Symmetries in QFT

This document contains notes from the graduate lecture course, "Symmetries in QFT" given by J.F.Wheater at Oxford University in Hilary term. The course gives an informal introduction to QFT.Comment: Lecture note

An Ultraviolet Fe II Image of SN 1885 in M31

Ultraviolet imaging of the remnant of Supernova 1885 in M31 with the Hubble Space Telescope using the F255W filter on the WFPC2 reveals a dark spot of Fe II absorption at the remnant's known position in the bulge of M31. The diameter of the absorbing spot is 0"55 +- 0"15, slightly smaller than, but consistent with, the 0"70 +- 0"05 diameter measured in the higher quality WFPC2 Ca II absorption image previously reported by us. The measured ratio of flux inside to outside SNR 1885 in the Fe II image is 0.24 +- 0.17, consistent with the ratio 0.33 +- 0.04 expected on the basis of a model fit to the previously obtained near-UV FOS spectrum. The observed depth of Fe II absorption suggests that Fe II is fully saturated, with an iron mass in the range M_Fe = 0.1-1.0 Msun. Besides Fe, ion species Mg I, Mg II, and Mn I probably make some contribution to the absorption from the SN 1885 remnant in the F255W image.Comment: 7 pages, including 2 embedded PostScript figures, emulateapj.sty, submitted to Ap

Bandwidth in bolometric interferometry

Bolometric Interferometry is a technology currently under development that will be first dedicated to the detection of B-mode polarization fluctuations in the Cosmic Microwave Background. A bolometric interferometer will have to take advantage of the wide spectral detection band of its bolometers in order to be competitive with imaging experiments. A crucial concern is that interferometers are presumed to be importantly affected by a spoiling effect known as bandwidth smearing. In this paper, we investigate how the bandwidth modifies the work principle of a bolometric interferometer and how it affects its sensitivity to the CMB angular power spectra. We obtain analytical expressions for the broadband visibilities measured by broadband heterodyne and bolometric interferometers. We investigate how the visibilities must be reconstructed in a broadband bolometric interferometer and show that this critically depends on hardware properties of the modulation phase shifters. Using an angular power spectrum estimator accounting for the bandwidth, we finally calculate the sensitivity of a broadband bolometric interferometer. A numerical simulation has been performed and confirms the analytical results. We conclude (i) that broadband bolometric interferometers allow broadband visibilities to be reconstructed whatever the kind of phase shifters used and (ii) that for dedicated B-mode bolometric interferometers, the sensitivity loss due to bandwidth smearing is quite acceptable, even for wideband instruments (a factor 2 loss for a typical 20% bandwidth experiment).Comment: 13 pages, 14 figures, submitted to A&

Spatial Competition in Private Labels

Previous studies find that private labels increase retailers' bargaining power with manufacturers and allow retailers to price discriminate. We use a spatial discrete choice model to show that retailers also use store brands to create market power through store differentiation, but not as a means of building market share.Marketing,

Wide Angle Redshift Distortions Revisited

We explore linear redshift distortions in wide angle surveys from the point of view of symmetries. We show that the redshift space two-point correlation function can be expanded into tripolar spherical harmonics of zero total angular momentum $S_{l_1 l_2 l_3}(\hat x_1, \hat x_2, \hat x)$. The coefficients of the expansion $B_{l_1 l_2 l_3}$ are analogous to the $C_l$'s of the angular power spectrum, and express the anisotropy of the redshift space correlation function. Moreover, only a handful of $B_{l_1 l_2 l_3}$ are non-zero: the resulting formulae reveal a hidden simplicity comparable to distant observer limit. The $B_{l_1 l_2 l_3}$ depend on spherical Bessel moments of the power spectrum and $f = \Omega^{0.6}/b$. In the plane parallel limit, the results of \cite{Kaiser1987} and \cite{Hamilton1993} are recovered. The general formalism is used to derive useful new expressions. We present a particularly simple trigonometric polynomial expansion, which is arguably the most compact expression of wide angle redshift distortions. These formulae are suitable to inversion due to the orthogonality of the basis functions. An alternative Legendre polynomial expansion was obtained as well. This can be shown to be equivalent to the results of \cite{SzalayEtal1998}. The simplicity of the underlying theory will admit similar calculations for higher order statistics as well.Comment: 6 pages, 1 figure, ApJL submitte

