  We present a new approach for investigating quantum effects in laser-driven
plasma. Unlike the modelling strategies underpinning particle-in-cell codes
that include the effects of quantum electrodynamics, our new field theory
incorporates multi-particle effects from the outset. Our approach is based on
the path-integral quantisation of a classical bi-scalar field theory describing
the behaviour of a laser pulse propagating through an underdense plasma.
Results established in the context of quantum field theory on curved spacetime
are used to derive a non-linear, non-local, effective field theory that
describes the evolution of the laser-driven plasma due to quantum fluctuations.
As the first application of our new theory, we explore the behaviour of
perturbations to fields describing a uniform, monochromatic, laser beam
propagating through a uniform plasma. Our results suggest that quantum
fluctuations could play a significant role in the evolution of an underdense
plasma driven by an x-ray laser pulse.
