相关论文: Free Boundary Poisson Bracket Algebra in Ashtekar'…

We consider a general formalism for treating a Hamiltonian (canonical) field theory with a spatial boundary. In this formalism essentially all functionals are differentiable from the very beginning and hence no improvement terms are needed.…

de-Broglie--Bohm causal interpretation of canonical quantum gravity in terms of Ashtekar new variables is built. The Poisson brackets of (deBroglie--Bohm) constraints are derived and it is shown that the Poisson bracket of Hamiltonian with…

In this article we will analyze the possibility of a nontrivial central extension of the Poisson algebra of the diffeomorphism generators, which respect certain boundary conditions on the black hole bifurcation. The origin of a possible…

In this paper we introduce two classes of Poisson brackets on algebras (or on sheaves of algebras). We call them locally free and nonsingular Poisson brackets. Using the Fedosov's method we prove that any locally free nonsingular Poisson…

We show that if a generator of a differential Gerstenhaber algebra satisfies certain Cartan-type identities, then the corresponding Lie bracket is formal. Geometric examples include the shifted de Rham complex of a Poisson manifold and the…

The ordinary Poisson brackets in field theory do not fulfil the Jacobi identity if boundary values are not reasonably fixed by special boundary conditions. We show that these brackets can be modified by adding some surface terms to lift…

It is well-known that a formal deformation of a commutative algebra ${\mathcal A}$ leads to a Poisson bracket on ${\mathcal A}$ and that the classical limit of a derivation on the deformation leads to a derivation on ${\mathcal A}$, which…

We give a natural definition of a Poisson Differential Algebra. Consistence conditions are formulated in geometrical terms. It is found that one can often locally put the Poisson structure on differential calculus in a simple canonical form…

The covariant canonical formalism is a covariant extension of the traditional canonical formalism of fields. In contrast to the traditional canonical theory, it has a remarkable feature that canonical equations of gauge theories or gravity…

The paper is devoted to peculiarities of the deformation quantization in the algebro-geometric context. A direct application of the formality theorem to an algebraic Poisson manifold gives a canonical sheaf of categories deforming coherent…

We consider the Hamiltonian treatment of non-local theories and Ostrogradski's formalism. This has recently also been discussed by Woodard (hep-th/0006207) and by Gomis, Kamimura and Llosa (hep-th/0006235). In our approach we recast the…

It is shown that the Regge-Teitelboim criterion for fixing the unique boundary contribution to the Hamiltonian compatible with free boundary conditions should be modified if the Poisson structure is noncanonical. The new criterion requires…

General relativity has previously been extended to incorporate degenerate metrics using Ashtekar's hamiltonian formulation of the theory. In this letter, we show that a natural alternative choice for the form of the hamiltonian constraints…

We study a certain class of bulk-boundary systems in the Batalin-Vilkovisky (BV) formalism. We construct factorization algebras of observables for such bulk-boundary systems, and show that these factorization algebras have a natural Poisson…

It is shown that the Poisson bracket with boundary terms recently proposed by Bering (hep-th/9806249) can be deduced from the Poisson bracket proposed by the present author (hep-th/9305133) if one omits terms free of Euler-Lagrange…

A few generalizations of a Poisson algebra to field theory canonically formulated in terms of the polymomentum variables are discussed. A graded Poisson bracket on differential forms and an $(n+1)$-ary bracket on functions are considered.…

We develop here a simple quantisation formalism that make use of Lie algebra properties of the Poisson bracket. When the brackets $\{H,\phi_i\}$ and $\{\phi_i,\phi_j\}$, where $H$ is the Hamiltonian and $\phi_i$ are primary and secondary…

In the paper we discuss the process of regularization of the Hamiltonian constraint in the Ashtekar approach to quantizing gravity. We show in detail the calculation of the action of the regulated Hamiltonian constraint on Wilson loops. An…

The fully coupled dynamic interaction problem of the free surface of an incompressible fluid and a rigid body beneath it, in an inviscid, irrotational framework and in the absence of surface tension, is considered. Evolution equations of…

It is described how the standard Poisson bracket formulas should be modified in order to incorporate integrals of divergences into the Hamiltonian formalism and why this is necessary. Examples from Einstein gravity and Yang-Mills gauge…