  A way to construct Boltzmann entropy, i.e., the entropy as a function of a
microscopic pure state, for quantum field systems is proposed. Operators that
shift the field in wavevector space are used in the construction. By employing
an assumption, it is shown that, for almost all states in the ensemble of pure
states corresponding to a thermodynamic state, the value of the proposed
Boltzmann entropy coincides with that of the thermodynamic entropy for the
thermodynamic state. For general self-interacting fields, the Boltzmann entropy
evolves with time under Hamiltonian dynamics, so that it is capable of
characterizing the thermalization of isolated quantum field systems.
