Renormalization in reparametrization invariance

Abstract

The renormalization issue of the reparameterization invariance in heavy quark effective theory and NRQCD is investigated. I argue that the renormalization of the transformation of the heavy quark field under the variation of the velocity parameter V is attributed to the renormalization of the small component field in the proposed transformation. I show that the matching condition for determining the renormalized small component field can be obtained by imposing an infinitesimal transformation of V on the relations between the Green's functions in QCD full theory and those in the effective theory. As an application, I determine the renormalized transformation to order 1/m 2 using the matching condition. The obtained result is in disagreement with that determined by indirect method.

The plane wave expansion, infinite integrals and identities involving spherical Bessel functions

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“…On the other hand, there are many other applications in nuclear physics that encounter these types of integrals amongst which are distorted wave calculations [2] and nuclear response function calculations [3]. These types of integrals have in the past been calculated analytically (many references exist, see for example references [2] and [4][5][6][7][8][9][10][11]), or numerically using complex-plane methods (see for example references [12][13][14]). In this paper, an additional advantage to the plane wave expansion is presented, whereby the expansion itself is used to derive analytical solutions to integrals over spherical Bessel functions and identities involving them.…”

Demonstration of Angle-Dependent Casimir Force between Corrugations

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Proposal for measurement of repulsive Casimir forces using silicon membranes

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