Quantum Vacuum on the Worldline

The <strong>Quantum</strong> <strong>Vacuum</strong>
Worldline Approach
Worldline applications
Worldline representation of Γ.
⊲ pedestrian approach
Γ[A] =
λ
= −
= −
∞
1/Λ 2
∞
1/Λ 2
ln λ 2 + m 2
Effective Action from Worldline Techniques
Worldline numerics
dT
T e−m2
T
Tr exp D(A) 2
T
dT
T e−m2
T
N
x(T )=x(0)
= Tr ln −(D(A)) 2 + m 2
=〈x|e iH(iT ) |x〉
Dx(τ) e −
TR “ ”
˙x 2
dτ 4 +ie ˙x·A(xτ)
0
Holger Gies <strong>Quantum</strong> <strong>Vacuum</strong> on the Worldline