How Does Advertising Affect Market Performance? The Case of Generic Advertising

The effect of advertising on market performance has been a long-standing debate. Advertising that increases the dispersion of consumers’ valuations for advertised goods raises the market power of firms, while advertising that decreases the dispersion of consumers’ valuations leads to narrower price-cost margins and superior performance in markets for advertised goods. Numerous challenges confound the empirical identification of advertising effects on market performance. This paper proposes a simple method that relies on the revealed preferences of firms participating in generic advertising programs. Generic advertising programs provide a unique window through which to observe advertising effects on market performance, because changes in the dispersion of consumers’ valuations systematically redistributes rents among firms according to observable characteristics on producer size. We examine producer attitudes towards generic advertising in the “Beef. It’s What’s for Dinner” campaign of the U.S. Beef Checkoff program and find the likelihood a producer favors an expansion of the advertising program increases in operating scale. This finding is consistent with advertising effects that have led to a decrease in the dispersion of consumers’ valuations for beef products and a commensurate increase in market performance.Advertising, Oligopoly, Marketing, L1, M37,

OBESITY AND HYPERBOLIC DISCOUNTING: AN EXPERIMENTAL ANALYSIS

Behavioral economists maintain that addictions such as alcoholism, smoking and over-eating represent examples of present-bias in decision making that is fundamentally irrational. In this article, we develop a model of present bias and apparently hyperbolic discounting that is fully consistent with rational behavior. We construct an experiment to test our hypothesis and to determine whether discount rates differ for individuals who engage in behaviors that could endanger their health. Our results show that discount functions are quasi-hyperbolic in shape, and that obesity and drinking are positively related to the discount rate. Anti-obesity policy, therefore, would be best directed to informing individuals as to the long-term implications of short-term gratification, rather than taxing foods directly.addiction, discounting, experiments, hyperbolic, obesity, time-inconsistency, Agricultural and Food Policy, Consumer/Household Economics, Demand and Price Analysis, Food Consumption/Nutrition/Food Safety, Food Security and Poverty, Health Economics and Policy, C91, D12, D91, I18,

Obesity and Hyperbolic Discounting: An Experimental Analysis

Behavioral economists maintain that addictions such as alcoholism, smoking and over-eating represent examples of present-bias in decision making that is fundamentally irrational. In this article, we develop a model of present bias and apparently hyperbolic discounting that is fully consistent with rational behavior. We construct an experiment to test our hypothesis and to determine whether discount rates differ for individuals who engage in behaviors that could endanger their health. Our results show that discount functions are quasi-hyperbolic in shape, and that obesity and drinking are positively related to the discount rate. Anti-obesity policy, therefore, would be best directed to informing individuals as to the long-term implications of short-term gratification, rather than taxing foods directly.addiction, discounting, experiments, hyperbolic, obesity, time-inconsistency., Consumer/Household Economics, Food Consumption/Nutrition/Food Safety, Health Economics and Policy, Institutional and Behavioral Economics, C91, D12, D91, I18.,

Power Spectrum Correlations Induced by Non-Linear Clustering

Gravitational clustering is an intrinsically non-linear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys. Non-Gaussian effects not only increase the individual error bars compared to the Gaussian case but, most importantly, lead to non-trivial cross-correlations between different band-powers. We calculate the power-spectrum covariance matrix in non-linear perturbation theory (weakly non-linear regime), in the hierarchical model (strongly non-linear regime), and from numerical simulations in real and redshift space. We discuss the impact of these results on parameter estimation from power spectrum measurements and their dependence on the size of the survey and the choice of band-powers. We show that the non-Gaussian terms in the covariance matrix become dominant for scales smaller than the non-linear scale, depending somewhat on power normalization. Furthermore, we find that cross-correlations mostly deteriorate the determination of the amplitude of a rescaled power spectrum, whereas its shape is less affected. In weak lensing surveys the projection tends to reduce the importance of non-Gaussian effects. Even so, for background galaxies at redshift z=1, the non-Gaussian contribution rises significantly around l=1000, and could become comparable to the Gaussian terms depending upon the power spectrum normalization and cosmology. The projection has another interesting effect: the ratio between non-Gaussian and Gaussian contributions saturates and can even decrease at small enough angular scales if the power spectrum of the 3D field falls faster than 1/k^2.Comment: 34 pages, 15 figures. Revised version, includes a clearer explanation of why the hierarchical ansatz does not provide a good model of the covariance matrix in the non-linear regime, and new constraints on the amplitudes Ra and Rb for general 4-pt function configurations in the non-linear regim