Based on general and minimal properties of the {\it discrete} circuit
complexity, we define the complexity in {\it continuous} systems in a
geometrical way. We first show that the Finsler metric naturally emerges in the
geometry of the complexity in continuous systems. Due to fundamental symmetries
of quantum field theories, the Finsler metric is more constrained and
consequently, the complexity of SU(n) operators is uniquely determined as a
length of a geodesic in the Finsler geometry. Our Finsler metric is
bi-invariant contrary to the right-invariance of discrete qubit systems. We
clarify why the bi-invariance is relevant in quantum field theoretic systems.
After comparing our results with discrete qubit systems we show most results in
k-local right-invariant metric can also appear in our framework. Based on the
bi-invariance of our formalism, we propose a new interpretation for the
Schr\"{o}dinger's equation in isolated systems - the quantum state evolves by
the process of minimizing "computational cost."Comment: Published version; added a short introduction on Finsler geometr
