A Fock space representation is given for the quantum Lorentz gas, i.e., for random Schrödinger operators of the form H(ω)=p2+Vω=p2+∑ φ(x−xj(ω)), acting in ℋ=L2(Rd), with Poisson distributed xjs. An operator H is defined in 𝒦=ℋ⊗𝒫=ℋ⊗L2(Ω,P(dω))=L2(Ω,P(dω);ℋ) by the action of H(ω) on its fibers in a direct integral decomposition. The stationarity of the Poisson process allows a unitarily equivalent description in terms of a new family {H(k)‖k∈Rd}, where each H(k) acts in 𝒫 [A. Tip, J. Math. Phys. 35, 113 (1994)]. The space 𝒫 is then unitarily mapped upon the symmetric Fock space over L2(Rd,ρdx), with ρ the intensity of the Poisson process (the average number of points xj per unit volume; the scatterer density), and the equivalent of H(k) is determined. Averages now become vacuum expectation values and a further unitary transformation (removing ρ in ρdx) is made which leaves the former invariant. The resulting operator HF(k) has an interesting structure: On the nth Fock layer we encounter a single particle moving in the field of n scatterers and the randomness now appears in the coefficient √ρ in a coupling term connecting neighboring Fock layers. We also give a simple direct self-adjointness proof for HF(k), based upon Nelson’s commutator theorem. Restriction to a finite number of layers (a kind of low scatterer density approximation) still gives nontrivial results, as is demonstrated by considering an example.