457 research outputs found
On the Nonlinear Dynamical Equation in the p-adic String Theory
In this work nonlinear pseudo-differential equations with the infinite number
of derivatives are studied. These equations form a new class of equations which
initially appeared in p-adic string theory. These equations are of much
interest in mathematical physics and its applications in particular in string
theory and cosmology.
In the present work a systematical mathematical investigation of the
properties of these equations is performed. The main theorem of uniqueness in
some algebra of tempored distributions is proved. Boundary problems for bounded
solutions are studied, the existence of a space-homogenous solution for odd p
is proved. For even p it is proved that there is no continuous solutions and it
is pointed to the possibility of existence of discontinuous solutions.
Multidimensional equation is also considered and its soliton and q-brane
solutions are discussed.Comment: LaTex, 18 page
Nonlocal Dynamics of p-Adic Strings
We consider the construction of Lagrangians that might be suitable for
describing the entire -adic sector of an adelic open scalar string. These
Lagrangians are constructed using the Lagrangian for -adic strings with an
arbitrary prime number . They contain space-time nonlocality because of the
d'Alembertian in argument of the Riemann zeta function. We present a brief
review and some new results.Comment: 8 page
Interaction between dust grains near a conducting wall
The effect of the conducting electrode on the interaction of dust grains in a
an ion flow is discussed. It is shown that two grains levitating above the
electrode at the same height may attract one another. This results in the
instability of a dust layer in a plasma sheath.Comment: 9 pages. 3 figures. Submitted to Plasma Physics Report
New concept of relativistic invariance in NC space-time: twisted Poincar\'e symmetry and its implications
We present a systematic framework for noncommutative (NC) QFT within the new
concept of relativistic invariance based on the notion of twisted Poincar\'e
symmetry (with all 10 generators), as proposed in ref. [7]. This allows to
formulate and investigate all fundamental issues of relativistic QFT and offers
a firm frame for the classification of particles according to the
representation theory of the twisted Poincar\'e symmetry and as a result for
the NC versions of CPT and spin-statistics theorems, among others, discussed
earlier in the literature. As a further application of this new concept of
relativism we prove the NC analog of Haag's theorem.Comment: 15 page
On p-Adic Sector of Adelic String
We consider construction of Lagrangians which are candidates for p-adic
sector of an adelic open scalar string. Such Lagrangians have their origin in
Lagrangian for a single p-adic string and contain the Riemann zeta function
with the d'Alembertian in its argument. In particular, we present a new
Lagrangian obtained by an additive approach which takes into account all p-adic
Lagrangians. The very attractive feature of this new Lagrangian is that it is
an analytic function of the d'Alembertian. Investigation of the field theory
with Riemann zeta function is interesting in itself as well.Comment: 10 pages. Presented at the 2nd Conf. on SFT and Related Topics,
Moscow, April 2009. Submitted to Theor. Math. Phy
Application of p-adic analysis to models of spontaneous breaking of the replica symmetry
Methods of p-adic analysis are applied to the investigation of the
spontaneous symmetry breaking in the models of spin glasses. A p-adic
expression for the replica matrix is given and moreover the replica matrix in
the models of spontaneous breaking of the replica symmetry in the simplest case
is expressed in the form of the Vladimirov operator of p-adic fractional
differentiation. Also the model of hierarchical diffusion (that was proposed to
describe relaxation of spin glasses) investigated using p-adic analysis.Comment: Latex, 8 page
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Quantization of the Riemann Zeta-Function and Cosmology
Quantization of the Riemann zeta-function is proposed. We treat the Riemann
zeta-function as a symbol of a pseudodifferential operator and study the
corresponding classical and quantum field theories. This approach is motivated
by the theory of p-adic strings and by recent works on stringy cosmological
models. We show that the Lagrangian for the zeta-function field is equivalent
to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of
the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and
the Langlands program is indicated. The Beilinson conjectures on the values of
L-functions of motives are interpreted as dealing with the cosmological
constant problem. Possible cosmological applications of the zeta-function field
theory are discussed.Comment: 14 pages, corrected typos, references and comments adde
Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric
A general class of cosmological models driven by a nonlocal scalar field
inspired by the string field theory is studied. Using the fact that the
considering linear nonlocal model is equivalent to an infinite number of local
models we have found an exact special solution of the nonlocal Friedmann
equations. This solution describes a monotonically increasing Universe with the
phantom dark energy.Comment: 18 pages, 3 figures, a few misprints in Section 5 have been correcte
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