The well-established formulation of string theory is Polyakov’s Euclidean path integral, which is based on perturbation theory. Although it has already been well-understood, not much is known about its Minkowskian version. In this talk, we derive the Minkowskian path integral equivalent to Polyakov’s Euclidean path
integral for critical closed string theory. Remarkably, the Minkowskian path integral automatically realises a causal structure. For the non-perturbative formulation of superstring theory, we then obtain a matrix model from the Minkowskian path integral for the type IIB superstring, maintaining the stringy causality, which results in a “causal” matrix model.