Interpreting Mathematics in Physics: Charting the Applications of SU(2) in 20th Century Physics
Abstract
The role mathematics plays within physics has been of sustained interest for physicists as well as for philosophers and historians of science. We explore this topic by tracing the role the mathematical structure associated with SU(2) has played in three key episodes in 20th century physics  intrinsic spin, isospin, and gauge theory and electroweak unification. We also briefly consider its role in loop quantum gravity. Each episode has led to new physical notions of a space other than the traditional ones of space and spacetime, and each has had associated with it a complex and in places, contested history. The episodes also reveal ways mathematical structures provide resources for new physical theorizing and we propose our study as a contribution to a need Roger Penrose has identified to develop a "profoundly sensitive aesthetic" sense for locating physically relevant mathematics.
 Publication:

arXiv eprints
 Pub Date:
 May 2006
 DOI:
 10.48550/arXiv.physics/0605012
 arXiv:
 arXiv:physics/0605012
 Bibcode:
 2006physics...5012A
 Keywords:

 Physics  History of Physics
 EPrint:
 19 pages