81,555 research outputs found

    S-Duality in Gauge Theories as a Canonical Transformation

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    We show that S-duality in four dimensional non-supersymmetric abelian gauge theories can be formulated as a canonical transformation in the phase space of the theory. This transformation is the usual interchange between electric and magnetic degrees of freedom. It is shown that in phase space the modular anomaly emerges as the result of integrating out the momenta degrees of freedom. The generalization to d dimensional abelian gauge theories of p forms is also considered. In the case of non-abelian gauge theories a careful analysis of the constraints implied by the canonical transformation shows that it does not relate Yang-Mills theories with inverted couplings. In fact the dual theory is shown to be of Freedman- Townsend's type, also with τ~=−1/τ{\tilde \tau}=-1/\tau, τ=Ξ2π+4πig2\tau=\frac{\theta}{2\pi}+\frac{4\pi i}{g^2}.Comment: 13 pages, latex file, important changes in the non-abelian case. Some references adde

    Duality and Canonical Transformations

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    We present a brief review on the canonical transformation description of some duality symmetries in string and gauge theories. In particular, we consider abelian and non-abelian T-dualities in closed and open string theories as well as S-duality in abelian and non-abelian non-supersymmetric gauge theories.Comment: 21 pgs, latex file, talk given at the Argonne Duality Institute, June 27-July 12, 1996, to appear in the e-proceeding

    Savage Desert, American Garden: citrus labels and the selling of California, 1877-1929

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    In 1877, a year after the railroad reached Southern California, the first shipment of California oranges left the Los Angeles groves of William Wolfskill, bound for St. Louis, Missouri. The box-ends were branded ‘Wolfskill California Oranges’, ensuring that the geographical origins of the fruit were emphasised from the very beginning of their exportation to the Midwest and East. During the 1880s, the innovations of irrigation and refrigerated cars combined with new railroads, massive in-migration and land development to turn California into, in Douglas Sackman’s words, an ‘orange empire’. By 1900, this empire had surpassed Florida as the United States’ leading producer of fruit, while, as one historian explains, ‘the orange crop had passed the cash returns from gold’ found in California. From virtually none a few decades earlier, the average American in 1914 ate over 40 oranges per year, and orange juice had become part of the standard American breakfast. By then some thirty thousand railroad carloads—approximately twelve million orange crates—valued at $20 million, were steaming east from the Golden State each year. Adorning these crates were, in the words of Kevin Starr, ‘the inventive labels’ whose ‘selling of California along with oranges as an image in the national imagination’ are the focus of this article

    EEOC v. Polycon Industries, INC

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