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1 year ago in Physics , Theoretical Physics By Ezra

What is V–A theory and why are weak interactions short-ranged?

In the lab, we never "see" a wavefunction. A measurement is a specific, irreversible physical interaction that amplifies a quantum property into a classical record. For instance, to measure a photon's polarization, I send it through a birefringent crystal that routes it based on that property to one of two distinct, macroscopic detectors. The "collapse" is our updating of knowledge upon seeing which detector clicks. From a practical standpoint, decoherence the entanglement of the quantum system with the vast number of degrees of freedom in the detector and environment is what makes this record definite and irreversible. We then read that classical environment.

While studying the Standard Model's development, the V-A theory stands out as a historic milestone. I understand it's a chiral, parity-violating theory. However, the explanation for the force's short range typically jumps to the massive W/Z bosons from later gauge theory. I'm trying to understand what, if anything, in the old V-A current-current formulation itself hints at or necessitates this short-range character.

WeakInteraction VA_Theory

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By Sara Answered 11 months ago

This is an excellent insight. The original V-A theory, like Fermi's earlier theory, was a contact interaction: the four-fermion currents interacted at a single spacetime point. In quantum field theory, such a point-like vertex in the Lagrangian is mathematically equivalent to the propagator of a force-carrying boson having no momentum dependence which only occurs if the boson's mass is infinite. An infinite-mass mediator cannot propagate, resulting in zero range. So, the V-A structure itself didn't create the short range; rather, its contact-interaction form was the symptom of assuming an effectively instantaneous, point-like force, which later gauge theory corrected by introducing the massive, finite-range W and Z bosons.

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What is V–A theory and why are weak interactions short-ranged?

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