1,966,238 research outputs found
An Expansion Term In Hamilton's Equations
For any given spacetime the choice of time coordinate is undetermined. A
particular choice is the absolute time associated with a preferred vector
field. Using the absolute time Hamilton's equations are
+ (\delta H_{c})/(\delta \pi)=\dot{q}\Theta = V^{a}_{.;a}N\equiv exp(-\int\Theta d \ta)\pi^{N}\pi^N$. Briefly the possibility of a non-standard sympletic form
and the further possibility of there being a non-zero Finsler curvature
corresponding to this are looked at.Comment: 10 page
Background field method in the gradient flow
In perturbative consideration of the Yang--Mills gradient flow, it is useful
to introduce a gauge non-covariant term ("gauge-fixing term") to the flow
equation that gives rise to a Gaussian damping factor also for gauge degrees of
freedom. In the present paper, we consider a modified form of the gauge-fixing
term that manifestly preserves covariance under the background gauge
transformation. It is shown that our gauge-fixing term does not affect
gauge-invariant quantities as the conventional gauge-fixing term. The
formulation thus allows a background gauge covariant perturbative expansion of
the flow equation that provides, in particular, a very efficient computational
method of expansion coefficients in the small flow time expansion. The
formulation can be generalized to systems containing fermions.Comment: 19 pages, the final version to appear in PTE
Ranking expansion terms using partial and ostensive evidence
In this paper we examine the problem of ranking candidate expansion terms for query expansion. We show, by an extension to the traditional F4 scheme, how partial relevance assessments (how relevant a document is) and ostensive evidence (when a document was assessed relevant) can be incorporated into a term ranking function. We then investigate this new term ranking function in three user experiments, examining the performance of our function for automatic and interactive query expansion. We show that the new function not only suggests terms that are preferred by searchers but suggests terms that can lead to more use of expansion terms
The factorisation of glue and mass terms in SU(N) gauge theories
In this paper we investigate the structure of the glue in Zwanziger's gauge
invariant expansion for the A^2-type mass term in Yang-Mills theory. We show
how to derive this expansion, in terms of the inverse covariant Laplacian, and
extend it to higher orders. In particular, we give an explicit expression, for
the first time, for the next to next to leading order term. We further show
that the expansion is not unique and give examples of the resulting ambiguity.Comment: 22 page
New Wrinkles on an Old Model: Correlation Between Liquid Drop Parameters and Curvature Term
The relationship between the volume and surface energy coefficients in the
liquid drop A^{-1/3} expansion of nuclear masses is discussed. The volume and
surface coefficients in the liquid drop expansion share the same physical
origin and their physical connection is used to extend the expansion with a
curvature term. A possible generalization of the Wigner term is also suggested.
This connection between coefficients is used to fit the experimental nuclear
masses. The excellent fit obtained with a smaller number of parameters
validates the assumed physical connection.Comment: 6 pages, 2 figure
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