Seminar A. Kiselev

Speaker: 
A. Kiselev
Affiliation: 
Chair of Algebra, J. Bernoulli Institute Groningen
Title: 
Built-in jet bundles in gauge and string geometry
Abstract: 

I shall track two instances of infinite jet superbundles in the geometry of string and gauge models, respectively. Suppose first that the action is trivial (S=0) and there is no gauge freedom (G=1), but let a variational Poisson bi-vector be given. With this setup we associate the odd evolutionary vector field, Q^2=0, on an infinite jet superbundle which is inhabited by the antifields (i.e., we discover the representation of the variational Poisson-Lie algebroids in terms of the BRST-homological vector fields [1]); we show why the traditional construction of such fields does not fully grasp the geometry of strings.

Second, we preserve S=0 but discard any Poisson dynamics so that only the gauge degrees of freedom may be available. For a given gauge Lie group (G>1) we derive the generally covariant way of commutation closure for the gauge generators. In addition to the gauge field which is itself a connection, we prove the existence of another curious affine connection with bi-differential Christoffel symbols [2]. With this setup we again associate the odd, BRST-homological evolutionary vector field on an infinite jet superbundle which is inhabited by the ghosts; we explain why the traditional description of such fields does not fully grasp the geometry of gauge systems.

References:
 [1] A.V.Kiselev and J.W.van de Leur (2011) <http://arxiv.org/abs/1006.4227>
 [2] A.V.Kiselev and J.W.van de Leur (2011) <http://arxiv.org/abs/0904.1555>
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During the talk I shall refer to the standard material in Ch.3,12,15,17 of "Quantization of gauge systems" by M.Henneaux and C.Teitelboim (WARNING: this covers the differential setup of (super-)manifolds and not the variational setup of jet (super-)bundles for maps of manifolds).

Location: 
5118.-152
Date: 
Monday, June 20, 2011 - 12:30 - 13:30