{"id": "card_maxwell_gauge_charge", "kind": "reference", "title": "U(1) gauge symmetry → conservation of charge", "body": "Electromagnetism is the U(1) gauge theory, and by Noether its symmetry gives conservation of electric charge - the continuity equation d(rho)/dt + div J = 0 is built into Maxwell's equations. The symmetry IS the source of the conserved charge.", "source": {"label": "Narrow Highway — Maxwell's equations", "url": "", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "maxwell", "bands": ["maxwell", "pillar", "gauge_charge", "one map"], "subject": "U(1) gauge symmetry → conservation of charge", "connections": [{"to_card_id": "card_floor_maxwells_equations", "relationship": "part_of", "evidence": "a pillar of the electromagnetic unification (U(1) gauge symmetry → conservation of charge)"}, {"to_card_id": "card_floor_noethers_theorem", "relationship": "connects_at", "evidence": "the U(1) gauge symmetry -> conserved charge, via Noether's theorem"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.maxwell", "facets": {"subject": ["gauge_charge", "one map", "pillar"]}, "presentation": {"glyph": "•", "kind_label": "maxwell", "by": "Narrow Highway — Maxwell's equations", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_maxwells_equations", "title": "Maxwell's equations — the first unification", "relationship": "part of", "why": "a pillar of the electromagnetic unification (U(1) gauge symmetry → conservation of charge)", "href": "/card/card_floor_maxwells_equations", "resolved": true}, {"id": "card_floor_noethers_theorem", "title": "Noether's theorem — symmetry is the source of conservation", "relationship": "connects at", "why": "the U(1) gauge symmetry -> conserved charge, via Noether's theorem", "href": "/card/card_floor_noethers_theorem", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_maxwell_gauge_charge", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_maxwell_gauge_charge"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}