### Abstract

In this article we discuss the one loop renormalization and scaling behavior of non-Abelian gauge field theories in a general curved spacetime. A generating functional is constructed which forms the basis for both the perturbation expansion and the Ward identities. Local momentum space representations for the vector and ghost particles are developed and used to extract the divergent parts of Feynman integrals. The one loop diagram for the ghost propagator and the vector-ghost vertex are shown to have no divergences not present in Minkowski space. The Ward identities insure that this is true for the vector propagator as well. It is shown that the above renormalizations render the three- and four-vector vertices finite. Finally, a renormalization group equation valid in curved spacetimes is derived. Its solution is given and the theory is shown to be asymptotically free as in Minkowski space.

Original language | English (US) |
---|---|

Pages (from-to) | 417-444 |

Number of pages | 28 |

Journal | Annals of Physics |

Volume | 147 |

Issue number | 2 |

DOIs | |

State | Published - 1983 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*147*(2), 417-444. https://doi.org/10.1016/0003-4916(83)90215-4

**Renormalization and scaling behavior of non-Abelian gauge fields in curved spacetime.** / Leen, T. K.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 147, no. 2, pp. 417-444. https://doi.org/10.1016/0003-4916(83)90215-4

}

TY - JOUR

T1 - Renormalization and scaling behavior of non-Abelian gauge fields in curved spacetime

AU - Leen, T. K.

PY - 1983

Y1 - 1983

N2 - In this article we discuss the one loop renormalization and scaling behavior of non-Abelian gauge field theories in a general curved spacetime. A generating functional is constructed which forms the basis for both the perturbation expansion and the Ward identities. Local momentum space representations for the vector and ghost particles are developed and used to extract the divergent parts of Feynman integrals. The one loop diagram for the ghost propagator and the vector-ghost vertex are shown to have no divergences not present in Minkowski space. The Ward identities insure that this is true for the vector propagator as well. It is shown that the above renormalizations render the three- and four-vector vertices finite. Finally, a renormalization group equation valid in curved spacetimes is derived. Its solution is given and the theory is shown to be asymptotically free as in Minkowski space.

AB - In this article we discuss the one loop renormalization and scaling behavior of non-Abelian gauge field theories in a general curved spacetime. A generating functional is constructed which forms the basis for both the perturbation expansion and the Ward identities. Local momentum space representations for the vector and ghost particles are developed and used to extract the divergent parts of Feynman integrals. The one loop diagram for the ghost propagator and the vector-ghost vertex are shown to have no divergences not present in Minkowski space. The Ward identities insure that this is true for the vector propagator as well. It is shown that the above renormalizations render the three- and four-vector vertices finite. Finally, a renormalization group equation valid in curved spacetimes is derived. Its solution is given and the theory is shown to be asymptotically free as in Minkowski space.

UR - http://www.scopus.com/inward/record.url?scp=33750805501&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750805501&partnerID=8YFLogxK

U2 - 10.1016/0003-4916(83)90215-4

DO - 10.1016/0003-4916(83)90215-4

M3 - Article

AN - SCOPUS:33750805501

VL - 147

SP - 417

EP - 444

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 2

ER -