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Free classical particles have well-defined momentum and position, while freequantum particles have well-defined momentum but a position fully delocalizedover the sample volume. We develop a many-body formalism based on wave-packetoperators that connects these two limits, the thermal energy being distributedbetween the state spatial extension and its thermal excitation. Thecorresponding `mixed quantum-classical' states, which render the Boltzmannoperator diagonal, are the physically relevant states when the temperature isfinite. The formulation of many-body Hamiltonians in terms of these thermallyexcited wave-packets and the resulting effective scatterings is provided.

Many-body formalism for thermally excited wave-packets: A way to connect the quantum regime to the classical regime