The Wightman axioms give requirements for these things, which have infinitely many degrees of freedom. For 10 points each:
[10m] Name these things that permeate space and are characterized by their Lagrangian density, such as in the Klein–Gordon equation. Particles arise from excitations in these things.
ANSWER: fields [or quantum fields]
[10h] Haag’s theorem argues that quantum field theories are ill-formed because these representations cannot exist. In this representation, both states and operators are time-dependent.
ANSWER: interaction picture [accept, but DO NOT REVEAL, Dirac picture]
[10e] This originator of quantum field theory names a relativistic generalization of the Schrödinger equation. This British physicist’s namesake delta function is infinite at the origin and vanishes everywhere else.
ANSWER: Paul Dirac [accept Dirac equation or Dirac delta function]
<Indiana A, Physics>