interaction process (as, e.g., captured in the interaction operator ˆ G defined in Sec. III) one can consider incoming and outgoing particles to be on-shell sufficiently far outside the interaction area [25]. Multiple particle states can be straightforwardly introduced as members of a Fock space over the Hilbert space of position states | x ; λ 〉 . First, in order to allow for multiparticle states with different types of particles, extend the position state of each individual particle with a particle type index n , such that Then, construct a basis for the Fock space of multiparticle states as symmetrized products of N single particle states: where the sum is over all permutations P of 1 , 2 , . . . , N . (When including Fermions, one needs to, of course, antisymmetrize rather than symmetrize the products [26].) It is then convenient to introduce a creation field operator ˆ ψ $^{†}$( x, n ; λ ) such that with the corresponding annihilation field ˆ ψ ( x, n ; λ ) having the commutation relation Further, define so that Identifying the field operators ˆ ψ ( x, n ; λ$_{0}$ ) and ˆ ψ ( x, n ) defined here with ˆ ψ ( n ) 0 ( x ) and ˆ ψ ( n $^{)}$( x ) defined in Sec. III then completes the grounding of the formalism used in the main text. [1] R. B. Griffiths, J. Stat. Phys. 36 , 219 (1984). 34 [ ˆ ψ ( x $^{′}$, n$^{′}$; λ ) , ˆ ψ $^{†}$( x, n ; λ$_{0}$ )] = δ$_{n}$ ′ $_{n}$Δ( x ′ − x ; λ − λ$_{0}$ ) . ˆ ψ ( x, n ) ≡ ∫ ∞ λ 0 d λ ˆ ψ ( x, n ; λ ) , [ ˆ ψ ( x $^{′}$, n$^{′}$) , ˆ ψ $^{†}$( x, n ; λ$_{0}$ )] = δ n ′ Δ( x ′ − x ) . ˆ ψ $^{†}$( x, n ; λ ) | x$_{1}$, n$_{1}$, λ$_{1}$ ; . . . ; x$_{N}$ , n$_{N}$, λ$_{N}$ 〉 = | x, n, λ ; x$_{1}$, n$_{1}$, λ$_{1}$ ; . . . ; x$_{N}$ , n$_{N}$, λ$_{N}$ 〉 , | x$_{1}$, n$_{1}$, λ$_{1}$ ; . . . ; x$_{N}$, n$_{N}$, λ$_{N}$ 〉 ≡ ( N !) − 1 / 2 ∑ perms P | x$_{P}$$_{1}$, n$_{P}$$_{1}$ ; λ$_{P}$$_{1}$ 〉 · · · | x$_{P}$$_{N}$, n$_{P}$$_{N}$ ; λ$_{P}$$_{N}$ 〉 , 〈 x $^{′}$, n$^{′}$; λ | x, n ; λ 〉 = δ$_{n}$ ′ $_{n}$δ $^{4}$( x ′ − x ) .