963 research outputs found
Quantization of Solitons and the Restricted Sine-Gordon Model
We show how to compute form factors, matrix elements of local fields, in the
restricted sine-Gordon model, at the reflectionless points, by quantizing
solitons. We introduce (quantum) separated variables in which the Hamiltonians
are expressed in terms of (quantum) tau-functions. We explicitly describe the
soliton wave functions, and we explain how the restriction is related to an
unusual hermitian structure. We also present a semi-classical analysis which
enlightens the fact that the restricted sine-Gordon model corresponds to an
analytical continuation of the sine-Gordon model, intermediate between
sine-Gordon and KdV.Comment: 29 pages, Latex, minor updatin
The Fuzzy Disc
We introduce a finite dimensional matrix model approximation to the algebra
of functions on a disc based on noncommutative geometry. The algebra is a
subalgebra of the one characterizing the noncommutative plane with a * product
and depends on two parameters N and theta. It is composed of functions which
decay exponentially outside a disc. In the limit in which the size of the
matrices goes to infinity and the noncommutativity parameter goes to zero the
disc becomes sharper. We introduce a Laplacian defined on the whole algebra and
calculate its eigenvalues. We also calculate the two--points correlation
function for a free massless theory (Green's function). In both cases the
agreement with the exact result on the disc is very good already for relatively
small matrices. This opens up the possibility for the study of field theories
on the disc with nonperturbative methods. The model contains edge states, a
fact studied in a similar matrix model independently introduced by
Balachandran, Gupta and Kurkcuoglu.Comment: 17 pages, 8 figures, references added and correcte
The beat of a fuzzy drum: fuzzy Bessel functions for the disc
The fuzzy disc is a matrix approximation of the functions on a disc which
preserves rotational symmetry. In this paper we introduce a basis for the
algebra of functions on the fuzzy disc in terms of the eigenfunctions of a
properly defined fuzzy Laplacian. In the commutative limit they tend to the
eigenfunctions of the ordinary Laplacian on the disc, i.e. Bessel functions of
the first kind, thus deserving the name of fuzzy Bessel functions.Comment: 30 pages, 8 figure
Non-factorizable corrections and effective field theories
We analyze the structure of higher-order radiative corrections for processes
with unstable particles. By subsequently integrating out the various scales
that are induced by the presence of unstable particles we obtain a hierarchy of
effective field theories. In the effective field theory framework the
separation of physically different effects is achieved naturally. In
particular, we automatically obtain a separation of factorizable and
non-factorizable corrections to all orders in perturbation theory. At one loop
this treatment is equivalent to the double-pole approximation (DPA) but
generalizes to higher orders and, at least in principle, to beyond the DPA. It
is known that one-loop non-factorizable corrections to invariant mass
distributions are suppressed at high energy. We study the mechanism of this
suppression and obtain estimates of higher-order non-factorizable corrections
at high energy.Comment: 45 page
Recommended from our members
Current driven due to localized electron power deposition in DIII-D
Due to spatial localization of electron cyclotron wave injection in DIII-D, electrons heated in an off-axis region must toroidally transit the tokamak 25--50 times before re-entering the heating region. This distance is of the order of the mean free path. The effect of such RF localization is simulated with a time-dependent Fokker-Planck code which is 2D-in-velocity, 1D-in-space-along-B, and periodic in space. An effective parallel electric field arises to maintain continuity of the driven current. Somewhat surprisingly, the localized current drive efficiency remains equal to that for a uniform medium
On Darboux-Treibich-Verdier potentials
It is shown that the four-parameter family of elliptic functions
introduced
by Darboux and rediscovered a hundred years later by Treibich and Verdier, is
the most general meromorphic family containing infinitely many finite-gap
potentials.Comment: 8 page
Search for light pseudoscalar sgoldstino in K- decays
A search for the light pseudoscalar sgoldstino production in the three body
K- decay K-->pipi0P has been performed with the ISTRA+ detector exposed to the
25 GeV negative secondary beam of the U70 proton synchrotron. No signal is
seen. An upper limit for the branching ratio Br(K->pipi0P), at 90% confidence
level, is found to be around 9*10**-6 in the effective mass m(P) range from 0
till 200 MeV, excluding the region near m(pi0) where it degrades to 3.5*10**-5.Comment: 10 pages, LATEX, 8 EPS figures, revised version, to be published in
Phys.Lett.
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