Understanding Single-Value Properties and Quantum Phase Changes in Physical Systems

Dec 26, 2025

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This text defines properties characterized by a single value, such as the color of an object. It discusses uniform changes that do not alter physics, highlighting the significance of quantum phase change governed by SU(2). The concept of combining two entities is illustrated through the mixture of spin-½ z-components, which parallels rotations in internal 3-4 space. It further considers the transformation's dependency on position and explains how to rotate through 90 degrees, along with examples from weak quantum chromodynamics (QCD) and pion exchange.

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Understanding Single-Value Properties and Quantum Phase Changes in Physical Systems

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Presentation Transcript

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
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.
Local • Transformation depends on position