{"id":"W4287373071","doi":"10.48550/arxiv.2101.10118","title":"Lagrangian and Hamiltonian Formulation of Classical Electrodynamics\\n without Potentials","year":2021,"lang":"","type":"preprint","venue":"arXiv (Cornell University)","topic":"Quantum and Classical Electrodynamics","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia, Okanagan Campus","funders":"","keywords":"Hamiltonian (control theory); Nabla symbol; Mathematical physics; Phase space; Lagrangian; Physics; Poisson bracket; Lagrange multiplier; Gauss; Constraint algorithm; Maxwell's equations; Classical mechanics; Mathematics; Quantum mechanics; Omega","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002808218,0.0007636992,0.001255588,0.000254359,0.0003283632,0.0001705745,0.0005613791,0.0006185868,0.0001731234],"category_scores_gemma":[0.00002166854,0.0009116522,0.0007418953,0.0007267523,0.0004178497,0.0004058907,0.000677341,0.001224029,0.00001662166],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002543813,"about_ca_system_score_gemma":0.0006072755,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003554097,"about_ca_topic_score_gemma":0.0004460227,"domain_scores_codex":[0.9962758,0.0003219425,0.0007165077,0.001608845,0.0001956541,0.000881281],"domain_scores_gemma":[0.9972274,0.0001500051,0.0008337314,0.0009457745,0.0004217742,0.0004212995],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0005201462,0.001090166,0.04908006,0.0004303875,0.001326953,0.00007408868,0.000406321,0.03421062,0.01509621,0.892837,0.00001980352,0.00490825],"study_design_scores_gemma":[0.002011553,0.0003572128,0.02485517,0.0003040561,0.001277388,0.000005998416,0.0006677513,0.9256716,0.0009771913,0.0425095,0.0002449923,0.001117569],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8308602,0.0001030611,0.1663009,0.0001308143,0.0002294889,0.0004681718,0.00009678863,0.0000390162,0.001771591],"genre_scores_gemma":[0.9967577,0.0004045059,0.0002431847,0.00002837008,0.0001960742,0.000001602643,0.0004267427,0.00007110547,0.001870658],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.891461,"threshold_uncertainty_score":0.9993334,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02031516321061016,"score_gpt":0.1815321368933561,"score_spread":0.1612169736827459,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}