1,283 research outputs found
Effective Field calculations of the Energy Spectrum of the -Symmetric () Potential
In this work, we show that the traditional effective field approach can be
applied to the -symmetric wrong sign () quartic
potential. The importance of this work lies in the possibility of its extension
to the more important -symmetric quantum field theory while the
other approaches which use complex contours are not willing to be applicable.
We calculated the effective potential of the massless theory as well
as the full spectrum of the theory. Although the calculations are carried out
up to first order in the coupling, the predicted spectrum is very close to the
exact one taken from other works. The most important result of this work is
that the effective potential obtained, which is equivalent to the Gaussian
effective potential, is bounded from below while the classical potential is
bounded from above. This explains the stability of the vacuum of the theory.
The obtained quasi-particle Hamiltonian is non-Hermitian but
-symmetric and we showed that the calculation of the metric
operator can go perturbatively. In fact, the calculation of the metric operator
can be done even for higher dimensions (quantum field theory) which, up till
now, can not be calculated in the other approaches either perturbatively or in
a closed form due to the possible appearance of field radicals. Moreover, we
argued that the effective theory is perturbative for the whole range of the
coupling constant and the perturbation series is expected to converge rapidly
(the effective coupling ).Comment: 14 pages, 5 figure
Vacuum Stability of the -Symmetric Scalar Field Theory
In this work, we study the vacuum stability of the classical unstable scalar field potential. Regarding this, we obtained the
effective potential, up to second order in the coupling, for the theory in
and space-time dimensions. We found that the obtained effective
potential is bounded from below, which proves the vacuum stability of the
theory in space-time dimensions higher than the previously studied case.
In our calculations, we used the canonical quantization regime in which one
deals with operators rather than classical functions used in the path integral
formulation. Therefore, the non-Hermiticity of the effective field theory is
obvious. Moreover, the method we employ implements the canonical equal-time
commutation relations and the Heisenberg picture for the operators. Thus, the
metric operator is implemented in the calculations of the transition
amplitudes. Accordingly, the method avoids the very complicated calculations
needed in other methods for the metric operator. To test the accuracy of our
results, we obtained the exponential behavior of the vacuum condensate for
small coupling values, which has been obtained in the literature using other
methods. We assert that this work is interesting, as all the studies in the
literature advocate the stability of the theory at
the quantum mechanical level while our work extends the argument to the level
of field quantization.Comment: 20 pages, 4 figures, appendix added and more details have been added
to
SHARP: A Spatially Higher-order, Relativistic Particle-in-Cell Code
Numerical heating in particle-in-cell (PIC) codes currently precludes the
accurate simulation of cold, relativistic plasma over long periods, severely
limiting their applications in astrophysical environments. We present a
spatially higher-order accurate relativistic PIC algorithm in one spatial
dimension, which conserves charge and momentum exactly. We utilize the
smoothness implied by the usage of higher-order interpolation functions to
achieve a spatially higher-order accurate algorithm (up to fifth order). We
validate our algorithm against several test problems -- thermal stability of
stationary plasma, stability of linear plasma waves, and two-stream instability
in the relativistic and non-relativistic regimes. Comparing our simulations to
exact solutions of the dispersion relations, we demonstrate that SHARP can
quantitatively reproduce important kinetic features of the linear regime. Our
simulations have a superior ability to control energy non-conservation and
avoid numerical heating in comparison to common second-order schemes. We
provide a natural definition for convergence of a general PIC algorithm: the
complement of physical modes captured by the simulation, i.e., those that lie
above the Poisson noise, must grow commensurately with the resolution. This
implies that it is necessary to simultaneously increase the number of particles
per cell and decrease the cell size. We demonstrate that traditional ways for
testing for convergence fail, leading to plateauing of the energy error. This
new PIC code enables us to faithfully study the long-term evolution of plasma
problems that require absolute control of the energy and momentum conservation.Comment: 26 pages, 19 figures, discussion about performance is added,
published in Ap
Growth of beam-plasma instabilities in the presence of background inhomogeneity
We explore how inhomogeneity in the background plasma number density alters
the growth of electrostatic unstable wavemodes of beam plasma systems. This is
particularly interesting for blazar-driven beam-plasma instabilities, which may
be suppressed by inhomogeneities in the intergalactic medium as was recently
claimed in the literature. Using high resolution Particle-In-Cell simulations
with the SHARP code, we show that the growth of the instability is local, i.e.,
regions with almost homogeneous background density will support the growth of
the Langmuir waves, even when they are separated by strongly inhomogeneous
regions, resulting in an overall slower growth of the instability. We also show
that if the background density is continuously varying, the growth rate of the
instability is lower; though in all cases, the system remains within the linear
regime longer and the instability is not extinguished. In all cases, the beam
loses approximately the same fraction of its initial kinetic energy in
comparison to the uniform case at non-linear saturation. Thus, inhomogeneities
in the intergalactic medium are unlikely to suppress the growth of
blazar-driven beam-plasma instabilities.Comment: 10 pages, 6 figures, Accepted by ApJ, comments welcom
Importance of resolving the spectral support of beam-plasma instabilities in simulations
Many astrophysical plasmas are prone to beam-plasma instabilities. For
relativistic and dilute beams, the {\it spectral} support of the beam-plasma
instabilities is narrow, i.e., the linearly unstable modes that grow with rates
comparable to the maximum growth rate occupy a narrow range of wave numbers.
