Twistor integral representations of fundamental solutions of massless field equations |
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| Institution: | 1. Department of Mathematics, School of Science, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan;2. Numazu College of Technology, 3600 Ooka, Numazu-shi, Shizuoka 410, Japan;1. Institut des Sciences Analytiques – Université Claude Bernard Lyon 1, 43 Boulevard du 11 Novembre 1918, 69100, Villeurbanne, Lyon, France;2. Department of Chemistry and Industrial Chemistry – University of Pisa, via Giuseppe Moruzzi 13, 56124, Pisa, Italy;3. Institute of Clinical Physiology, Laboratory of Bioinformatics, National Research Council, via Giuseppe Moruzzi 1, 56124, Pisa, Italy;1. Department of Psychiatry and Psychology, Mayo Clinic, Rochester, MN, USA;2. Department of Health Sciences Research, Mayo Clinic, Rochester, MN, USA;3. Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden;1. Human Nutrition Research Centre, Population Health Sciences Institute, Newcastle University, Newcastle upon Tyne, UK;2. School of Sport, Exercise and Health Science, Loughborough University, Loughborough, UK;3. Department of Integrative Physiology, University of Colorado Boulder, Boulder, CO, USA;1. School of Pharmacy, Monash University Malaysia, Selangor, Malaysia;2. School of Medical Sciences, Universiti Sains Malaysia, Kelantan, Malaysia;3. Center of Pharmaceutical Outcomes Research (CPOR), Department of Pharmacy Practice, Faculty of Pharmaceutical Sciences, Naresuan University, Phitsanulok, Thailand;4. School of Pharmacy, University of Wisconsin, Madison, USA;5. School of Population Health, University of Queensland, Brisbane, Australia |
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| Abstract: | We consider the general dimensional (complex) Minkowski spaces and the extended twistor spaces. We show that the fundamental solutions of the complex wave or Laplace equations are explicitly represented by the integrals of some closed forms on the twistor spaces. The closed form is defined from labeled trees explained in graphs theory, and is written, as the cohomology class, by the linear combination of the logrithmic forms on some hyperplane configuration complement in some complex affine space. |
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