The Mathematics of the Casimir Effect - School of Mathematical ...

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The Casimir Effect Making Sense of Infinity - Infinity Conclusion Making (Physical) Sense of Infinity History Quantum Electrodynamics Zero-Point Energy Shift The zero-point energy shifts due to a restricted geometry In the presence of the boundary E discrete = ∑ n E 0,n is a sum over discrete energies E 0,n = 1 2 ω n In the absence of a boundary ∫ E = 2V The difference of the infinite zero-point energies is finite! ∆E = E discrete − E = − π2 c L 2 720 d 3 for a box of size L × L × d with d ≪ L E 0 ( ⃗ k) d 3 k (2π) 3 Thomas Prellberg The Mathematics of the Casimir Effect
The Casimir Effect Making Sense of Infinity - Infinity Conclusion Making (Physical) Sense of Infinity History Quantum Electrodynamics Zero-Point Energy Shift The zero-point energy shifts due to a restricted geometry In the presence of the boundary E discrete = ∑ n E 0,n is a sum over discrete energies E 0,n = 1 2 ω n In the absence of a boundary ∫ E = 2V The difference of the infinite zero-point energies is finite! ∆E = E discrete − E = − π2 c L 2 720 d 3 for a box of size L × L × d with d ≪ L E 0 ( ⃗ k) d 3 k (2π) 3 Thomas Prellberg The Mathematics of the Casimir Effect
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Page 5 and 6: Topic Outline The Casimir Effect Ma
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Page 27 and 28: Spectral Theory The Casimir Effect
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The Casimir Effect Making Sense of
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Outline The Casimir Effect Making S
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Conclusion The Casimir Effect Makin
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Conclusion The Casimir Effect Makin
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Zeta Function Regularisation Regula
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