40,379 research outputs found
On the Fixed-Point Structure of Scalar Fields
In a recent Letter (K.Halpern and K.Huang, Phys. Rev. Lett. 74 (1995) 3526),
certain properties of the Local Potential Approximation (LPA) to the Wilson
renormalization group were uncovered, which led the authors to conclude that
dimensional scalar field theories endowed with {\sl non-polynomial}
interactions allow for a continuum of renormalization group fixed points, and
that around the Gaussian fixed point, asymptotically free interactions exist.
If true, this could herald very important new physics, particularly for the
Higgs sector of the Standard Model. Continuing work in support of these ideas,
has motivated us to point out that we previously studied the same properties
and showed that they lead to very different conclusions. Indeed, in as much as
the statements in hep-th/9406199 are correct, they point to some deep and
beautiful facts about the LPA and its generalisations, but however no new
physics.Comment: Typos corrected. A Comment - to be published in Phys. Rev. Lett. 1
page, 1 eps figure, uses LaTeX, RevTex and eps
Convergence of derivative expansions of the renormalization group
We investigate the convergence of the derivative expansion of the exact
renormalization group, by using it to compute the beta function of scalar field
theory. We show that the derivative expansion of the Polchinski flow equation
converges at one loop for certain fast falling smooth cutoffs. The derivative
expansion of the Legendre flow equation trivially converges at one loop, but
also at two loops: slowly with sharp cutoff (as a momentum-scale expansion),
and rapidly in the case of a smooth exponential cutoff. Finally, we show that
the two loop contributions to certain higher derivative operators (not involved
in beta) have divergent momentum-scale expansions for sharp cutoff, but the
smooth exponential cutoff gives convergent derivative expansions for all such
operators with any number of derivatives.Comment: Latex inc axodraw. 20 page
Properties of derivative expansion approximations to the renormalization group
Approximation only by derivative (or more generally momentum) expansions,
combined with reparametrization invariance, turns the continuous
renormalization group for quantum field theory into a set of partial
differential equations which at fixed points become non-linear eigenvalue
equations for the anomalous scaling dimension . We review how these
equations provide a powerful and robust means of discovering and approximating
non-perturbative continuum limits. Gauge fields are briefly discussed.
Particular emphasis is placed on the r\^ole of reparametrization invariance,
and the convergence of the derivative expansion is addressed.Comment: (Minor touch ups of the lingo.) Invited talk at RG96, Dubna, Russia;
14 pages including 2 eps figures; uses LaTeX, epsf and sprocl.st
Sensitivity of Nonrenormalizable Trajectories to the Bare Scale
Working in scalar field theory, we consider RG trajectories which correspond
to nonrenormalizable theories, in the Wilsonian sense. An interesting question
to ask of such trajectories is, given some fixed starting point in parameter
space, how the effective action at the effective scale, Lambda, changes as the
bare scale (and hence the duration of the flow down to Lambda) is changed. When
the effective action satisfies Polchinski's version of the Exact
Renormalization Group equation, we prove, directly from the path integral, that
the dependence of the effective action on the bare scale, keeping the
interaction part of the bare action fixed, is given by an equation of the same
form as the Polchinski equation but with a kernel of the opposite sign. We then
investigate whether similar equations exist for various generalizations of the
Polchinski equation. Using nonperturbative, diagrammatic arguments we find that
an action can always be constructed which satisfies the Polchinski-like
equation under variation of the bare scale. For the family of flow equations in
which the field is renormalized, but the blocking functional is the simplest
allowed, this action is essentially identified with the effective action at
Lambda = 0. This does not seem to hold for more elaborate generalizations.Comment: v1: 23 pages, 5 figures, v2: intro extended, refs added, published in
jphy
Fatigue testing a plurality of test specimens and method
Described is a fatigue testing apparatus for simultaneously subjecting a plurality of material test specimens to cyclical tension loading to determine the fatigue strength of the material. The fatigue testing apparatus includes a pulling head having cylinders defined therein which carry reciprocating pistons. The reciprocation of the pistons is determined by cyclical supplies of pressurized fluid to the cylinders. Piston rods extend from the pistons through the pulling head and are attachable to one end of the test specimens, the other end of the test specimens being attachable to a fixed base, causing test specimens attached between the piston rods and the base to be subjected to cyclical tension loading. Because all the cylinders share a common pressurized fluid supply, the breaking of a test specimen does not substantially affect the pressure of the fluid supplied to the other cylinders nor the tension applied to the other test specimens
Pump less wearable microfluidic device for real time pH sweat monitoring
This paper presents the fabrication and the performance of a novel, wearable, robust, flexible and disposable
microfluidic device which incorporates micro-Light Emitting Diodes (Ό-LEDs) as a detection system, for
monitoring in real time mode the pH of the sweat generated during an exercising period
Strong coupling of magnons in a YIG sphere to photons in a planar superconducting resonator in the quantum limit
We report measurements of a superconducting coplanar waveguide resonator
(CPWR) coupled to a sphere of yttrium-iron garnet. The non-uniform CPWR field
allows us to excite various magnon modes in the sphere. Mode frequencies and
relative coupling strengths are consistent with theory. Strong coupling is
observed to several modes even with, on average, less than one excitation
present in the CPWR. The time response to square pulses shows oscillations at
the mode splitting frequency. These results indicate the feasibility of
combining magnonic and planar superconducting quantum devices.Comment: 5 pages, 4 figure
An Extended Star Formation History for the Galactic Center from Hubble Space Telescope/NICMOS Observations
We present Hubble Space Telescope (HST) Near-Infrared Camera and Multiobject
Spectrometer (NICMOS) observations as evidence that continuous star formation
has created much of the central stellar cusp of the Galaxy. The data are the
deepest ever obtained for a Galactic Center (GC) population, being 50%
complete for \mnk, or initial stellar masses 2 \Msun. We use
Geneva and Padova stellar evolution models to produce synthetic luminosity
functions for burst and continuous star formation scenarios, finding that the
observations are fit best by continuous star formation at a rate that is
consistent with the recent star formation activity that produced the three
massive young clusters in the central 50 \pc. Further, it is not possible to
fit the observations with ancient burst models, such as would be appropriate
for an old population like that in Baade's Window or NGC6528
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