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arXiv:1506.00497quant-ph

Avoiding Ultraviolet Divergence by Means of Interior-Boundary Conditions

Stefan Teufel, Roderich Tumulka

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Abstract

We describe here a novel way of defining Hamiltonians for quantum field theories (QFTs), based on the particle-position representation of the state vector and involving a condition on the state vector that we call an "interior-boundary condition." At least for some QFTs (and, we hope, for many), this approach leads to a well-defined, self-adjoint Hamiltonian without the need for an ultraviolet cut-off or renormalization.

arXiv comments
18 pages LaTeX, 2 figures; presentation given at the conference "Quantum Mathematical Physics" in Regensburg (Germany), Sept. 29-Oct. 2, 2014 (http://www.uni-regensburg.de/Fakultaeten/nat_Fak_I/qft2014/index.html)
Journal reference
Pages 293-311 in Felix Finster, Johannes Kleiner, Christian Röken, and Jürgen Tolksdorf (editors), Quantum Mathematical Physics - A Bridge between Mathematics and Physics. Basel: Birkhäuser (2016)
DOI
doi:10.1007/978-3-319-26902-3_14
Subjects
quant-phQuantum Physics math-phMathematical Physics

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Linked by 1 identifiable commenter in 4 comments across 4 threads, from Jul 2016 to Jul 2023.

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Discussed in comments4 threads

  1. A physicist who bets that gravity can’t be quantized 1 comment

    • Here are a some papers: Avoiding Ultraviolet Divergence by Means of Interior-Boundary Conditions https://arxiv.org/abs/1506.00497 This is perhaps the first of the papers and so may be a good place to start. Bohmian Trajectories for Hamiltonians with Interior-Boundary Condition…

      jostylrView on HNParent context

  2. Why don't more physicists subscribe to pilot wave theory? 1 comment

    • There are various versions, but the one I recommend to date loses determinism (that was never the point) and allows for annihilation and creation of particles: https://arxiv.org/abs/quant-ph/0208072 In addition, the ideas of Bohmian mechanics has led to a new direction in…

      jostylrView on HNParent context

  3. How Schrödinger’s Cat Became Such a Violent Fable 1 comment

    • It is all a matter of what you want out of science. Some people, such as myself, enjoy having a narrative about how the universe works consistent with experiments. This is both satisfying and useful in finding new directions to push or ways to solve problems (such as a recent…

      jostylrView on HNParent context

  4. Has Physics Gotten Something Really Important Really Wrong? 1 comment

    • Why do you say that? There are adaptations that have creation and annihilation of particles in Bohmian mechanics: http://arxiv.org/abs/quant-ph/0303156 The main issue is that QFT does not generate a mathematically well-defined evolution of the wave function, but there are…

      jostylrView on HNParent context

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