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Local quantum field theories involving the U(1) current algebra on the circle

โœ Scribed by Roman R. Paunov; Ivan Todorov

Publisher
Springer
Year
1989
Tongue
English
Weight
603 KB
Volume
17
Category
Article
ISSN
0377-9017

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โœฆ Synopsis

The OPE algebra Q = Q(ga) generated by a pair of oppositely charged 'currents' ~b(z, + g) (Izl = 1) of spin s = 89 (2s --1, 2, 3 .... ) is specified by the leading terms in the small distance expansions of qJ(zl,g)~/(z 2, -g) and ~b(zl,g)~(z2,g). The 'current' ~b(z,g) splits into a product of a U(l)-Thirring field and a Zamolodchikov-Fateev'parafermionic' current. The quasiloeal (i.e. single-or double-valued) representations of Q are classified. The level k states involve 2(k + 1) (ks -k + 1) lowest weights (dimensions). The results can be viewed as an extension of the (known) representation theory of the SU(2) current algebra in the bosonic case corresponding to even values of g2 and of the N = 2 extended superconformal algebra in the fermionic case corresponding to odd g2.

๐Ÿ“œ SIMILAR VOLUMES

On the relations between quantum fields
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โœ Manfred Wollenberg ๐Ÿ“‚ Article ๐Ÿ“… 1989 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 878 KB

It is shown that quantum fields over a curved space-time with a transitive group of isometriesare well-defined objects at each space-time point in the meaning of sesquilinear forms. If these quantum fields are associated with a local net of observables then they can be obtained as limits of sequence