  Wigner-Smith (WS) time delay concepts have been used extensively in quantum
mechanics to characterize delays experienced by particles interacting with a
potential well. This paper formally extends WS time delay theory to Maxwell's
equations and explores its potential applications in electromagnetics. The WS
time delay matrix relates a lossless and reciprocal system's scattering matrix
to its frequency derivative and allows for the construction of modes that
experience well-defined group delays when interacting with the system. The
matrix' entries for guiding, scattering, and radiating systems are energy-like
overlap integrals of the electric and/or magnetic fields that arise upon
excitation of the system via its ports. The WS time delay matrix has numerous
applications in electromagnetics, including the characterization of group
delays in multiport systems, the description of electromagnetic fields in terms
of elementary scattering processes, and the characterization of frequency
sensitivities of fields and multiport antenna impedance matrices.
