In this note we formulate the Kalman-YakuboviE-Popov Lemma for generalized first-order systems, both in continuousand discrete-time.

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The conventional path integral expression for the Yang-Mills transition amplitude with flat measure and gauge-fixing built in via the Faddeev-Popov method has been claimed to fall short of guaranteeing gauge invariance in the nonperturbative regime. We show, however, that it yields the gauge invariant partition function where the projection onto gauge invariant wave functions is explicitly perf...

Kalman–Yakubovich–Popov (KYP). The very historical heritage of our field is at war. Do we need a new proof?

A Popov criterion is derived for systems with slowly timevarying parameters. The parameters and their time derivatives are assumed to take values in convex polytopes.