This places stringent requirements on the box-sizes when simulating the
evolution of the instabilities. We identify the implied lower limits on the box
size imposed by the longitudinal beam plasma instability, i.e., typically the
most stringent condition required to correctly capture the linear evolution of
the instabilities in multidimensional simulations. We find that sizes many
orders of magnitude larger than the resonant wavelength are typically required.
Using one-dimensional particle-in-cell simulations, we show that the failure to
sufficiently resolve the spectral support of the longitudinal instability
yields slower growth and lower levels of saturation, potentially leading to
erroneous physical conclusion.Comment: 7 pages, 9 figures, accepted by Ap
Representation Dependence of Superficial Degree of Divergences in Quantum Field Theory
In this work, we investigate a very important but unstressed result in the
work of Carl M. Bender, Jun-Hua Chen, and Kimball A. Milton (
J.Phys.A39:1657-1668, 2006). In this article, Bender \textit{et.al} have
calculated the vacuum energy of the scalar field theory and its
Hermitian equivalent theory up to order of calculations. While all the
Feynman diagrams of the theory are finite in space-time
dimensions, some of the corresponding Feynman diagrams in the equivalent
Hermitian theory are divergent. In this work, we show that the divergences in
the Hermitian theory originate from superrenormalizable, renormalizable and
non-renormalizable terms in the interaction Hamiltonian even though the
calculations are carried out in the space-time dimensions. Relying on
this interesting result, we raise the question, is the superficial degree of
divergence of a theory is representation dependent? To answer this question, we
introduce and study a class of non-Hermitian quantum field theories
characterized by a field derivative interaction Hamiltonian. We showed that the
class is physically acceptable by finding the corresponding class of metric
operators in a closed form. We realized that the obtained equivalent Hermitian
and the introduced non-Hermitian representations have coupling constants of
different mass dimensions which may be considered as a clue for the possibility
of considering non-Renormalizability of a field theory as a non-genuine
problem. Besides, the metric operator is supposed to disappear from path
integral calculations which means that physical amplitudes can be fully
obtained in the simpler non-Hermitian representation.Comment: 14 pages one figure. The title has been change
A Novel phase in the phase structure of the field theoretic model
In view of the newly discovered and physically acceptable symmetric and
non-Hermitian models, we reinvestigated the phase structure of the
() Hermitian model. The reinvestigation concerns
the possibility of a phase transition from the original Hermitian and
symmetric phase to a non-Hermitian and symmetric one. This kind of phase
transition, if verified experimentally, will lead to the first proof that
non-Hermitian and symmetric models are not just a mathematical research
framework but are a nature desire. To do the investigation, we calculated the
effective potential up to second order in the couplings and found a Hermitian
to Non-Hermitian phase transition. This leads us to introduce, for the first
time, hermiticity as a symmetry which can be broken due to quantum corrections,
\textit{i.e.}, when starting with a model which is Hermitian in the classical
level, quantum corrections can break hermiticity while the theory stays
physically acceptable. In fact, ignoring this phase will lead to violation of
universality when comparing this model predictions with other models in the
same class of universality. For instance, in a previous work we obtained a
second order phase transition for the symmetric and non-Hermitian
and according to universality, this phase should exist in the
phase structure of the () model for negative . Finally,
among the novelties in this letter, in our calculation for the effective
potential, we introduced a new renormalization group equation which describes
the invariance of the bare vacuum energy under the change of the scale. We
showed that without this invariance, the original theory and the effective one
are inequivalent.Comment: 13 pages, 4 figure
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