4,801 research outputs found
Boundary terms and their Hamiltonian dynamics
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
field theory are given.Comment: Talk at 29th Ahrenshoop Symposium in Buckow 1995, 6 pages,
espcrc2.sty, twoside.sty, fleqn.sty, amssymb.sty, no figure
Two-phonon -vibrational states in rotating triaxial odd- nuclei
Distribution of the two phonon vibrational collectivity in the
rotating triaxial odd- nucleus, Nb, that is one of the three
nuclides for which experimental data were reported recently, is calculated in
the framework of the particle vibration coupling model based on the cranked
shell model plus random phase approximation. This framework was previously
utilized for analyses of the zero and one phonon bands in other mass region and
is applied to the two phonon band for the first time. In the present
calculation, three sequences of two phonon bands share collectivity almost
equally at finite rotation whereas the state is the purest at zero
rotation.Comment: 15 pages, 3 figures, accepted for publication in Physical Review
On localization properties of Fourier transforms of hyperfunctions
In [Adv. Math. 196 (2005) 310-345] the author introduced a new generalized
function space which can be naturally interpreted as the
Fourier transform of the space of Sato's hyperfunctions on . It was shown
that all Gelfand--Shilov spaces () of
analytic functionals are canonically embedded in . While the
usual definition of support of a generalized function is inapplicable to
elements of and , their
localization properties can be consistently described using the concept of {\it
carrier cone} introduced by Soloviev [Lett. Math. Phys. 33 (1995) 49-59; Comm.
Math. Phys. 184 (1997) 579-596]. In this paper, the relation between carrier
cones of elements of and is
studied. It is proved that an analytic functional is carried by a cone if and only if its
canonical image in is carried by .Comment: 21 pages, final version, accepted for publication in J. Math. Anal.
App
Quadratic algebras and integrable chains
Using Krichever-Phong's universal formula, we show that a multiplicative
representation linearizes Sklyanin quadratic brackets for a multi-pole Lax
function with a spectral parameter. The spectral parameter can be either
rational or elliptic. As a by-product, we obtain an extension of a Sklyanin
algebra in the elliptic case. Krichever-Phong's formula provides a hierarchy of
symplectic structures, and we show that there exists a non-trivial cubic
bracket in Sklyanin's case.Comment: 24 page
Integrability of the Pentagram Map
The pentagram map was introduced by R. Schwartz in 1992 for convex planar
polygons. Recently, V. Ovsienko, R. Schwartz, and S. Tabachnikov proved
Liouville integrability of the pentagram map for generic monodromies by
providing a Poisson structure and the sufficient number of integrals in
involution on the space of twisted polygons. In this paper we prove
algebraic-geometric integrability for any monodromy, i.e., for both twisted and
closed polygons. For that purpose we show that the pentagram map can be written
as a discrete zero-curvature equation with a spectral parameter, study the
corresponding spectral curve, and the dynamics on its Jacobian. We also prove
that on the symplectic leaves Poisson brackets discovered for twisted polygons
coincide with the symplectic structure obtained from Krichever-Phong's
universal formula.Comment: 33 pages, 1 figure; v3: substantially revise
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
Gravitationally dresed RG flows and zig-zag invariant strings
We propose a world-sheet realization of the zigzag-invariant bosonic and
fermionic strings as a perturbed Wess-Zumino-Novikov-Witten model at large
negative level on a group manifold coupled to 2D gravity. In the large
limit the zigzag symmetry can be obtained as a result of a self-consistent
solution of the gravitationally dressed RG equation. The only solution found
for simple group is . More general target-space geometries can be
obtained via tensoring of various cosets based on SL(2). In the supersymmetric
case the zigzag symmetry fixes the maximal target-space dimension of the
confining fermionic string to be seven.Comment: 16 pages, corrected typos, version to be published in Phys.Lett.
- …