689 research outputs found
Recursive Graphical Construction of Feynman Diagrams in phi^4 Theory: Asymmetric Case and Effective Energy
The free energy of a multi-component scalar field theory is considered as a
functional W[G,J] of the free correlation function G and an external current J.
It obeys non-linear functional differential equations which are turned into
recursion relations for the connected Greens functions in a loop expansion.
These relations amount to a simple proof that W[G,J] generates only connected
graphs and can be used to find all such graphs with their combinatoric weights.
A Legendre transformation with respect to the external current converts the
functional differential equations for the free energy into those for the
effective energy Gamma[G,Phi], which is considered as a functional of the free
correlation function G and the field expectation Phi. These equations are
turned into recursion relations for the one-particle irreducible Greens
functions. These relations amount to a simple proof that Gamma[G,J] generates
only one-particle irreducible graphs and can be used to find all such graphs
with their combinatoric weights. The techniques used also allow for a
systematic investigation into resummations of classes of graphs. Examples are
given for resumming one-loop and multi-loop tadpoles, both through all orders
of perturbation theory. Since the functional differential equations derived are
non-perturbative, they constitute also a convenient starting point for other
expansions than those in numbers of loops or powers of coupling constants. We
work with general interactions through four powers in the field.Comment: 34 pages; abstract expanded; section IV.E about absorption of
tadpoles and one related reference added; eqs. (20) and (23) corrected;
further references added; some minor beautifications; to be published by
Phys.Rev.
The Coexistence of Contradictory Properties in the Same Subject According to Aristotle
In Metaphysics, Book Gamma, Aristotle argues that he who asserts a
contradiction is committed to a rejection of degrees. On the other
hand, though, Aristotle claims that there can be no intermediary
situation in-between pure or entire truth or existence and utter,
complete falseness or nonexistence. Such a combination of views can be
rendered noncontradictory at best through objectionable manoeuvres.
Although Aristotle accepts that two contrary properties can be both
present in the same object to some extent, he is, in order to keep
clear of contradictions, bound to regard intermediary situations as
something irreducibly different from both extremes.Peer reviewe
Measurement of e⁺e⁻-->e⁺e⁻ and e⁺e⁻-->gammagamma at energies up to 36.7 GeV
e+e- +- +- ... + e e und e e + yy wurden bel Energlen zwischen 33.0 und 36.7 GeV gemessen. Die Ergebnisse stimmen mit den Vorhersagen der Quantenelektrodynamik überein. Ein Vergleich mit dem Standardmodell der elektroschwachen Wechselwirkung liefert sin 20w= 0.25 ± 0.13
Quantifying measures to limit wind driven resuspension of sediments for improvement of the ecological quality in some shallow Dutch lakes
Although phosphorus loadings are considered the main pressure for most shallow lakes, wind-driven resuspension can cause additional problems for these aquatic ecosystems. We quantified the potential effectiveness of measures to reduce the contribution of resuspended sediments, resulting from wind action, to the overall light attenuation for three comparable shallow peat lakes with poor ecological status in the Netherlands: Loosdrecht, Nieuwkoop, and Reeuwijk (1.8–2.7 m depth, 1.6–2.5 km fetch). These measures are: 1. wave reducing barriers, 2. water level fluctuations, 3. capping of the sediment with sand, and 4. combinations of above. Critical shear stress of the sediments for resuspension (Vcrit), size distribution, and optical properties of the suspended material were quantified in the field (June 2009) and laboratory. Water quality monitoring data (2002–2009) showed that light attenuation by organic suspended matter in all lakes is high. Spatial modeling of the impact of these measures showed that in Lake Loosdrecht limiting wave action can have significant effects (reductions from 6% exceedance to 2% exceedance of Vcrit), whereas in Lake Nieuwkoop and Lake Reeuwijk this is less effective. The depth distribution and shape of Lake Nieuwkoop and Lake Reeuwijk limit the role of wind-driven resuspension in the total suspended matter concentration. Although the lakes are similar in general appearance (origin, size, and depth range) measures suitable to improve their ecological status differ. This calls for care when defining the programme of measures to improve the ecological status of a specific lake based on experience from other lakes.
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