During our QFT course this semester we’ve seen how a relatively minimal set of initial postulates about the structure of spacetime and of course the non-commutative nature of quantum observables leads almost inevitably to the framework of quantum field theory. A recent article in Quanta Magazine describes some of the remarkable results going back to the 1960s indicating that the mere combination of spin and relativistic structure predicts almost all of the particle dynamics we observe in Nature.
We’ve directly played with some of these ideas: When we define the theory of a massless spin-1 particle, we more-or-less are forced to introduce gauge invariance and a set of dynamical equations that have the same mathematical form as Maxwell’s equations. Massless spin-2 particles similarly lead to the infinitesimal or linearized form of Einstein’s equation for general relativity.
What’s truly amazing is that similar arguments reveal that the simplest interactions you can add to these free theories are once again more-or-less restricted to the ones we observe. If you want interacting spin-1 particles you are forced to introduce multiple species of them and–poof!–the theoretical structure that emerges is Yang-Mills theory, which is a generalization of Maxwell theory that describes the self interactions of gluons and very high energy weak bosons. Do the same analysis for spin-2 and you discover that the massless spin-2 particle must be unique and has to couple universally to the energy-momentum of other matter or fields.
Incidentally, these results largely explain why string theory takes the form that it does. Structures like gravity, Yang-Mills theory, and so on basically are forced on the low-energy effective approximations to the full theory, though string theory adds additional constraints that require all of these fields to be present (and others that I haven’t mentioned as well). String theory is a much more restrictive framework than general quantum field theory.
