Investigación

 

Matthews' theorem in effective Yang-Mills theories

 

L.T. López-Lozano¹ and J.J. Toscano²

 

¹ Departamento de Física, Centro de Investigación y de Estudios Avanzados. Apartado postal 14-740, 07000 México, D.F., México.

² Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla. Apartado postal 1152, Puebla, Pue., México.

 

Recibido el 24 de agosto de 2001.
Aceptado el 16 de noviembre de 2001.

 

Abstract

We study the quantization of effective Yang-Mills theories within the path integral formalism. In particular, the equivalence of the Hamiltonian and Lagrangian path integral quantization (Matthews' theorem) is probed for an effective Yang-Mills Lagrangian without matter fields, which includes all the invariant terms up to dimension six. This theorem is probed from point of views of both the gauge and BRST symmetries. The importance of the BRST symmetry in probing this theorem is stressed. We found that the functional integration on the generalized momenta are of Gaussian type and that they do not contribute to physical quantities as a consequence of the symmetries of the effective Lagrangian, which leads to a Lorentz and BRST invariant Lagrangian path integral.

Keywords: Effective lagrangians; constraints.

 

Resumen

Se estudia la cuantización de teorías efectivas de Yang-Mills en el contexto del formalismo de integral de trayectoria. En particular, se prueba la equivalencia de la cuantización por las integrales de trayectoria hamiltoniana y lagrangiana (teorema de Matthews) para un lagrangiano efectivo de Yang-Mills sin campos de materia, el cual incluye todos los términos invariantes de hasta dimensión seis. Este teorema es probado desde los puntos de vista de la simetría de norma y de la simetría BRST. Se enfatiza la importancia de la simetría BRST en la prueba de este teorema. Se encuentra que las integrales funcionales en los momentos generalizados son de tipo gaussiano y que no contribuyen a cantidades físicas como consecuencia de las simetrías del lagrangiano efectivo, lo cual conduce a una integral de trayectoria Lagrangiana invariante de Lorentz y BRST.

Palabras clave: Lagrangianos efectivos; constricciones.

 

PACS: 11.10.Ef; 11.30.Cp; 11.30.Ly

 

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References

ª. In the following, always we refer to the general case, it must be understood that the effective Lagrangian in consideration is gauge invariant and contain all invariant structures of arbitrary dimension, including matter fields.

^b. It is possible to construct another independent term by substituting in one of the strength tensor by its dual: a6i2.jpg">= (1/2) ε_μυλpF^aλp , but this class of structures will be not considered here, for simplicity.

^c. Through the paper, we will write weak equations using the symbol ≈.

^d. For large values of the fields, the Gribov phenomenon arises and no gauge-fixing is possible [14].

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