The pioneering work of early non-relativistic quantum theory led to the understanding that quantum dynamics on Hilbert space is a comprehensive predictive framework for microscopic phenomena. From the Bohr atom, through the nonrelativistic quantum theory of Schrödinger and Heisenberg, and the relativistic Dirac equation for hydrogen, agreement between calculation and experiment improved rapidly...

I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the ‘naive’ quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is to...

We discuss shuffle identities between Feynman graphs using the Hopf algebra structure of perturbative quantum field theory. For concrete exposition, we discuss vertex function in massless Yukawa theory.

The construction of a relativistic quantum field is still an open problem for fields in spacetime dimension d ≥ 4. The conceptual difficulty that sometimes led to fear an incompatibility between nontrivial quantum systems and special relativity has however been solved in the case of dimension d = 2, 3 although, so far, has not influenced the corresponding debate on the foundations of quantum me...