Phase space action for minimal surfaces of any dimension in curved spacetime |
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| Affiliation: | 1. Department of Physics of Complex Systems, Eötvös Loránd University, Pázmány Péter sétány 1/a, Budapest, 1117, Hungary;2. Wigner Research Center for Physics, 29–33 Konkoly–Thege Miklos Str, Budapest, 1121, Hungary;3. Department of Programming Languages and Compilers, Eötvös Loránd University, Pázmány Péter sétány 1/a, Budapest, 1117, Hungary;4. Maxeler Technologies, a Groq company, 16192 Coastal Hwy, Lewes, 19958, DE, United States;5. Algorithmiq Ltd, Kanavakatu 3C, Helsinki, 00160, Finland;1. University of Science and Technology, Zewail City of Science and Technology, October Gardens 12578, 6th of October City, Giza, Egypt;2. Center for Photonics and Smart Materials (CPSM), Zewail City of Science and Technology, October Gardens, 6th of October City, Giza 12578, Egypt;3. Department of Physics, College of Sciences, University of Bisha, Bisha 61922, P.O. Box 344, Saudi Arabia;4. Physics Department, Faculty of Science, Al-Azhar University, 71524 Assiut, Egypt;5. Coding and Information Theory Lab, University of Ulsan, Ulsan 44610, South Korea;6. Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza 12613, Egypt;7. Deanship of Research and Graduate Studies, Applied Science University, P.O. Box 5055, 55222 Manama, Bahrain;8. Department of Applied Sciences and Mathematics, College of Arts and Sciences, Abu Dhabi University, Abu Dhabi, United Arab Emirates;9. Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX 77843, USA;10. Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt |
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| Abstract: | The phase space action, depending on coordinates, momenta and Lagrange multipliers (which turn out to be components of the induced metric), has been written down for a world sheet of arbitary dimension (a string generalized to membranes) in a curved embedding spacetime. Canonical and hamiltonian formalisms have been formulated in a covariant and general way with the true dynamical variables being separated from the redundant ones. The membrane constraints follow directly from the variation of our action; their suitable superposition gives a hamiltonian from which we derive the equations of motion for a membrane via the Poisson brackets. The same hamiltonian we obtain also in a different way from a variation of the action. For n = 2 all equations coincide with those of strings. |
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