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Theoretical physicists love symmetries and very few assumptions to describe Nature. For example, people knew there is "some force" that attracts an apple from the tree and there exists "a force" that binds moon to earth. But Newton realized they are the same force and their motions are described by same simple law which is called law of gravity. This is the ...

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There is no analogy of "voltage", "current", "charge" or "flux" to electromagnetism for the weak force, at least none that would be helpful. The reason for this is that all of these are classical concepts, while the notion of the weak force is completely quantum. Taking the classical limit just makes it vanish because the classical force law of forces with ...

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Are there analogs to resistance, inductance, capacitance, and memristance connecting the weak force to electromagnetism? Yes, but not the way you're thinking. Take a look at weak interaction on Wikipedia and note this: "The first type is called the 'charged-current interaction' because it is mediated by particles that carry an electric charge (the W+ ...

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The scalar potential of your theory is $$V(\phi) = \lambda (\phi^a \phi^a - v^2)^2,$$ where I suspect you meant to take the square as I've written here. This potential is minimized when $\sqrt{\phi^a \phi^a} = v$. Think of $\phi=\frac{1}{2} \phi^a \sigma^a$ as a vector with components $\phi^a$ in a 3-dimensional vector space with basis vectors $\sigma_a/2$. ...

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