## PhD Era Research Interests: Nielsen Identities

The framework for understanding particle physics in the latter part of the 20th century was that of gauge symmetry. The Standard Model in particle physics was constructed by bolting together gauge theories for electromagnetism and the Strong and Weak interactions, with the essential additional ingredient of the Higgs Boson to generate mass while preserving the gauge symmetries. The mechanism for such mass generation was spontaneous symmetry breaking, where the vacuum solutions of the theory had less symmetry than the Lagrangian describing the theory.

In order to perform perturbative calculations in such theories it was necessary (or at least convenient) to "fix the gauge", which led to results for physical quantities, such as the mass of particles, which apparently depended on unphysical parameters introduced in the gauge fixing. My job in my thesis was to show with explicit calculations in a particular model that such dependence was illusory and that, in fact, all was well. The work made use of the so-called Nielsen Identities to demonstrate the gauge-independence of physical quantities.

## Some Associated Published Papers

Nucl. Phys. B253 (1985) 687-700: Nielsen Identities in the 't Hooft Gauge

J. Phys. A19 (1986) 141-157: Convexity of the Effective Potential

Zeit. fur Phys. C31 (1986) 129-133: Convexity and Tadpoles

Phys. Lett. B182 (1986) 177-180: The Wess-Zumino Gauge is a "Good" Gauge

Phys. Lett. B189 (1987) 311-314: Gauge Dependence of the One-Loop Effective Action in Gravity

Nucl. Phys. B283 (1987) 317-330: Nielsen Identities for Gauge-Fixing Vectors and Composite Effective Potentials

Phys. Lett. B186 (1987) 185-188: Coleman-Weinberg, Nielsen and Daisies

Nucl. Phys. B293 (1987) 229-240: Gauge Independence of Mass Counterterms in the Abelian Higgs Model and Gravity

Nucl. Phys. B297 (1988) 721-732: Sedentary Ghost poles in Higher Derivative Gravity

What a preprint (my first...) used to look like in those prehistoric days before TeX (1984): Nielsen Identities in the 't Hooft Gauge

What a thesis (my only...) used to look like in those prehistoric days before TeX (1986): Gauge Properties and Convexity of the Effective Potential

Tassos Vladikas produced a nice set of photos of the PhD students and staff from that time to commemorate a reunion that took place in summer 2018. Note that clicking on the link to the photos (a 156MB pdf download) will give some scary Google Drive warning about being too big to scan for viruses, it's clean.