Quantum Vacuum on the Worldline

The <strong>Quantum</strong> <strong>Vacuum</strong>
Worldline Approach
Worldline applications
Fermions on the worldline I.
⊲ Grassmann loops
Γ 1
spin = ln det γ µ ∂µ + ieγ µ
Aµ + m
1
= −
2(4π) D/2
∞
1/Λ 2
Generalized Heisenberg-Euler Effective Actions
Casimir Effect
Nonperturbative Worldline Dynamics
dT
T 1+D/2 e−m2
T
Lspin = 1
4 ˙x 2 + ie ˙x µ Aµ+ 1
2 ψµ ˙ψ µ − ieψ µ F µνψ ν
Holger Gies <strong>Quantum</strong> <strong>Vacuum</strong> on the Worldline
P
Dx Dψ e
A
− R T
0 dτLspin