1,838 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
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
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
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