Path integrals with discarded degrees of freedom

Publication date: Available online 3 December 2018Source: Physics Letters AAuthor(s): Luke M. ButcherAbstractWhenever variables ϕ=(ϕ1,ϕ2,…) are discarded from a system, and the discarded information capacity S(x) depends on the value of an observable x, a quantum correction ΔVeff(x) appears in the effective potential [1]. Here I examine the origins and implications of ΔVeff within the path integral, which I construct using Synge's world function. I show that the ϕ variables can be ‘integrated out’ of the path integral, reducing the propagator to a sum of integrals over observable paths x(t) alone. The phase of each path is equal to the semiclassical action (divided by ħ) including the same correction ΔVeff as previously derived. This generalises the prior results beyond the limits of the Schrödinger equation; in particular, it allows us to consider discarded variables with a history-dependent information capacity S=S(x,∫tf(x(t′))dt′). History dependence does not alter the formula for ΔVeff.

Source: Physics Letters A - December 4, 2018 Category: Physics Source Type: research