University Physics V · Conservation Laws and Particle Reactions · 19.04

Electric charge, global U(1) phase, and superselection

Invariance under ψ → exp(i q α) psi gives a Noether current satisfying d_μ j^μ = 0, that is d(ρ)/dt + div j = 0, so the volume-integrated charge operator obeys [H, Q] = 0.

Course-map guide · not a complete lesson or simulation

Scope & orientation

What this subsection covers

Invariance under ψ → exp(i q α) psi gives a Noether current satisfying d_μ j^μ = 0, that is d(ρ)/dt + div j = 0, so the volume-integrated charge operator obeys [H, Q] = 0.

A strong response uses feynman diagrams with labelled vertices and states where the model stops being reliable.

Reasoning checklist

Evidence, assumptions and limits

Assumptions to state

State the system, observable, approximation, and conditions held fixed before using a model.

Evidence to collect

What endpoint energy does a calibrated spectrum from a sealed beta source support, and how much energy per decay is unaccounted for if nothing but an electron leaves?

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What endpoint energy does a calibrated spectrum from a sealed beta source support, and how much energy per decay is unaccounted for if nothing but an electron leaves? Useful evidence includes an energy calibration from a conversion-electron line such as Bi-207 or Cs-137, a background-subtracted spectrum, a Kurie fit with an interval on the endpoint compared with the tabulated Q value, and detector resolution and backscatter named as the limit that blocks any neutrino-mass claim.

Limits to state

This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus.

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This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus. It is written for a four-credit course of roughly three lecture hours plus two to three laboratory or computational hours a week across fifteen weeks, and it is deliberately more mathematical than University Physics I–IV: linear algebra and differential equations are working tools here, not background. Twenty units are mapped against a suggested fifteen-week delivery, so several units share a teaching week. Departments differ widely in how much formalism they expect at this stage; follow your institution's published scope, notation, laboratory programme, and assessment rules. A result should be checked against units, signs, limiting cases, and the conditions under which its model was derived.

Diagram & examples

Work the claim before choosing an equation

Interactive concept map

Follow the model from claim to evidence.

01 · Physical claimElectric charge, global U(1) phase, and superselection

Invariance under ψ → exp(i q α) psi gives a Noether current satisfying d_μ j^μ = 0, that is d(ρ)/dt + div j = 0, so the volume-integrated charge operator obeys [H, Q] = 0.

Read the complete note

Invariance under ψ → exp(i q α) psi gives a Noether current satisfying d_μ j^μ = 0, that is d(ρ)/dt + div j = 0, so the volume-integrated charge operator obeys [H, Q] = 0. Gauging the phase, α → α(x), ties exact conservation to a massless photon, and charge is superselected, so no physical state superposes different Q. Limits on electron decay beyond 1e28 years are the experimental test.

02 · RepresentationThe subsection's claim

Model, evidence, and boundary

03 · TestPrediction before measurement

What must be stated before selecting an equation for Electric charge, global U(1) phase, and superselection?

04 · Evidence & boundaryDecide, then qualify

What endpoint energy does a calibrated spectrum from a sealed beta source support, and how much energy per decay is unaccounted for if nothing but an electron leaves?

Read the complete note

Interactive diagram for Electric charge, global U(1) phase, and superselection: follow the physical claim through its representation, proposed test, evidence, and model boundary.

modelModel, evidence, and boundary turns the stated idea into a representation that can make a prediction.

Example questions

Try the reasoning before revealing the structure.

Diagram check

What must be stated before selecting an equation for Electric charge, global U(1) phase, and superselection?

Quick check

Test the reasoning, not recall

What must be stated before selecting an equation for Electric charge, global U(1) phase, and superselection?

Choose an answer to test the model.