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Translation Group and Particle Representations in Quantum Field Theory

By (author) Hans-JÃ¼rgen Borchers

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At the time I learned quantum field theory it was considered a folk theoÂ rem that it is easy to construct field theories fulfilling either the locality or the spectrum condition. The construction of an example for the latter case is particularly easy. Take for instance an irreducible representation of the Poincare group with positive energy, and as an algebra of observables all compact operators in that representation space. This algebra of observables is even an asymptotically Abelian algebra. Since it has only a single repreÂ sentation - except for multiples of this one - it is hardly possible to replace locality in order to obtain a theory with a reasonable physical structure. This example shows that it is not sufficient to replace locality by asymptotic Abelian-ness. The construction of a theory fulfilling locality without a posÂ itive energy representation was first done by Doplicher, Regge, and Singer [DRS]. However, modern investigations on the locality ideal in the algebra oftest functions, started by Alcantara and Yngvason [AY], seem to indicate that this is a general feature; this means that most of the algebras of obÂ servables fulfilling the locality condition will not have representations that also fulfil the spectrum condition. This discussion shows that quantum field theory becomes a subject of interest only if both conditions are satisfied at the same time.

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The Ballerina and the Bull: Anarchist Utopias in the Age of Finance

Johanna Isaacson
Paperback / softback
288 pages
was: R 306.95
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Our moment has seen the resurgence of an anarchist sensibility, from the uprisings in Seattle in 1999 to the Occupy movement of 2011.

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Fifteen Dogs

AndrÃ© Alexis
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176 pages
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A pack of dogs are granted the power of human thought - but what will it do to them? A surprising and insightful look at the beauty and perils of consciousness.

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Bonsai Success in Southern Africa

Carl Morrow
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160 pages
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In this uniquely Southern African book, Carl Morrow and Keith Kirsten guide readers step by step into the magical realms of bonsai as a hobby, horticultural practice and art form.

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