14 research outputs found
Simple model of self-organized biological evolution as completely integrable dissipative system
The Bak-Sneppen model of self-organized biological evolution of an infinite
ecosystem of randomly interacting species is represented in terms of an
infinite set of variables which can be considered as an analog to the set of
integrals of motion of completely integrable system. Each of this variables
remains to be constant but its influence on the evolution process is restricted
in time and after definite moment its value is excluded from description of the
system dynamics.Comment: LaTeX, 7 page
Casimir energy of finite width mirrors: renormalization, self-interaction limit and Lifshitz formula
We study the field theoretical model of a scalar field in presence of spacial
inhomogeneities in form of one and two finite width mirrors (material slabs).
The interaction of the scalar field with the defect is described with
position-dependent mass term. Within this model we derive the interaction of
two finite width mirrors, establish the correspondence of the model to the
Lifshitz formula and construct limiting procedure to obtain finite self-energy
of a single mirror without any normalization condition.Comment: 5 pages, based on the presentation on the Ninth Conference on Quantum
Field Theory under the influence of External Conditions, Oklahoma, 200
Renormalization Group and Infinite Algebraic Structure in D-Dimensional Conformal Field Theory
We consider scalar field theory in the D-dimensional space with nontrivial
metric and local action functional of most general form. It is possible to
construct for this model a generalization of renormalization procedure and
RG-equations. In the fixed point the diffeomorphism and Weyl transformations
generate an infinite algebraic structure of D-Dimensional conformal field
theory models. The Wilson expansion and crossing symmetry enable to obtain sum
rules for dimensions of composite operators and Wilson coefficients.Comment: 16 page
Field of homogeneous Plane in Quantum Electrodynamics
We study quantum electrodynamics coupled to the matter field on singular
background, which we call defect. For defect on the infinite plane we
calculated the fermion propagator and mean electromagnetic field. We show that
at large distances from the defect plane, the electromagnetic field is constant
what is in agreement with the classical results. The quantum corrections
determining the field near the plane are calculated in the leading order of
perturbation theory.Comment: 16 page
Parity violating cylindrical shell in the framework of QED
We present calculations of Casimir energy (CE) in a system of quantized
electromagnetic (EM) field interacting with an infinite circular cylindrical
shell (which we call `the defect'). Interaction is described in the only
QFT-consistent way by Chern-Simon action concentrated on the defect, with a
single coupling constant .
For regularization of UV divergencies of the theory we use % physically
motivated Pauli-Villars regularization of the free EM action. The divergencies
are extracted as a polynomial in regularization mass , and they renormalize
classical part of the surface action.
We reveal the dependence of CE on the coupling constant . Corresponding
Casimir force is attractive for all values of . For we
reproduce the known results for CE for perfectly conducting cylindrical shell
first obtained by DeRaad and Milton.Comment: Typos corrected. Some references adde