Dispersive calculation of B_7^{3/2} and B_8^{3/2} in the chiral limit

We show how the isospin vector and axialvector current spectral functions rho_V and rho_A can be used to determine in leading chiral order the low energy constants B_7^{3/2} and B_8^{3/2}. This is accomplished by matching the Operator Product Expansion to the dispersive analysis of vacuum polarization functions. The data for the evaluation of these dispersive integrals has been recently enhanced by the ALEPH measurement of spectral functions in tau decay, and we update our previous phenomenological determination. Our calculation yields in the NDR renormalization scheme and at renormalization scale mu = 2 GeV the values B_7^{3/2} = 0.55 +- 0.07 +- 0.10 and B_8^{3/2} = 1.11 +- 0.16 +- 0.23 for the quark mass values m_s + m = 0.1 GeV.Comment: 16 pages, 1 figur

William Thomas Thornton’s family, ancestry, and early years: Some findings from recently discovered manuscripts and letters

The article discusses information about the family, life, and ancestry of economist William Thomas Thornton found in some of his manuscripts and letters. The importance of the lack of information surrounding Thornton\u27s personal life is explored. The available sources on Thornton\u27s life are described, including the book Collected Works of John Stuart Mill, which contains letters between Mill and Thornton. The discovery of the Thornton family letters is discussed and the usefulness of these documents to the study of Thornton\u27s life is also examined

The early economic writings of William Thomas Thornton

The aim of this article is to evaluate Thornton’s early contributions to the great public debates of the mid-Victorian period. Specifically, it reveals his methods for resolving pressing public concerns of the day through the application of the postulates of classical economics. It also highlights the divergence of his conclusions from the orthodox formulations prescribed by some leading classical writers. The remainder of the article is organized as follows. The first section covers briefly Thornton’s views on the causes of and remedies for overpopulation and poverty in rural Britain. Sections 2 and 3 discuss his views, respectively, on the Old Poor Laws and the New Poor Laws. Section 4 reviews his recommendations on the reform of the industrial workplace and factory system. Section 5 covers his views on land tenure reform, with special reference to the so-called Irish land question. The next section presents a variety of responses by leading Victorian figures to Thornton’s early economic writings. It also highlights the pastoral verse he published in the 1850s as a literary device intended to extol the virtues of a bygone agrarian era. Some concluding remarks follow in section 7

We need a minimum standard of living for all citizens if we wish to achieve community cohesion

Many debates about welfare policy rest on implicit or explicit claims about the social ramifications of welfare spending. Matthew Donoghue suggests that community cohesion is a crucial issue to be considered as part of such debates. He argues that individual autonomy, ensured by a minimum standard of living, stands as a necessary condition for community cohesion

The effective field theory treatment of quantum gravity

This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.Comment: Presented at the Sixth International School on Field Theory and Gravitation, Petropolis, Brazil, April 2012, to be published in the proceedings. 22 pages, 3 figure

Correspondence principle in quantum gravity

The problem of consistent formulation of the correspondence principle in quantum gravity is considered. The usual approach based on the use of the two-particle scattering amplitudes is shown to be in disagreement with the classical result of General Relativity given by the Schwarzschild solution. It is shown also that this approach fails to describe whatever non-Newtonian interactions of macroscopic bodies. An alternative interpretation of the correspondence principle is given directly in terms of the effective action. Gauge independence of the \hbar^0 part of the one-loop radiative corrections to the gravitational form factors of the scalar particle is proved, justifying the interpretation proposed. Application to the black holes is discussed.Comment: Talk presented at the international meeting "Quantum Gravity and Spectral Geometry", Naples, July 2001. 4 pages, 1 figur

On the Marriage of Chiral Perturbation Theory and Dispersion Relations

I describe the methodology for the use of dispersion relations in connection with chiral perturbation theory. The conditions for matching the two formalisms are given at $O(E^2)$ and $O(E^4)$. The two have several complementary features, as well as some limitations, and these are described by the use of examples, which include chiral sum rules related to the Weinberg sum rules, form factors, and a more complicated reaction, $\gamma \gamma \rightarrow \pi \pi$. (Invited talk presented at the International Workshop on Chiral Dynamics in Hadrons and Nuclei, Feb 6-10, 1995, Seoul, Korea)Comment: 20 pages, Late