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The energy of a system of relativistic massless bosons bound by oscillator pair potentials
Institution:1. Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montréal, Québec H3G 1M8, Canada;2. Institut für Hochenergiephysik, Österreichische Akademie der Wissenschaften, Nikolsdorfergasse 18, A-1050 Wien, Austria;3. Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, A-1090 Wien, Austria;1. Medical Device Research Institute, School of Computer Science, Engineering and Mathematics, Flinders University, Adelaide, Australia;2. Trinity Centre for Bioengineering, University of Dublin, Trinity College, Dublin, Ireland;1. Discipline of Chemical Engineering, School of Engineering, Monash University Malaysia, Jalan Lagoon Selatan, Bandar Sunway, Selangor Darul Ehsan 47500, Malaysia;2. School of Resources and Civil Engineering, Northeastern University, Wenhua Road, Heping District, Shenyang 110819, China;3. School of Natural and Built Environment, Faculty of Science, Engineering and Computing, Kingston University, London, UK;4. Department of Civil Engineering, Monash University, 23 College Walk, Clayton 3800, Victoria, Australia;5. School of Civil and Resource Engineering, University of Science and Technology Beijing, Xueyuan Road, Haidian District, Beijing 100083, China;6. College of Engineering, Swansea University, Bay Campus, Swansea SA1 8EN, Wales, UK;1. The Dow Chemical Company, Core R&D, Midland, MI 48674, USA;2. Dow Electronic Materials, Hwasung, South Korea;1. Laboratory for Biomedical Photonics, Institute of Laser Engineering, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China;2. Laboratory for Advanced Laser Technology and Applications, Institute of Laser Engineering, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China;3. Department of Bioengineering, Imperial College London, London SW7 2AZ, United Kingdom;4. Key Laboratory of Trans-scale Laser Manufacturing Technology, Ministry of Education, China;5. Beijing Engineering Research Center of Laser Technology, Beijing, China;1. Nanotechnology Department, School of Advanced Technologies, Iran University of Science and Technology, Tehran, Iran;2. Biomaterials and Tissue Engineering Research Group, Department of Interdisciplinary Technologies, Breast Cancer Research Center, Motamed Cancer Institute, ACECR, Tehran, Iran;3. Department of Mechanical Engineering (BK21 Four), College of Engineering, Kyung Hee University, Yongin, Republic of Korea;1. Department of Chemistry, Renmin Hospital of Wuhan University, Hubei Key Lab on Organic and Polymeric Optoelectronic Materials, Wuhan University, Wuhan, 430072, People''s Republic of China;2. Central Laboratory, Scientific Research Department, Renmin Hospital of Wuhan University, Wuhan, 430060, People''s Republic of China;3. Shenzhen Key Laboratory of New Information Display and Storage Materials, College of Materials Science and Engineering, Shenzhen University, Shenzhen, 518060, People''s Republic of China;4. Changjiang Institute of Technology, Wuhan, 430212, People''s Republic of China
Abstract:We study the lowest energy E of a semirelativistic system of N identical massless bosons with Hamiltonian H=i=1Npi2+j>i=1Nγ|rirj|2,γ>0. We prove AγN2(N−1)21/3⩽E⩽BγN2(N−1)21/3, where A=2.33810741 and B=811/3=2.3447779. The average of these bounds determines E with an error less than 0.15% for all N⩾2.
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