= Quantum-to-classical imaginary-time mapping
A local $d$-dimensional <quantum field> at finite <temperature> can often be represented by an anisotropic classical-looking <action> in $d+1$ dimensions, with a finite extra imaginary-time extent. The zero-temperature limit makes that extent infinite. A real nonnegative statistical weight is an additional requirement: fermionic signs and imaginary terms can obstruct interpretation as an ordinary classical <probability> <distribution>.
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