Making Sense of Singular Gauge Transformations in 1+1 and 2+1 Fermion Models

We study the problem of decoupling fermion fields in 1+1 and 2+1 dimensions, in interaction with a gauge field, by performing local transformations of the fermions in the functional integral. This could always be done if singular (large) gauge transformations were allowed, since any gauge field configuration may be represented as a singular pure gauge field. However, the effect of a singular gauge transformation of the fermions is equivalent to the one of a regular transformation with a non-trivial action on the spinorial indices. For example, in the two dimensional case, singular gauge transformations lead naturally to chiral transformations, and hence to the usual decoupling mechanism based on Fujikawa Jacobians. In 2+1 dimensions, using the same procedure, different transformations emerge, which also give rise to Fujikawa Jacobians. We apply this idea to obtain the v.e.v of the fermionic current in a background field, in terms of the Jacobian for an infinitesimal decoupling transformation, finding the parity violating result.Comment: 14 pages, Late

On the Areas of Cyclic and Semicyclic Polygons

We investigate the ``generalized Heron polynomial'' that relates the squared area of an n-gon inscribed in a circle to the squares of its side lengths. For a (2m+1)-gon or (2m+2)-gon, we express it as the defining polynomial of a certain variety derived from the variety of binary (2m-1)-forms having m-1 double roots. Thus we obtain explicit formulas for the areas of cyclic heptagons and octagons, and illuminate some mysterious features of Robbins' formulas for the areas of cyclic pentagons and hexagons. We also introduce a companion family of polynomials that relate the squared area of an n-gon inscribed in a circle, one of whose sides is a diameter, to the squared lengths of the other sides. By similar algebraic techniques we obtain explicit formulas for these polynomials for all n <= 7.Comment: 22 page

Bialik in the Ghettos

Great books were being sold for a song in the ghetto streets and later would be abandoned and recycled for toilet paper. A universal Jewish culture now lay in ruins. Yet a short list of titles might still appeal to those readers living within an unfolding situation of absolute extremity, readers who hungered for an accurate description of their own historical condition. How different were those fortunate Jews in Erets Israel, that tiny handful of Zionist youth who lived at the farthest possible remove from Bialik's poem. While they have been faulted for consistently misreading "Be'ir hahareigah" (Shapira 2005), the same poem was reread by the overwhelming majority of world Jewry, who saw themselves living inside the poem

The Emancipation of Yiddish

The Nahman-Perl rivalry is an exemplum of the dialectic between continuity and change, integration and rebellion, that has structured the basic patterns of controversy in all forms of the Jewish spirit for the past two hundred years. It is the great debate on Emancipation and its discontents. The sudden access to modern life effected by Emancipation gave rise to an intoxicated embrace of the new and rejection of the old, but fears of the eventual consequences of this embrace in turn fostered a spirit of qualification that sought to preserve tradition in a modern age. Perhaps no area of Jewish life had so much invested in the promise of Emancipation, was so brutally crushed by its failure, and then revised its assumptions so profoundly, as Yiddish culture. It has been the particular fate of the study of Yiddish to continue after the loss of its cultural base. To examine the pattern of its rebirth against the backdrop of recent history is to discover how scholarship revived the essential debate after the culture itself was decimated, and to appreciate anew the relation of criticism to culture

The Treasures of Howe and Greenberg

In the first two decades of this century, when literary manifestos were very much in vogue, the burning issue was that of cultural renewal: Was it to come from within, by reappropriating the past, or from without, by celebrating the present and incorporating its chaotic norms? Neo-classicists and symbolists squared off against Futurists and Expressionists. The revival of folklore, myth and metaphysics was countered by the supremacy of the masses, the machine and the psyche. One rarely thinks of editors and translators, those workhorses of the literary establishment, venturing forth into such treacherous terrain, but as Dov Sadan was the first to note, the Jewish centers of Odessa and Warsaw with Bialik at the head of one and Frischman at the head of the other, were divided over this very issue, and much of their competing energies were channeled into the work of translation. Each was additionally in charge of the means of production—Bialik as editor-in-chief of the Dvir Publishing House and Frischman of Stiebel—so that policy was translated into the distribution of real books

The Holocaust According to Its Anthologists

One way that the Jews responded to their forcible concentration was through the creative anthology. At three known points on the Holocaust compass—Warsaw, Lodz, and Auschwitz-Birkenau—the very subjects of this coerced ingathering compiled anthologies whose aim it was to encompass the temporal and spatial, the linguistic and societal contours of the German blueprint. Just as the literature of and on World War I attempted to reflect the multinational and intergenerational scope of this first total war, which just yesterday had divided all of Europe along the Western, Eastern, and home fronts, so the aim of contemporary wartime anthologists was to reflect the pan-Jewish scope of this unprecedented slaughter

The Story's the Thing: Afterword

The Beleaguered South Bronx is not the only ground where the ancient and medieval traditions of Jewish storytelling flourished. As the articles in this issue point to some of the stopping places along the way—thirteenth-century Ashkenaz and sixteenth-century Safed—so in the modern period the map became global in scope. The eastern European heartland gave rise to a modern school of folktale writing in both Hebrew and Yiddish and when the Jews of this community dispersed—to Western Europe, America and Palestine—so too did their storytellers. Agnon, foremost among them, bridged the languages and the lands of the Jewish dispersion. In North Africa, meanwhile, the first French-speaking writers recaptured the indigenous storytelling traditions in Judeo-Arabic even as they adapted the fictional forms of modern Europe. When American Jewish writing came into its own after World War II, storytellers such as Malamud and Ozick assumed a prominent place alongside the novelists

The Task of the Jewish Translator: A Valedictory Address

There is nothing more tedious and thankless than the task of the Jewish translator. Since your average Jewish author was multilingual, possessing as many as three internal languages, the translator must be a polyglot, possessing at least one external language to boot. The author gets all the glory. The translator gets all the blame

The Last of the Purim Players: Itzik Manger

After 1920, there was only one place left on earth where Yiddish storytelling could grow and prosper, and that place was Poland. The pace and political pressures of Jewish life in the Americas, the Soviet "Republics," and Palestine had turned folklore, fantasy, and the stylized folktale either into pablum for progressive children or into the lethal vestige of a petit-bourgeois and reactionary past. In Poland, with poverty so great, the pace of change so gradual, and the vestigial presence of the past so much a part of the living present, ethnography was just about the only thing the Jews were producing in abundance