a statistical theory.

It is shown that the new Poisson brackets proposed in Part I of this work (J. Math. Phys. 34, 5747(hep-th/9305133)) arise naturally an extension formal variational calculus incorporating divergences. The linear spaces local functionals, evolutionary vector fields, functional forms, multi-vectors and differential operators become graded with respect to Bilinear operations, such as action fields onto commutator interior product forms vectors Schouten-Nijenhuis bracket are compatible grading. A...

A harmonic-coil measurement system is presented. The main task of the to determine harmonic coefficients magnetic field in aperture superconducting (SC) magnet such as dipoles, quadrupoles, sextupoles, and octupoles. hardware includes a rotating shaft with coil array, motor controller linked personal computer (PC) via CAN bus data acquisition PC by USB bus. operation based on synchronization step delta-sigma ADC, measuring voltage induced during coil's rotation. Such mode provides an...

It is shown that the Regge-Teitelboim criterion for fixing unique boundary contribution to Hamiltonian compatible with free conditions should be modified if Poisson structure noncanonical. The new requires cancellation of contributions equations motion. At same time, variation are allowed. Ashtekar formalism gravity and hydrodynamics ideal fluid a surface in Clebsch variables treated as an example.

It is shown that the new formula for field theory Poisson brackets arises naturally in proposed extension of formal variational calculus incorporating divergences. The linear spaces local functionals, evolutionary vector fields, functional forms, multi-vectors and differential operators become graded with respect to bilinear operations, such as action fields onto commutator interior product forms vectors Schouten–Nijenhuis bracket are compatible grading. A definition adjoint operator...