  This paper defines a complexity between states in quantum field theory by
introducing a Finsler structure based on ladder operators (the generalization
of creation and annihilation operators). Two simple models are shown as
examples to clarify the differences between complexity and other conceptions
such as complexity of formation and entanglement entropy. When it is applied
into thermofield double (TFD) states in $d$-dimensional conformal field theory,
results show that the complexity density between them and corresponding vacuum
states are finite and proportional to $T^{d-1}$, where $T$ is the temperature
of TFD state. Especially, a proof is given to show that fidelity susceptibility
of a TFD state is equivalent to the complexity between it and corresponding
vacuum state, which gives an explanation why they may share the same object in
holographic duality. Some enlightenments to holographic conjectures of
complexity are also discussed.
