Batalin-Vilkovisky field-antifield quantisation of fluctuations around classical field configurations

  • The Lagrangian field-antifield formalism of Batalin and Vilkovisky (BV) is used to investigate the application of the collec- tive coordinate method to soliton quantisation. In field theories with soliton solutions, the Gaussian fluctuation operator has zero modes due to the breakdown of global symmetries of the Lagrangian in the soliton solutions. It is shown how Noether identities and local symmetries of the Lagrangian arise when collective coordinates are introduced in order to avoid divergences related to these zero modes. This transformation to collective and fluctuation degrees of freedom is interpreted as a canonical transformation in the symplectic field-antifield space which induces a time-local gauge symmetry. Separating the corresponding Lagrangian path integral of the BV scheme in lowest order into harmonic quantum fluctuations and a free motion of the collective coordinate with the classical mass of the soliton, we show how the BV approach clarifies the relation between zero modes, collective coordinates, gauge invariance and the center- of-mass motion of classical solutions in quantum fields. Finally, we apply the procedure to the reduced nonlinear O(3) oe-model.^L

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Author:F. Zimmerschied
URN (permanent link):urn:nbn:de:hbz:386-kluedo-8549
Document Type:Preprint
Language of publication:English
Year of Completion:1996
Year of Publication:1996
Publishing Institute:Technische Universität Kaiserslautern
Faculties / Organisational entities:Fachbereich Physik
DDC-Cassification:530 Physik

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