In recent decades, quantum field theory (QFT) has become the framework for
several basic and outstandingly successful physical theories. Indeed, it has
become the lingua franca of entire branches of physics and even mathematics.
The universal scope of QFT opens fascinating opportunities for philosophy.
Accordingly, although the philosophy of physics has been dominated by the
analysis of quantum mechanics, relativity and thermo-statistical physics,
several philosophers have recently undertaken conceptual analyses of QFT.
One common feature of these analyses is the emphasis on rigorous approaches,
such as algebraic and constructive QFT; as against the more heuristic and
physical formulations of QFT in terms of functional (also knows as: path)
integrals.
However, I will follow the example of some recent mathematicians such as
Atiyah, Connes and Kontsevich, who have adopted a remarkable pragmatism and
opportunism with regard to heuristic QFT, not corseted by rigor (as Connes
remarks). I will conceptually discuss the advances that have marked
heuristic QFT, by analysing some of the key ideas that accompanied its
development. I will also discuss the interactions between these concepts in
the various relevant fields, such as particle physics, statistical
mechanics, gravity and geometry.