Fields, Geometry and Physical Reality

I seek a 3-year post-doctoral position to be held at Mathematics (DAMTP), Cambridge, to assess philosophically the geometry of field theories, both classical and quantum. Most of the budget would be for salary; a small proportion would be for organizing conferences and outreach. The strategic opportunity: It has long been recognized that quantum field theory (QFT) dominates our view of the physical world; and that classical field theory underpins it, conceptually and technically. That is reason enough to seek a philosophical analysis of field theories. But it is now especially timely to analyze their geometric aspects. For in the last 40 years, there has been a veritable revolution in understanding field theories, both classical and quantum, in terms of geometry. Yet the philosophical literature on QFT has so far ignored these aspects---presenting philosophy with virgin territory. I propose as three main themes for this project, the philosophical aspects of: (C): The classical geometric underpinning of QFT; (S): Topological Solitons; (D): Duality transformations. To give just one example: a soliton is, in short, a complex 'woven' structure of field and-or space itself that acts in various ways like a particle. So what are the implications for traditional philosophical categories like substance, individuation and persistence through time? The core output will be scholarly articles by the appointee, guided by my experience in the philosophy of physics. He/she will also present the results in courses, in conferences and in outreach activities. I see this project as the first part of a larger one: to revive the philosophy of geometry. The 19th century revolution in geometry had a profound influence on philosophy, through such figures as Reichenbach. But philosophers have yet to reflect on the last several decades' developments in geometry, especially in relation to QFT. So here lies a golden opportunity.