1,044 research outputs found
Simple Amplitudes for \Phi^3 Feynman Ladder Graphs
Recently, we proposed a new approach for calculating Feynman graphs amplitude
using the Gaussian representation for propagators which was proven to be exact
in the limit of graphs having an infinite number of loops. Regge behavior was
also found in a completely new way and the leading Regge trajectory calculated.
Here we present symmetry arguments justifying the simple form used for the
polynomials in the Feynman parameters , where is the mean-value for these parameters, appearing in the amplitude for
the ladder graphs. (Taking mean-values is equivalent to the Gaussian
representation for propagators).Comment: 11 Plain TeX pages, 2 PostScript figures include
Factorization of Spanning Trees on Feynman Graphs
In order to use the Gaussian representation for propagators in Feynman
amplitudes, a representation which is useful to relate string theory and field
theory, one has to prove first that each - parameter (where is
the parameter associated to each propagator in the -representation of
the Feynman amplitudes) can be replaced by a constant instead of being
integrated over and second, prove that this constant can be taken equal for all
propagators of a given graph. The first proposition has been proven in one
recent letter when the number of propagators is infinite. Here we prove the
second one. In order to achieve this, we demonstrate that the sum over the
weighted spanning trees of a Feynman graph can be factorized for disjoint
parts of . The same can also be done for cuts on , resulting in a
rigorous derivation of the Gaussian representation for super-renormalizable
scalar field theories. As a by-product spanning trees on Feynman graphs can be
used to define a discretized functional space.Comment: 47 pages, Plain Tex, 3 PostScript figure
Regge behaviour and Regge trajectory for ladder graphs in scalar field theory
Using the gaussian representation for propagators (which can be proved to be
exact in the infinite number of loops limit) we are able to derive the Regge
behaviour for ladder graphs of field theory in a completely new way.
An analytic expression for the Regge trajectory is found in
terms of the mean-values of the Feynman -parameters.
is calculated in the range . The intercept
agrees with that obtained from earlier calculations using the Bethe-Salpeter
approach for \alpha (0) \gsim 0.3.Comment: 10 PlainTex pages, 2 PostScript Figures include
Trigonometric weighted generalized convolution operator associated with Fourier cosine-sine and Kontorovich-Lebedev transformations
The main objective of this work is to introduce the generalized convolution
with trigonometric weighted involving the Fourier cosine-sine
and Kontorovich-Lebedev transforms, and to study its fundamental results. We
establish boundedness properties in a two-parametric family of Lebesgue spaces
for this convolution operator. Norm estimation in the weighted space is
obtained and applications of the corresponding class of convolution
integro-differential equations are discussed. The conditions for the
solvability of these equations in space are also founded.Comment: 12 page
Aspects of Availability Enforcing timed properties to prevent denial of service
We propose a domain-specific aspect language to prevent denial of service caused by resource management. Our aspects specify availability policies by enforcing time limits in the allocation of resources. In our language, aspects can be seen as formal timed properties on execution traces. Programs and aspects are specified as timed automata and the weaving process as an automata product. The benefit of this formal approach is two-fold: the user keeps the semantic impact of weaving under control and (s)he can use a model-checker to optimize the woven program and verify availability properties
Exotic dynamic behavior of the forced FitzHugh-Nagumo equations
AbstractSpace-clamped FitzHugh-Nagumo nerve model subjected to a stimulating electrical current of form Io + I cos γt is investigated via Poincaré map and numerical continuation. If I = 0, it is known that Hopf bifurcation occurs when Io is neither too small nor too large. Given such an Io. If γ is chosen close to the natural frequency of the Hopf bifurcated oscillation, a series of exotic phenomena varying with I are observed numerically. Let 2πλγ denote the generic period we watched. Then the scenario consists of two categories of period-adding bifurcation. The first category consists of a sequence of hysteretic, λ → λ + 2 period-adding starting with λ = 1 at I = 0+, and ending at some finite I, say I∗, as λ → ∞. The second category contains multiple levels of period-adding bifurcation. The top level consists of a sequence of λ → λ + 1, period-adding starting with λ = 2 at I = I∗. From this sequence, a hierarchy of m → m + n → n, period-adding in between are derived. Such a regular pattern is sometimes interrupted by a series of chaos. This category of bifurcation also terminates at some finite I. Harmonic resonance sets in afterwards. Lyapunov exponents, power spectra, and fractal dimensions are used to assist these observations
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