1,041 research outputs found
Bering's proposal for boundary contribution to the Poisson bracket
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
derivatives ("annihilation principle"). This corresponds to another definition
of the formal product of distributions (or, saying it in other words, to
another definition of the pairing between 1-forms and 1-vectors in the formal
variational calculus). We extend the formula (initially suggested by Bering
only for the ultralocal case with constant coefficients) onto the general
non-ultralocal brackets with coefficients depending on fields and their spatial
derivatives. The lack of invariance under changes of dependent variables (field
redefinitions) seems a drawback of this proposal.Comment: 18 pages, LaTeX, amssym
Ultralocal energy density in massive gravity
We provide a space-time covariant Hamiltonian treatment for a finite-range
gravitational theory. The Kuchar approach is used to demonstrate the bimetric
picture of space-time in its most transparent form. This Hamiltonian formalism
is applied for the straightforward realization of the Poincar\'e algebra in
Dirac brackets. It uncovers the simplest form of the Poincar\'e generators
expressed as spatial integrals of ultralocal quantities constructed pure
algebraically by means of the two space-time metrics.Comment: 17 pages, no figures, LaTe
Boundary values as Hamiltonian variables. I. New Poisson brackets
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 this restriction. The new brackets generalize a canonical bracket
considered by Lewis, Marsden, Montgomery and Ratiu for the free boundary
problem in hydrodynamics. Our definition of Poisson brackets permits to treat
boundary values of a field on equal footing with its internal values and
directly estimate the brackets between both surface and volume integrals. This
construction is applied to any local form of Poisson brackets. A prescription
for delta-function on closed domains and a definition of the {\it full}
variational derivative are proposed.Comment: 26 pages, LaTex, IHEP 93-4
Bigravity in Kuchar's Hamiltonian formalism. 2. The special case
It is proved, that, in order to avoid the ghost mode in bigravity theory, it
is sufficient to impose four conditions on the potential of interaction of the
two metrics. First, the potential should allow its expression as a function of
components of the two metrics' 3+1 decomposition. Second, the potential must
satisfy the first order linear differential equations which are necessary for
the presence of four first class constraints in bigravity. Third, the potential
should be a solution of the Monge-Ampere equation, where the lapse and shift
are considered as variables. Fourth, the potential must have a nondegenerate
Hessian in the shift variables. The proof is based on the explicit derivation
of the Hamiltonian constraints, the construction of Dirac brackets on the base
of a part of these constraints, and calculation of other constraints' algebra
in these Dirac brackets. As a byproduct, we prove that these conditions are
also sufficient in the massive gravity case.Comment: 31 pages,5 tables, references added, typos remove
Free Boundary Poisson Bracket Algebra in Ashtekar's Formalism
We consider the algebra of spatial diffeomorphisms and gauge transformations
in the canonical formalism of General Relativity in the Ashtekar and ADM
variables. Modifying the Poisson bracket by including surface terms in
accordance with our previous proposal allows us to consider all local
functionals as differentiable. We show that closure of the algebra under
consideration can be achieved by choosing surface terms in the expressions for
the generators prior to imposing any boundary conditions. An essential point is
that the Poisson structure in the Ashtekar formalism differs from the canonical
one by boundary terms.Comment: 19 pages, Latex, amsfonts.sty, amssymb.st
Two classes of generalized functions used in nonlocal field theory
We elucidate the relation between the two ways of formulating causality in
nonlocal quantum field theory: using analytic test functions belonging to the
space (which is the Fourier transform of the Schwartz space )
and using test functions in the Gelfand-Shilov spaces . We prove
that every functional defined on has the same carrier cones as its
restrictions to the smaller spaces . As an application of this
result, we derive a Paley-Wiener-Schwartz-type theorem for arbitrarily singular
generalized functions of tempered growth and obtain the corresponding extension
of Vladimirov's algebra of functions holomorphic on a tubular domain.Comment: AMS-LaTeX, 12 pages, no figure
Twisted convolution and Moyal star product of generalized functions
We consider nuclear function spaces on which the Weyl-Heisenberg group acts
continuously and study the basic properties of the twisted convolution product
of the functions with the dual space elements. The final theorem characterizes
the corresponding algebra of convolution multipliers and shows that it contains
all sufficiently rapidly decreasing functionals in the dual space.
Consequently, we obtain a general description of the Moyal multiplier algebra
of the Fourier-transformed space. The results extend the Weyl symbol calculus
beyond the traditional framework of tempered distributions.Comment: LaTeX, 16 pages, no figure
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