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Understanding Bosons and Chiral Symmetry in Quantum Mechanics

Exploring the interplay of particles and forces, focusing on bosons and chiral symmetry in quantum mechanics, with emphasis on quarks, spinors, and transformations in internal spaces. Discusses properties characterized by single values, global uniform changes, and local transformations.

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Understanding Bosons and Chiral Symmetry in Quantum Mechanics

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  1. Particles and Forces

  2. Bosons

  3. Chiral For m=0 the helicity and the chirality are the same. The form of the spinor for m=0 maintains the strict relationship between the spin direction and the action of the gamma-5 matrix. In the limit of quark mass 0 there is a chiral symmetry for quarks

  4. U(1) • Define a property characterized by a single value. • E.G. Objects color • Change it uniformally (globally) without changing physics • Change is QM change of phase

  5. SU(2) • Mixture of two things • Same as misture of spin ½ z-components • Equivalent to a rotation in a internal 3-4 space. • Changes the direction of the axis of quantization.

  6. Local • Transformation depends on position

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