21,419 research outputs found
Some Issues in a Gauge Model of Unparticles
We address in a recent gauge model of unparticles the issues that are
important for consistency of a gauge theory, i.e., unitarity and Ward identity
of physical amplitudes. We find that non-integrable singularities arise in
physical quantities like cross section and decay rate from gauge interactions
of unparticles. We also show that Ward identity is violated due to the lack of
a dispersion relation for charged unparticles although the Ward-Takahashi
identity for general Green functions is incorporated in the model. A previous
observation that the unparticle's (with scaling dimension d) contribution to
the gauge boson self-energy is a factor (2-d) of the particle's has been
extended to the Green function of triple gauge bosons. This (2-d) rule may be
generally true for any point Green functions of gauge bosons. This implies that
the model would be trivial even as one that mimics certain dynamical effects on
gauge bosons in which unparticles serve as an interpolating field.Comment: v1:16 pages, 3 figures. v2: some clarifications made and presentation
improved, calculation and conclusion not modified; refs added and updated.
Version to appear in EPJ
Hopf Bifurcation and Chaos in Tabu Learning Neuron Models
In this paper, we consider the nonlinear dynamical behaviors of some tabu
leaning neuron models. We first consider a tabu learning single neuron model.
By choosing the memory decay rate as a bifurcation parameter, we prove that
Hopf bifurcation occurs in the neuron. The stability of the bifurcating
periodic solutions and the direction of the Hopf bifurcation are determined by
applying the normal form theory. We give a numerical example to verify the
theoretical analysis. Then, we demonstrate the chaotic behavior in such a
neuron with sinusoidal external input, via computer simulations. Finally, we
study the chaotic behaviors in tabu learning two-neuron models, with linear and
quadratic proximity functions respectively.Comment: 14 pages, 13 figures, Accepted by International Journal of
Bifurcation and Chao
On the Convergence of the Expansion of Renormalization Group Flow Equation
We compare and discuss the dependence of a polynomial truncation of the
effective potential used to solve exact renormalization group flow equation for
a model with fermionic interaction (linear sigma model) with a grid solution.
The sensitivity of the results on the underlying cutoff function is discussed.
We explore the validity of the expansion method for second and first-order
phase transitions.Comment: 12 pages with 10 EPS figures included; revised versio
Flow Equations for U_k and Z_k
By considering the gradient expansion for the wilsonian effective action S_k
of a single component scalar field theory truncated to the first two terms, the
potential U_k and the kinetic term Z_k, I show that the recent claim that
different expansion of the fluctuation determinant give rise to different
renormalization group equations for Z_k is incorrect. The correct procedure to
derive this equation is presented and the set of coupled differential equations
for U_k and Z_k is definitely established.Comment: 5 page
Investigation into O(N) Invariant Scalar Model Using Auxiliary-Mass Method at Finite Temperature
Using auxiliary-mass method, O(N) invariant scalar model is investigated at
finite temperature. This mass and an evolution equation allow us to calculate
an effective potential without an infrared divergence. Second order phase
transition is indicated by the effective potential. The critical exponents are
determined numerically.Comment: LaTex 8 pages with 3 eps figure
Renormalization Group Approach to Field Theory at Finite Temperature
Scalar field theory at finite temperature is investigated via an improved
renormalization group prescription which provides an effective resummation over
all possible non-overlapping higher loop graphs. Explicit analyses for the
lambda phi^4 theory are performed in d=4 Euclidean space for both low and high
temperature limits. We generate a set of coupled equations for the mass
parameter and the coupling constant from the renormalization group flow
equation. Dimensional reduction and symmetry restoration are also explored with
our improved approach.Comment: 29 pages, can include figures in the body of the text using epsf.st
Coarse-Graining and Renormalization Group in the Einstein Universe
The Kadanoff-Wilson renormalization group approach for a scalar
self-interacting field theor generally coupled with gravity is presented. An
average potential that monitors the fluctuations of the blocked field in
different scaling regimes is constructed in a nonflat background and explicitly
computed within the loop-expansion approximation for an Einstein universe. The
curvature turns out to be dominant in setting the crossover scale from a
double-peak and a symmetric distribution of the block variables. The evolution
of all the coupling constants generated by the blocking procedure is examined:
the renormalized trajectories agree with the standard perturbative results for
the relevant vertices near the ultraviolet fixed point, but new effective
interactions between gravity and matter are present. The flow of the conformal
coupling constant is therefore analyzed in the improved scheme and the infrared
fixed point is reached for arbitrary values of the renormalized parameters.Comment: 18 pages, REVTex, two uuencoded figures. (to appear in Phys. Rev.
D15, July) Transmission errors have been correcte
On the Connection Between Momentum Cutoff and Operator Cutoff Regularizations
Operator cutoff regularization based on the original Schwinger's proper-time
formalism is examined. By constructing a regulating smearing function for the
proper-time integration, we show how this regularization scheme simulates the
usual momentum cutoff prescription yet preserves gauge symmetry even in the
presence of the cutoff scales. Similarity between the operator cutoff
regularization and the method of higher (covariant) derivatives is also
observed. The invariant nature of the operator cutoff regularization makes it a
promising tool for exploring the renormalization group flow of gauge theories
in the spirit of Wilson-Kadanoff blocking transformation.Comment: 28 pages in plain TeX, no figures. revised and expande
- …