## Abstract

The authors have developed a matrix element approach to quantum field theory on S{sub 4}, and used a complex l-plane method of performing the resulting angular momentum sums. The methods have been used to reproduce previous results for both one-loop and two-loop vacuum amplitudes for an Abelian gauge theory, including Dirac fermions and scalar bosons. In this paper they extend the formalism to non-Abelian gauge theory and show how the new complex l-plane methods allow the calculation of two-loop vacuum amplitudes involving ghost and gauge fields. It is shown how it is possible to overcome previous calculational limitations, resulting from the form of the ghost and gauge propagators, by performing the entire calculation in angular momentum space without reference to any particular configuration space form of the propagators. The two-loop interacting vacuum amplitude is derived in a non-Abelian gauge theory on a curved background and the required counterterm to renormalise the background gravitational action on S{sub 4} is given. 12 refs., 4 figs.

## Citation Formats

Harris, B A, and Joshi, G C.
Two-loop vacuum amplitudes in a non-Abelian gauge theory on S{sub 4}.
Australia: N. p.,
1994.
Web.

Harris, B A, & Joshi, G C.
Two-loop vacuum amplitudes in a non-Abelian gauge theory on S{sub 4}.
Australia.

Harris, B A, and Joshi, G C.
1994.
"Two-loop vacuum amplitudes in a non-Abelian gauge theory on S{sub 4}."
Australia.

@misc{etde_10113738,

title = {Two-loop vacuum amplitudes in a non-Abelian gauge theory on S{sub 4}}

author = {Harris, B A, and Joshi, G C}

abstractNote = {The authors have developed a matrix element approach to quantum field theory on S{sub 4}, and used a complex l-plane method of performing the resulting angular momentum sums. The methods have been used to reproduce previous results for both one-loop and two-loop vacuum amplitudes for an Abelian gauge theory, including Dirac fermions and scalar bosons. In this paper they extend the formalism to non-Abelian gauge theory and show how the new complex l-plane methods allow the calculation of two-loop vacuum amplitudes involving ghost and gauge fields. It is shown how it is possible to overcome previous calculational limitations, resulting from the form of the ghost and gauge propagators, by performing the entire calculation in angular momentum space without reference to any particular configuration space form of the propagators. The two-loop interacting vacuum amplitude is derived in a non-Abelian gauge theory on a curved background and the required counterterm to renormalise the background gravitational action on S{sub 4} is given. 12 refs., 4 figs.}

place = {Australia}

year = {1994}

month = {Dec}

}

title = {Two-loop vacuum amplitudes in a non-Abelian gauge theory on S{sub 4}}

author = {Harris, B A, and Joshi, G C}

abstractNote = {The authors have developed a matrix element approach to quantum field theory on S{sub 4}, and used a complex l-plane method of performing the resulting angular momentum sums. The methods have been used to reproduce previous results for both one-loop and two-loop vacuum amplitudes for an Abelian gauge theory, including Dirac fermions and scalar bosons. In this paper they extend the formalism to non-Abelian gauge theory and show how the new complex l-plane methods allow the calculation of two-loop vacuum amplitudes involving ghost and gauge fields. It is shown how it is possible to overcome previous calculational limitations, resulting from the form of the ghost and gauge propagators, by performing the entire calculation in angular momentum space without reference to any particular configuration space form of the propagators. The two-loop interacting vacuum amplitude is derived in a non-Abelian gauge theory on a curved background and the required counterterm to renormalise the background gravitational action on S{sub 4} is given. 12 refs., 4 figs.}

place = {Australia}

year = {1994}

month = {Dec}

}