122 research outputs found
Derivation of the particle dynamics from kinetic equations
We consider the microscopic solutions of the Boltzmann-Enskog equation
discovered by Bogolyubov. The fact that the time-irreversible kinetic equation
has time-reversible microscopic solutions is rather surprising. We analyze this
paradox and show that the reversibility or irreversibility property of the
Boltzmann-Enskog equation depends on the considered class of solutions. If the
considered solutions have the form of sums of delta-functions, then the
equation is reversible. If the considered solutions belong to the class of
continuously differentiable functions, then the equation is irreversible. Also,
we construct the so called approximate microscopic solutions. These solutions
are continuously differentiable and they are reversible on bounded time
intervals. This analysis suggests a way to reconcile the time-irreversible
kinetic equations with the time-reversible particle dynamics. Usually one tries
to derive the kinetic equations from the particle dynamics. On the contrary, we
postulate the Boltzmann-Enskog equation or another kinetic equation and treat
their microscopic solutions as the particle dynamics. So, instead of the
derivation of the kinetic equations from the microdynamics we suggest a kind of
derivation of the microdynamics from the kinetic equations.Comment: 18 pages; some misprints have been corrected, some references have
been adde
Dressing the Giant Magnon II
We extend our earlier work by demonstrating how to construct classical string
solutions describing arbitrary superpositions of scattering and bound states of
dyonic giant magnons on S^5 using the dressing method for the SU(4)/Sp(2) coset
model. We present a particular scattering solution which generalizes solutions
found in hep-th/0607009 and hep-th/0607044 to the case of arbitrary magnon
momenta. We compute the classical time delay for the scattering of two dyonic
magnons carrying angular momenta with arbitrary relative orientation on the
S^5.Comment: 13 pages, harvma
Exact noncommutative solitons in p-adic strings and BSFT
The tachyon field of p-adic string theory is made noncommutative by replacing
ordinary products with noncommutative products in its exact effective action.
The same is done for the boundary string field theory, treated as the p -> 1
limit of the p-adic string. Solitonic lumps corresponding to D-branes are
obtained for all values of the noncommutative parameter theta. This is in
contrast to usual scalar field theories in which the noncommutative solitons do
not persist below a critical value of theta. As theta varies from zero to
infinity, the solution interpolates smoothly between the soliton of the p-adic
theory (respectively BSFT) to the noncommutative soliton.Comment: 1+14 pages (harvmac b), 1 eps figure, v2: references added, typos
correcte
Explicit Formulas for Neumann Coefficients in the Plane-Wave Geometry
We obtain explicit formulas for the Neumann coefficients and associated
quantities that appear in the three-string vertex for type IIB string theory in
a plane-wave background, for any value of the mass parameter mu. The derivation
involves constructing the inverse of a certain infinite-dimensional matrix, in
terms of which the Neumann coefficients previously had been written only
implicitly. We derive asymptotic expansions for large mu and find unexpectedly
simple results, which are valid to all orders in 1/mu. Using BMN duality, these
give predictions for certain gauge theory quantities to all orders in the
modified 't Hooft coupling lambda'. A specific example is presented.Comment: 28 pages, 2 figures, v2: reference added, new comments and appendix,
typos fixed in eqs. (86) and (89
Dynamics with Infinitely Many Derivatives: The Initial Value Problem
Differential equations of infinite order are an increasingly important class
of equations in theoretical physics. Such equations are ubiquitous in string
field theory and have recently attracted considerable interest also from
cosmologists. Though these equations have been studied in the classical
mathematical literature, it appears that the physics community is largely
unaware of the relevant formalism. Of particular importance is the fate of the
initial value problem. Under what circumstances do infinite order differential
equations possess a well-defined initial value problem and how many initial
data are required? In this paper we study the initial value problem for
infinite order differential equations in the mathematical framework of the
formal operator calculus, with analytic initial data. This formalism allows us
to handle simultaneously a wide array of different nonlocal equations within a
single framework and also admits a transparent physical interpretation. We show
that differential equations of infinite order do not generically admit
infinitely many initial data. Rather, each pole of the propagator contributes
two initial data to the final solution. Though it is possible to find
differential equations of infinite order which admit well-defined initial value
problem with only two initial data, neither the dynamical equations of p-adic
string theory nor string field theory seem to belong to this class. However,
both theories can be rendered ghost-free by suitable definition of the action
of the formal pseudo-differential operator. This prescription restricts the
theory to frequencies within some contour in the complex plane and hence may be
thought of as a sort of ultra-violet cut-off.Comment: 40 pages, no figures. Added comments concerning fractional operators
and the implications of restricting the contour of integration. Typos
correcte
Tachyon condensation in open-closed p-adic string theory
We study a simple model of p-adic closed and open strings. It sheds some
light on the dynamics of tachyon condensation for both types of strings. We
calculate the effect of static and decaying D-brane configurations on the
closed string background. For closed string tachyons we find lumps analogous to
D-branes. By studying their fluctuation spectrum and the D-branes they admit,
we argue that closed string lumps should be interpreted as spacetimes of lower
dimensionality described by some noncritical p-adic string theory.Comment: 21 pages, 3 figures; v2: discussion of the fluctuations of the double
lump substantially improve
Mixed-symmetry massive fields in AdS(5)
Free mixed-symmetry arbitrary spin massive bosonic and fermionic fields
propagating in AdS(5) are investigated. Using the light-cone formulation of
relativistic dynamics we study bosonic and fermionic fields on an equal
footing. Light-cone gauge actions for such fields are constructed. Various
limits of the actions are discussed.Comment: v3: 24 pages, LaTeX-2e; typos corrected, footnote 7 and 2 references
added, published in Class. Quantum Gra
Toward Open-Closed String Theoretical Description of Rolling Tachyon
We consider how the time-dependent decay process of an unstable D-brane
should be described in the full (quantum) open-closed string theory. It is
argued that the system, starting from the unstable D-brane configuration, will
evolve in time into the time-independent open string tachyon vacuum
configuration which we assume to be finite, with the total energy conserved. As
a concrete realization of this idea, we construct a toy model describing the
open and closed string tachyons which admits such a time-dependent solution.
The structure of our model has some resemblance to that of open-closed string
field theory.Comment: 1+10 pages, 6 figures. v2: a reference adde
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