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Quantum chains and regularisation of quantum dynamics
KTH, School of Engineering Sciences (SCI), Applied Physics. Univ Ulm, Inst Quantenphys, D-89069 Ulm, Germany.;KTH, Royal Inst Technol, Phys Dept, Stockholm, Sweden.;HUT, Lab Computat Engn, Espoo, Finland..
2018 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 93, no 10, article id 104002Article in journal (Refereed) Published
Abstract [en]

We argue that the origin of ultraviolet divergences in quantum field theory (QFT) may be not in the perturbative expansion, but in the fact that, mathematically, the Heisenberg equations of motion are not properly defined. Divergences similar to those in QFT are shown to exist in seemingly simple quantum problems with parametric Hamiltonians. These divergences may be suppressed by formally replacing the system in question by a quantum chain. The latter is a dynamically regularised system specified by two postulates, imposing conditions on its response properties. The kinematical postulate specifies the linear response, the dynamical postulate extends it to nonlinear dynamics. The kinematical postulate uniquely determines the mathematical environment (quantisation with indefinite metric), hence the term. Using the Klein-Gordon, Gupta-Bleuler and Dirac fields as examples we show that the concept of quantum chain generalises seamlessly to relativistic quantum fields. Perspectives of using quantum chains as regularisation devices in QFT are discussed.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2018. Vol. 93, no 10, article id 104002
Keywords [en]
quantum dynamics, divergences and regularisations, quantum field theory, response theory
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-234559DOI: 10.1088/1402-4896/aad5ffISI: 000442724800001Scopus ID: 2-s2.0-85054012445OAI: oai:DiVA.org:kth-234559DiVA, id: diva2:1249406
Note

QC 20180919

Available from: 2018-09-19 Created: 2018-09-19 Last updated: 2018-10-16Bibliographically approved

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