BCS as Foundation and Inspiration: The Transmutation of Symmetry

The BCS theory injected two powerful ideas into the collective consciousness of theoretical physics: pairing and spontaneous symmetry breaking. In the 50 years since the seminal work of Bardeen, Cooper, and Schrieffer, those ideas have found important use in areas quite remote from the stem application to metallic superconductivity. This is a brief and eclectic sketch of some highlights, emphasizing relatively recent developments in QCD and in the theory of quantum statistics, and including a few thoughts about future directions. A common theme is the importance of symmetry {\it transmutation}, as opposed to the simple {\it breaking} of electromagnetic $U(1)$ symmetry in classic metallic superconductors.Comment: 25 pages, 4 figures. Contribution to "Fifty Years of Bardeen, Cooper, and Schrieffer'', to be published by World Scientific. Also to appear in IJMP

Radical Conservatism and Nucleon Decay

Unification of couplings, observation of neutrino masses in the expected range, and several other considerations confirm central implications of straightforward gauge unification based on SO(10) or a close relative and incorporating low-energy supersymmetry. The remaining outstanding consequence of this circle of ideas, yet to be observed, is nucleon instability. Clearly, we should aspire to be as specific as possible regarding the rate and form of such instability. I argue that not only esthetics, but also the observed precision of unification of couplings, favors an economical symmetry-breaking (Higgs) structure. Assuming this, one can exploit its constraints to build reasonably economical, overconstrained yet phenomenologically viable models of quark and lepton masses. Putting it all together, one arrives at reasonably concrete, hopeful expectations regarding nucleon decay. These expectations are neither ruled out by existing experiments, nor hopelessly inaccessible.Comment: LaTeX, 14 pages, 4 figures; moved reference, corrected typo, improved two figure

Unification of Force and Substance

Maxwell's mature presentation of his equations emphasized the unity of electromagnetism and mechanics, subsuming both as "dynamical systems". That intuition of unity has proved both fruitful, as a source of pregnant concepts, and broadly inspiring. A deep aspect of Maxwell's work is its use of redundant potentials, and the associated requirement of gauge symmetry. Those concepts have become central to our present understanding of fundamental physics, but they can appear to be rather formal and esoteric. Here I discuss two things: The physical significance of gauge invariance, in broad terms; and some tantalizing prospects for further unification, building on that concept, that are visible on the horizon today. If those prospects are realized, Maxwell's vision of the unity of field and substance will be brought to a new level.Comment: Talk at Royal Society Symposium, "Unifying Physics and Technology in the Light of Maxwell's Equations", November 2015. 26 pages, no figure

Opportunities, Challenges, and Fantasies in Lattice QCD

Some important problems in quantitative QCD will certainly yield to hard work and adequate investment of resources, others appear difficult but may be accessible, and still others will require essentially new ideas. Here I identify several examples in each class.Comment: 10 pages, 2 figures; Keynote talk at Lattice 2002, Boston, June 2002. (Text unchanged; figure formatting corrected.) Email correspondence to [email protected]

Emergent Majorana Mass and Axion Couplings in Superfluids

Axions (in the general sense) may acquire qualitatively new couplings inside superfluids. Their conventional couplings to fermions, in empty space, involve purely imaginary masses; the new couplings involve emergent Majorana masses. The possibility of weak links for axions, recently put forward, is analyzed, rejected, and replaced with a non-local analogue.Comment: 10 pages, no figures. v2: Additional comment on non-local Josephson effects, additional expository remark

From "Not Wrong" to (Maybe) Right

This is a short, light spirited account of how some possibly important science actually happened. It very much conflicts with Popper's contention that the key to scientific progress is falsification.Comment: This is, in essence, a solicited "Turning Points" feature written for Nature. It appeared, in a slightly abbreviated form, in the March 18 issu