The modal-Hamiltonian interpretation and the Galilean covariance of quantum mechanics |
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| Authors: | Olimpia Lombardi Mario Castagnino Juan Sebastián Ardenghi |
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| Affiliation: | 1. CONICET-Universidad de Buenos Aires, Crisólogo Larralde 3440, 1430, Buenos Aires, Argentina;2. CONICET-IAFE-Universidad de Buenos Aires, Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires, Argentina;1. Center for Theoretical Physics and Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;2. Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada;3. Dept. of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA;1. Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Straße 9, D-48149 Münster, Germany;2. DESY, D-15738 Zeuthen, Germany;3. Institut für Physik und Astronomie, Universität Potsdam, D-14476 Potsdam, Germany;4. II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany;1. Institiute of Socio, Arts and Sciences, The University of Tokushima, 1-1 Minamijosanjimacho Tokushima city, Tokushima, 770-8502, JAPAN;2. Research Center for Nuclear Physics, Osaka University, 10-1 Mihogaoka Ibaraki city, Osaka, 567-0042, JAPAN;3. Graduate School and Faculty of Human Environment, Osaka Sangyo University, 3-1-1 Nakagaito, Daito, Osaka, 574-8530, Japan;4. Research Center for Neutrino Science, Tohoku University 6-3, Aramaki Aza Aoba,Aobaku Sendai,Miyagi,980-8578, JAPAN;5. I.S.C. Lab., 7-7-20 Saito Asagi Ibaraki City, 567-0085 Osaka, JAPAN;6. Kavli Institute for the Physics and Mathematics of the Universe, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan |
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| Abstract: | The aim of this paper is to analyze the modal-Hamiltonian interpretation of quantum mechanics in the light of the Galilean group. In particular, it is shown that the rule of definite-value assignment proposed by that interpretation has the same properties of Galilean covariance and invariance as the Schrödinger equation. Moreover, it is argued that, when the Schrödinger equation is invariant, the rule can be reformulated in an explicitly invariant form in terms of the Casimir operators of the Galilean group. Finally, the possibility of extrapolating the rule to quantum field theory is considered. |
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