A Complexity for Quantum Field Theory and Application in Thermofield Double States

Run-Qiu Yang

Published 2017-09-04Version 1

This paper defines a complexity between states in quantum field theory by introducing a Finsler structure based on created and annihilated operators. Two simple models are computed as examples and to clarify the differences between complexity and other conceptions such as complexity of formation and entanglement entropy. When it is applied into thermofield double state, result shows the complexity between it and corresponding vacuum state is finite and proportional to $T^{d-1}$ in $d$-dimensional conformal field. Some enlightenments to holographic conjectures of complexity are also discussed.