DBI Analysis of Open String Bound States on Non-compact D-branes
DBI Analysis of Open String Bound States on Non-compact D-branes
DBI Analysis of Open String Bound States on Non-compact D-branes
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7.1.4 Perturbed equati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> moti<strong>on</strong> . . . . . . . . . . . . . . . . . . . 897.1.5 Soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> the PDE . . . . . . . . . . . . . . . . . . . . . . . . . 897.2 D1-brane <strong>on</strong> the trumpet . . . . . . . . . . . . . . . . . . . . . . . . . . 917.2.1 Metric and acti<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . 927.2.2 Classical soluti<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . 927.2.3 Adding perturbati<strong>on</strong>s . . . . . . . . . . . . . . . . . . . . . . . . 937.2.4 Perturbed equati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> moti<strong>on</strong> . . . . . . . . . . . . . . . . . . . 947.2.5 Soluti<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> the PDE . . . . . . . . . . . . . . . . . . . . . . . . . 948 Computati<strong>on</strong>s 968.1 Metric and field strength . . . . . . . . . . . . . . . . . . . . . . . . . . . 968.2 Classical soluti<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 978.3 Field strength variati<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . 988.4 Regularized Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . 998.5 Equati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> moti<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1018.6 Road to differential equati<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . 1018.7 Differential equati<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1028.8 Hypergeometric equati<strong>on</strong>? . . . . . . . . . . . . . . . . . . . . . . . . . . 1039 C<strong>on</strong>clusi<strong>on</strong> & Final Thoughts 105Bibliography 107List <str<strong>on</strong>g>of</str<strong>on</strong>g> Abbreviati<strong>on</strong>s 109iii