Here is a question I have been pondering for some time. Is there a fundamental reason why there is no classical electroweak theory? Is there a factor of ħ hidden in the definition of the weak currents, for example? Of course, one might ask why anyone would consider looking for a classical theory; the standard model seems to provide whatever theoretical structure is needed. My answer is that most of the machinery that provides the foundation for physics research and engineering is based on classical electromagnetic theory. It would be difficult, for example, to design an efficient electric motor if the only theory available were quantum electrodynamics. A classical theory of the electroweak interaction might provide similar practical insight.
Of course, the coupling constant is small, and the weak currents and fields are largely confined to the nucleus by the mass of the intermediate vector bosons. However, if the coupling between the weak and electromagnetic currents does not vanish in the classical limit, then the possibility exists of observable macroscopic effects, particularly if some sort of collective behavior can be exploited. The speculative possibilities are intriguing: electromagnetic control or initiation of weak interactions, electroweak generation of electric currents for power, and so on.
Is there a possible lacuna in our current understanding of the electroweak interaction? I would be interested in knowing what the experts have to say about this.
