## PhD Era Research Interests: Nielsen Identities

The framework for understanding particle physics over the past decades has been 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 is spontaneous symmetry breaking, where the vacuum solutions of the theory have less symmetry than the Lagrangian describing the theory.

In order to perform perturbative calculations in such theories it is necessary (or at least convenient) to "fix the gauge", which leads to results for physical quantities, such as the mass of particles, which apparently depend 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.

Tassos Vladikas has collected a nice set of photos (pdf document, 156MB download - will have some scary Google Drive warning about being too big to scan for viruses, it's clean....) of the PhD students and staff from that time for a reunion that took place in 2018.

## 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