Question 1: However, in order for a well-defined ________ operator to exist, one must introduce a new field, the gauge field, which also transforms in order for the local change of variables (the phase in our example) not to affect the derivative.

Question 2: These are precisely the relations obeyed by the ladder operators for an infinite set of independent ________, one for each single-particle state.

Question 6: Unfortunately, it proved extraordinarily difficult to show that any realistic field theory, including the ________, satisfied these axioms.

Question 7: Over the past several decades, there have been many attempts to put quantum field theory on a firm mathematical footing by formulating a set of ________ for it.

Question 9: For example, a quantum theory of the ________must be a quantum field theory, because it is impossible (for various reasons) to define a wavefunction for a single photon.

Question 10: From the point of view of quantum field theory, particles are identical ________ they are excitations of the same underlying quantum field.