University:
Boston University
Course:
CAS PY 211 | General Physics I
Academic year:

2024
Views:

458

Pages:

21
Author:

Deja Hood

Conserving Color Charge Noether’s Theorem Symmetry ↔ Conserved Quantity Noether’s Theorem Symmetry ↔ Conserved Quantity Gauge Symmetry Charge U(1) Electric charge SU(3) Color charge Electric Charge Electric Charge Electric Charge Noether’s Theorem Electric Charge Charge-current density jμ = j0 + ~j. ∫︀ Total charge Q = j0d3x. Noether’s Theorem Electric Charge Charge-current density jμ = j0 + ~j. ∫︀ Total charge Q = j0d3x. Noether Theorem: ∂μ jμ = 0. d Q dt = 0. Color Charge Noether’s Theorem Color Charge Current for color charge? Noether’s Theorem Color Charge Current for color charge? conservation of red conservation of blue conservation of green Currents • Electric Charge • Color Charge ∂ μ jμ = 0 ∂ μ ja μ = 0 Currents • Electric Charge • Color Charge ∂ μ jμ = 0 ∂ μ ja μ = 0 Question: How does Jaμ relate to red, blue, and green? Claims • Noether’s theorem does not show conservation of red, blue, and green. Claims • Noether’s theorem does not show conservation of red, blue, and green. • Noether’s theorem does show conservation of a relational quantity of combinations of color and anti-color. Scalar Electrodynamics charged scalar ﬁeld LE = Dμ ϕ(Dμ ϕ)∗ − mϕϕ∗ Scalar Electrodynamics charged scalar ﬁeld LE = Dμ ϕ(Dμ ϕ)∗ − mϕϕ∗ • ϕ is a matter ﬁeld • Dμ = ∂μ + iqAμ Scalar Electrodynamics Noether’s Theorem LE = Dμ ϕ(Dμ ϕ)∗ − mϕϕ∗ jμ = iq(ϕ∗ Dμ ϕ − ϕ(Dμ ϕ)∗ ) Scalar Electrodynamics Noether’s Theorem jμ = iq(ϕ∗ Dμ ϕ − ϕ(Dμ ϕ)∗ ) Q= ∫︁ d3xj0 . Scalar Electrodynamics Noether’s Theorem jμ = iq(ϕ∗ Dμ ϕ − ϕ(Dμ ϕ)∗ ) Q= ∫︁ d3xj0 . Q gives total amount of electric charge. Scalar Electrodynamics Interactions LE = Dμ ϕ(Dμ ϕ)∗ − mϕϕ∗