[Review of] Joseph Rothschild, Ethnopolitics, A Conceptual Framework

Whether ethnicity stems from certain intrinsic group characteristics or whether it is a definition conferred upon various groups because of their political, social, and economic environment has been a fundamental debate within the field of ethnic studies. Most students of ethnic studies would agree that ethnicity today embraces both factors, and more, that it is the result of the interactions between both sets of influences. How these factors interact in the political sphere is the core of Rothschild\u27s ambitious new book

N=0 Supersymmetry and the Non-Relativistic Monopole

We study some of the algebraic properties of the non-relativistic monopole. We find that we can construct theories that possess an exotic conserved fermionic charge that squares to the Casimir of the rotation group, yet do not possess an ordinary supersymmetry. This is in contrast to previous known examples with such exotic fermionic charges. We proceed to show that the presence of the exotic fermionic charge in the non-supersymmetric theory can nonetheless be understood using supersymmetric techniques, providing yet another example of the usefulness of supersymmetry in understanding non-supersymmetric theories.Comment: 9 pages, harvmac, no figure

Asians, Jews, and the Legacy of Midas

In much of the U.S. media today, Asian-Americans are being hailed as the new wonder group. Local newspapers seem to be filled with articles about how this student from Pakistan won the spelling bee and that student from Japan won the math contest. Weekly news magazines carry articles extolling this phenomenon, and many liberals and conservatives alike enthusiastically promote the stereotype: liberals because it combats the racist myth that people of color are intellectually inferior to Euro-Americans ( whites ) and conservatives because it can be used to promote the idea that any ethnic group can make it if only they work hard.[1] Therein lies one of the negative aspects of this media campaign

LpL^p-Taylor approximations characterize the Sobolev space W1,pW^{1,p}

In this note, we introduce a variant of Calder\'on and Zygmund's notion of $L^p$-differentiability - an \emph{$L^p$-Taylor approximation}. Our first result is that functions in the Sobolev space $W^{1,p}(\mathbb{R}^N)$ possess a first order $L^p$-Taylor approximation. This is in analogy with Calder\'on and Zygmund's result concerning the $L^p$-differentiability of Sobolev functions. In fact, the main result we announce here is that the first order $L^p$-Taylor approximation characterizes the Sobolev space $W^{1,p}(\mathbb{R}^N)$, and therefore implies $L^p$-differentiability. Our approach establishes connections between some characterizations of Sobolev spaces due to Swanson using Calder\'on-Zygmund classes with others due to Bourgain, Brezis, and Mironescu using nonlocal functionals with still others of the author and Mengesha using nonlocal gradients. That any two characterizations of Sobolev spaces are related is not surprising, however, one consequence of our analysis is a simple condition for determining whether a function of bounded variation is in a Sobolev space.Comment: 7 pages. Preprint of an article to appear in Comptes Rendus - the exposition of the two articles is substantially different and the full article will not be available as an arxiv paper. The title and abstract displaying on arxiv have been changed to that of the article in its more polished for

Anyon Statistics and the Witten Index

Using the theory of supersymmetric anyons, I extend the definition of the Witten index to 2+1 dimensions so as to accommodate the existence of anyon spin and statistics. I then demonstrate that, although in general the index receives irrational and complex contributions from anyonic states, the overall index is always integral, and I consider some of the implications and interpretations of this result.Comment: 10 pages, harvmac, no figures; revised to elaborate on two detail