18,185 research outputs found
Path integral quantization of scalar fluctuations above a kink
We quantize scalar fluctuations in 1+1 dimensions above a classical
background kink. The properties of the effective action for the corresponding
classical field are studied with an exact functional method, alternative to
exact Wilsonian renormalization, where the running parameter is a bare mass,
and the regulator of the quantum theory is fixed. We extend this approach, in
an appendix, to a Yukawa interaction in higher dimension.Comment: Comments adde
Non-renormalization for the Liouville wave function
Using an exact functional method, within the framework of the gradient
expansion for the Liouville effective action, we show that the kinetic term for
the Liouville field is not renormalized.Comment: 13 pages Latex, no figure
Singular value decomposition for the 2D fan-beam Radon transform of tensor fields
In this article we study the fan-beam Radon transform of
symmetrical solenoidal 2D tensor fields of arbitrary rank in a unit disc
as the operator, acting from the object space to the data space
The orthogonal polynomial basis of solenoidal tensor
fields on the disc was built with the help of Zernike polynomials
and then a singular value decomposition (SVD) for the operator
was obtained. The inversion formula for the fan-beam tensor transform follows from this decomposition. Thus obtained inversion formula can be
used as a tomographic filter for splitting a known tensor field into potential
and solenoidal parts. Numerical results are presented.Comment: LaTeX, 37 pages with 5 figure
An integer construction of infinitesimals: Toward a theory of Eudoxus hyperreals
A construction of the real number system based on almost homomorphisms of the
integers Z was proposed by Schanuel, Arthan, and others. We combine such a
construction with the ultrapower or limit ultrapower construction, to construct
the hyperreals out of integers. In fact, any hyperreal field, whose universe is
a set, can be obtained by such a one-step construction directly out of
integers. Even the maximal (i.e., On-saturated) hyperreal number system
described by Kanovei and Reeken (2004) and independently by Ehrlich (2012) can
be obtained in this fashion, albeit not in NBG. In NBG, it can be obtained via
a one-step construction by means of a definable ultrapower (modulo a suitable
definable class ultrafilter).Comment: 17 pages, 1 figur
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