Some comments on unitarity gauge
M.A. López-Osorio, E. Martínez-Pascual, and J.J. Toscano
Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, Puebla Pue., México.
Recibido el 21 de junio de 2002. ]]> Aceptado el 25 de julio de 2003.
Abstract
A pedagogical discussion on the unitarity gauge within the context of Hamiltonian path integral formalism is presented. A model based on the group O(N), spontaneously broken down to the subgroup O(N — 1), is used to illustrate the main aspects of this gauge-fixing procedure. Among the issues, discussed with some extent, are: (1) the structure of model's constraints following the Dirac's method, (2) the gauge-fixing procedure, using the unitarity gauge for the massive gauge fields and the Coulomb one for the massless gauge fields, (3) the absence of BRST symmetry in this gauge-fixing procedure and its implications on the renormalizability of the theory, and (4) the static role of the ghost and anti-ghost fields associated with the massive gauge fields and how their contributions can be eliminated by using the dimensional regularization scheme.
Keywords: Unitarity gauge; Hamiltonian path integra.
Resumen
Se presenta una discusión pedagógica de la norma unitaria en el contexto de integral de trayectoria hamiltoniana. Un modelo basado en el grupo O(N), roto espontáneamente al subgrupo O(N — 1), es usado para ilustrar los aspectos principales de este procedimiento de fijación de la norma. Entre los temas, discutidos con cierta extensión, están: (1) la estructura de las constricciones del modelo siguiendo el método de Dirac; (2) el procedimiento de fijación de la norma, usando la norma unitaria para los campos de norma masivos y la norma de Coulomb para los campos de norma sin masa, (3) la ausencia de la simetría BRST en este procedimiento de fijación de la norma y sus implicaciones sobre la renormalizabilidad de la teorí;a y (4) el papel estático de los campos fantasma asociados con los campos de norma masivos y cómo sus contribuciones pueden ser canceladas usando el esquema de regularización dimensional.
Descriptores: Norma unitaria; integral de trayectoria hamiltoniana.
]]> PACS: 11.10.Ef; 11.15.-q; 11.30.Qc
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Acknowledgment
We would like to thank J. M. Hernández for his comments. MAL and EM acknowledge support from CONACYT (México) under grant G28102. JJT also acknowledges support from CONACYT and SNI (México).
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