Abstract
Diffieties are analogues of algebraic varieties for partial differential equations. They are a kind of (generally, infinite-dimensional) manifolds supplied with an infinite-order contact structure. Secondary, or more speculatively, “quantized” calculus arises as a sort of differential calculus over filtered smooth function algebras on diffieties that respects the contact structure. This paper, written as an informal introduction and invitation to Secondary Calculus, is an account of the author's attempt to understand what should be the analogue of the Schrödinger equation for quantum field theory. So, more attention is paid to motivations than to exact constructions and formulas.
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