444 research outputs found
Zeta Nonlocal Scalar Fields
We consider some nonlocal and nonpolynomial scalar field models originated
from p-adic string theory. Infinite number of spacetime derivatives is
determined by the operator valued Riemann zeta function through d'Alembertian
in its argument. Construction of the corresponding Lagrangians L starts
with the exact Lagrangian for effective field of p-adic tachyon
string, which is generalized replacing p by arbitrary natural number n and then
taken a sum of over all n. The corresponding new objects we
call zeta scalar strings. Some basic classical field properties of these fields
are obtained and presented in this paper. In particular, some solutions of the
equations of motion and their tachyon spectra are studied. Field theory with
Riemann zeta function dynamics is interesting in its own right as well.Comment: 13 pages, submitted to Theoretical and Mathematical Physic
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
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
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
Genuine converging solution of self-consistent field equations for extended many-electron systems
Calculations of the ground state of inhomogeneous many-electron systems
involve a solving of the Poisson equation for Coulomb potential and the
Schroedinger equation for single-particle orbitals. Due to nonlinearity and
complexity this set of equations, one believes in the iterative method for the
solution that should consist in consecutive improvement of the potential and
the electron density until the self-consistency is attained. Though this
approach exists for a long time there are two grave problems accompanying its
implementation to infinitely extended systems. The first of them is related
with the Poisson equation and lies in possible incompatibility of the boundary
conditions for the potential with the electron density distribution. The
analysis of this difficulty and suggested resolution are presented for both
infinite conducting systems in jellium approximation and periodic solids. It
provides the existence of self-consistent solution for the potential at every
iteration step due to realization of a screening effect. The second problem
results from the existence of continuous spectrum of Hamiltonian eigenvalues
for unbounded systems. It needs to have a definition of Hilbert space basis
with eigenfunctions of continuous spectrum as elements, which would be
convenient in numerical applications. The definition of scalar product
specifying the Hilbert space is proposed that incorporates a limiting
transition. It provides self-adjointness of Hamiltonian and, respectively, the
orthogonality of eigenfunctions corresponding to the different eigenvalues. In
addition, it allows to normalize them effectively to delta-function and to
prove in the general case the orthogonality of the 'right' and 'left'
eigenfunctions belonging to twofold degenerate eigenvalues.Comment: 12 pages. Reported on Interdisciplinary Workshop "Nonequilibrium
Green's Functions III", August 22 - 26, 2005, University Kiel, Germany. To be
published in Journal of Physics: Conference Series, 2006; Typos in Eqs. (37),
(53) and (54) are corrected. The content of the footnote is changed.
Published version available free online at
http://www.iop.org/EJ/abstract/1742-6596/35/1/01
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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
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
p-Adic Models of Ultrametric Diffusion Constrained by Hierarchical Energy Landscapes
We demonstrate that p-adic analysis is a natural basis for the construction
of a wide variety of the ultrametric diffusion models constrained by
hierarchical energy landscapes. A general analytical description in terms of
p-adic analysis is given for a class of models. Two exactly solvable examples,
i.e. the ultrametric diffusion constraned by the linear energy landscape and
the ultrametric diffusion with reaction sink, are considered. We show that such
models can be applied to both the relaxation in complex systems and the rate
processes coupled to rearrangenment of the complex surrounding.Comment: 14 pages, 6 eps figures, LaTeX 2.0
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
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