42 research outputs found
Inflating in a Trough: Single-Field Effective Theory from Multiple-Field Curved Valleys
We examine the motion of light fields near the bottom of a potential valley
in a multi-dimensional field space. In the case of two fields we identify three
general scales, all of which must be large in order to justify an effective
low-energy approximation involving only the light field, . (Typically
only one of these -- the mass of the heavy field transverse to the trough -- is
used in the literature when justifying the truncation of heavy fields.) We
explicitly compute the resulting effective field theory, which has the form of
a model, with , as a function of these
scales. This gives the leading ways each scale contributes to any low-energy
dynamics, including (but not restricted to) those relevant for cosmology. We
check our results with the special case of a homogeneous roll near the valley
floor, placing into a broader context recent cosmological calculations that
show how the truncation approximation can fail. By casting our results
covariantly in field space, we provide a geometrical criterion for
model-builders to decide whether or not the single-field and/or the truncation
approximation is justified, identify its leading deviations, and to efficiently
extract cosmological predictions.Comment: 28 pages + 3 appendices, references added and typos corrected,
matches published versio
Bound-State Variational Wave Equation For Fermion Systems In QED
We present a formulation of the Hamiltonian variational method for QED which
enables the derivation of relativistic few-fermion wave equation that can
account, at least in principle, for interactions to any order of the coupling
constant. We derive a relativistic two-fermion wave equation using this
approach. The interaction kernel of the equation is shown to be the generalized
invariant M-matrix including all orders of Feynman diagrams. The result is
obtained rigorously from the underlying QFT for arbitrary mass ratio of the two
fermions. Our approach is based on three key points: a reformulation of QED,
the variational method, and adiabatic hypothesis. As an application we
calculate the one-loop contribution of radiative corrections to the two-fermion
binding energy for singlet states with arbitrary principal quantum number ,
and . Our calculations are carried out in the explicitly covariant
Feynman gauge.Comment: 26 page
Late Inspiral and Merger of Binary Black Holes in Scalar-Tensor Theories of Gravity
Gravitational wave observations will probe non-linear gravitational
interactions and thus enable strong tests of Einstein's theory of general
relativity. We present a numerical relativity study of the late inspiral and
merger of binary black holes in scalar-tensor theories of gravity. We consider
black hole binaries in an inhomogeneous scalar field, specifically binaries
inside a scalar field bubble, in some cases with a potential. We calculate the
emission of dipole radiation. We also show how these configurations trigger
detectable differences between gravitational waves in scalar-tensor gravity and
the corresponding waves in general relativity. We conclude that, barring an
external mechanism to induce dynamics in the scalar field, scalar-tensor
gravity binary black holes alone are not capable of awaking a dormant scalar
field, and are thus observationally indistinguishable from their general
relativistic counterparts.Comment: 4 pages, 5 figures, 1 tabl
Model-Independent Comparisons of Pulsar Timings to Scalar-Tensor Gravity
Observations of pulsar timing provide strong constraints on scalar-tensor
theories of gravity, but these constraints are traditionally quoted as limits
on the microscopic parameters (like the Brans-Dicke coupling, for example) that
govern the strength of scalar-matter couplings at the particle level in
particular models. Here we present fits to timing data for several pulsars
directly in terms of the phenomenological couplings (masses, scalar charges,
moment of inertia sensitivities and so on) of the stars involved, rather than
to the more microscopic parameters of a specific model. For instance, for the
double pulsar PSR J0737-3039A/B we find at the 68% confidence level that the
masses are bounded by 1.28 < m_A/m_sun < 1.34 and 1.19 < m_B/m_sun < 1.25,
while the scalar-charge to mass ratios satisfy |a_A| < 0.21, |a_B| < 0.21 and
|a_B - a_A| < 0.002$. These constraints are independent of the details of the
scalar tensor model involved, and of assumptions about the stellar equations of
state. Our fits can be used to constrain a broad class of scalar tensor
theories by computing the fit quantities as functions of the microscopic
parameters in any particular model. For the Brans-Dicke and quasi-Brans-Dicke
models, the constraints obtained in this manner are consistent with those
quoted in the literature.Comment: 19 pages, 7 figure
On the absence of bound-state stabilization through short ultra-intense fields
We address the question of whether atomic bound states begin to stabilize in
the short ultra-intense field limit. We provide a general theory of ionization
probability and investigate its gauge invariance. For a wide range of
potentials we find an upper and lower bound by non-perturbative methods, which
clearly exclude the possibility that the ultra intense field might have a
stabilizing effect on the atom. For short pulses we find almost complete
ionization as the field strength increases.Comment: 34 pages Late
New exact solution of Dirac-Coulomb equation with exact boundary condition
It usually writes the boundary condition of the wave equation in the Coulomb
field as a rough form without considering the size of the atomic nucleus. The
rough expression brings on that the solutions of the Klein-Gordon equation and
the Dirac equation with the Coulomb potential are divergent at the origin of
the coordinates, also the virtual energies, when the nuclear charges number Z >
137, meaning the original solutions do not satisfy the conditions for
determining solution. Any divergences of the wave functions also imply that the
probability density of the meson or the electron would rapidly increase when
they are closing to the atomic nucleus. What it predicts is not a truth that
the atom in ground state would rapidly collapse to the neutron-like. We
consider that the atomic nucleus has definite radius and write the exact
boundary condition for the hydrogen and hydrogen-like atom, then newly solve
the radial Dirac-Coulomb equation and obtain a new exact solution without any
mathematical and physical difficulties. Unexpectedly, the K value constructed
by Dirac is naturally written in the barrier width or the equivalent radius of
the atomic nucleus in solving the Dirac equation with the exact boundary
condition, and it is independent of the quantum energy. Without any divergent
wave function and the virtual energies, we obtain a new formula of the energy
levels that is different from the Dirac formula of the energy levels in the
Coulomb field.Comment: 12 pages,no figure
The Decay : A Test for Potential Models
We use a simple perturbation theory argument and measurements of charmonium
leptonic widths to estimate the ratio
\mbox{} in the general context of non-
relativistic potential models. We obtain . We then apply
well known potential model formulas, which include lowest order QCD
corrections, to find . The central value for
in the 1992 Particle Data Tables then
leads to a (non relativistic) prediction keV. This prediction is in good agreement with a
recent measurement by the ARGUS collaboration, is consistent with a recent
measurement by the L3 collaboration but is significantly higher than several
earlier measurements and than previous theoretical estimates, which usually
assume . The correction to is estimated to be smaller
but nonnegligible for the system. Using the current central
measurement for we find keV. A rough estimate
of relativistic corrections reduces the expected two photon rates to about 8.8
keV and 0.52 keV for the and mesons respectively. Such
correctionsComment: Estimates of likely relativistic corrections to the results have been
adde
Exploring new physics frontiers through numerical relativity
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology