The Mathematics of the Casimir Effect - School of Mathematical ...
The Mathematics of the Casimir Effect - School of Mathematical ...
The Mathematics of the Casimir Effect - School of Mathematical ...
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<strong>The</strong> <strong>Casimir</strong> <strong>Effect</strong><br />
Making Sense <strong>of</strong> Infinity - Infinity<br />
Conclusion<br />
Quantisation <strong>of</strong> <strong>the</strong> Field<br />
History<br />
Quantum Electrodynamics<br />
Zero-Point Energy Shift<br />
Each harmonic oscillator can be in a discrete state <strong>of</strong> energy<br />
(<br />
E m ( ⃗ k) = m + 1 )<br />
ω with ω = c|<br />
2<br />
⃗ k|<br />
Interpretation: m photons with energy ω and momentum ⃗ k<br />
In particular, <strong>the</strong> ground state energy 1 2ω is non-zero!<br />
This leads to a zero-point energy density <strong>of</strong> <strong>the</strong> field<br />
∫<br />
E<br />
V = 2<br />
E 0 ( ⃗ k) d 3 k<br />
(2π) 3<br />
(factor 2 due to polarisation <strong>of</strong> <strong>the</strong> field)<br />
Caveat: this quantity is infinite...<br />
Thomas Prellberg<br />
<strong>The</strong> <strong>Ma<strong>the</strong>matics</strong> <strong>of</strong> <strong>the</strong> <strong>Casimir</strong> <strong>Effect</strong>
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