  In this lecture, a limited introduction of gauge invariance in phase-space is
provided, predicated on canonical transformations in quantum phase-space. Exact
characteristic trajectories are also specified for the time-propagating Wigner
phase-space distribution function: they are especially simple - indeed,
classical - for the quantized simple harmonic oscillator. This serves as the
underpinning of the field theoretic Wigner functional formulation introduced.
Scalar field theory is thus reformulated in terms of distributions in field
phase-space. This is a pedagogical selection from work published in J Phys A32
(1999) 771 and Phys Rev D58 (1998) 025002, reported at the Yukawa Institute
Workshop "Gauge Theory and Integrable Models", 26-29 January, 1999.
