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Quantum Vacuum on the Worldline

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Magnetic Step.<br />

D = 3<br />

3/2 4π<br />

eB Leff(x)<br />

−0.2<br />

−0.4<br />

−0.6<br />

The <str<strong>on</strong>g>Quantum</str<strong>on</strong>g> <str<strong>on</strong>g>Vacuum</str<strong>on</strong>g><br />

<strong>Worldline</strong> Approach<br />

<strong>Worldline</strong> applicati<strong>on</strong>s<br />

0<br />

m=0, set A<br />

m=0, set B<br />

m=0, set C<br />

1/2<br />

m=0.5 B0 , set A<br />

1/2<br />

m=0.5 B0 , set B<br />

1/2<br />

m=0.5 B0 , set C<br />

Generalized Heisenberg-Euler Effective Acti<strong>on</strong>s<br />

Casimir Effect<br />

N<strong>on</strong>perturbative <strong>Worldline</strong> Dynamics<br />

−0.8<br />

−2 −1 0 1 2<br />

x √ eB<br />

Holger Gies <str<strong>on</strong>g>Quantum</str<strong>on</strong>g> <str<strong>on</strong>g>Vacuum</str<strong>on</strong>g> <strong>on</strong> <strong>the</strong> <strong>Worldline</strong><br />

(HG,LANGFELD’01)<br />

HE limit

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