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Stochastic bosonization for a \(d\geq 3\) Fermi system. (English) Zbl 0874.60092

Summary: We consider a system of fermions interacting via an external field and we prove, in \(d\geq 3\), that a suitable collective operator, bilinear in the fermionic fields, in the stochastic limit becomes a boson quantum Brownian motion. The evolution operator after the limit satisfies a quantum stochastic differential equation, in which the imaginary part of the Itô correction is the ground state shift while its real part is the liftime of the ground state.

MSC:

60K40 Other physical applications of random processes
81S25 Quantum stochastic calculus
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