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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 massive bosons is exponentially suppressed by their mass, and the W and Z bosons are quite heavy. You don't notice it as an actual classical force at scales where you could meaningfully talk about "flux" or "current".

However, the concepts of "charge" and "voltage", in some way, generalize. Voltage is just the (difference in the) potential of the electric field, and thus, relativistically, the time-component of the four-potential of electrodynamics. The concept of four-potential immediately generalizes to the weak force, where it then is no longer real-number-valued, but $\mathrm{SU}(2)$-matrix-valued. Much like the electromagnetic four-potential contains the creation operators for photons, the weak four-potential contains the creation operators for W and Z bosons.

"Charge", instead of being a positive or negative multiple of the elementary charge of quarks, would be more akin to spin (since both spin and weak numbers arise from the representation theory of the symmetry group $\mathrm{SU}(2)$), and hence you get particles with "half-integer total weak charge" and "directional weak charges" which can, in any spatial direction, take a value between + and - their total weak charge.

However, much like color is not an observablecolor is not an observable, this directional weak charge would likewise be unobservable because the weak gauge transformations freely change it.

There's little influence of electromagnetic fields on radioactive decay because, at our scales, the electroweak interaction is broken into the electromagnetic and weak force. The electroweak scale where they begin to merge again lies somewhere on the order of hundreds of $\textrm{GeV}$, and I'm pretty sure you don't reach an energy scale like that just by applying "strong" magnetic fields - afaik, the only processes this highly energetic are incoming cosmic rays and our own particle colliders.

In conclusion, I think there is, on the level of the quantities you mention, no useful analogy between the electromagnetic and the weak or electroweak force.

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 massive bosons is exponentially suppressed by their mass, and the W and Z bosons are quite heavy. You don't notice it as an actual classical force at scales where you could meaningfully talk about "flux" or "current".

However, the concepts of "charge" and "voltage", in some way, generalize. Voltage is just the (difference in the) potential of the electric field, and thus, relativistically, the time-component of the four-potential of electrodynamics. The concept of four-potential immediately generalizes to the weak force, where it then is no longer real-number-valued, but $\mathrm{SU}(2)$-matrix-valued. Much like the electromagnetic four-potential contains the creation operators for photons, the weak four-potential contains the creation operators for W and Z bosons.

"Charge", instead of being a positive or negative multiple of the elementary charge of quarks, would be more akin to spin (since both spin and weak numbers arise from the representation theory of the symmetry group $\mathrm{SU}(2)$), and hence you get particles with "half-integer total weak charge" and "directional weak charges" which can, in any spatial direction, take a value between + and - their total weak charge.

However, much like color is not an observable, this directional weak charge would likewise be unobservable because the weak gauge transformations freely change it.

There's little influence of electromagnetic fields on radioactive decay because, at our scales, the electroweak interaction is broken into the electromagnetic and weak force. The electroweak scale where they begin to merge again lies somewhere on the order of hundreds of $\textrm{GeV}$, and I'm pretty sure you don't reach an energy scale like that just by applying "strong" magnetic fields - afaik, the only processes this highly energetic are incoming cosmic rays and our own particle colliders.

In conclusion, I think there is, on the level of the quantities you mention, no useful analogy between the electromagnetic and the weak or electroweak force.

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 massive bosons is exponentially suppressed by their mass, and the W and Z bosons are quite heavy. You don't notice it as an actual classical force at scales where you could meaningfully talk about "flux" or "current".

However, the concepts of "charge" and "voltage", in some way, generalize. Voltage is just the (difference in the) potential of the electric field, and thus, relativistically, the time-component of the four-potential of electrodynamics. The concept of four-potential immediately generalizes to the weak force, where it then is no longer real-number-valued, but $\mathrm{SU}(2)$-matrix-valued. Much like the electromagnetic four-potential contains the creation operators for photons, the weak four-potential contains the creation operators for W and Z bosons.

"Charge", instead of being a positive or negative multiple of the elementary charge of quarks, would be more akin to spin (since both spin and weak numbers arise from the representation theory of the symmetry group $\mathrm{SU}(2)$), and hence you get particles with "half-integer total weak charge" and "directional weak charges" which can, in any spatial direction, take a value between + and - their total weak charge.

However, much like color is not an observable, this directional weak charge would likewise be unobservable because the weak gauge transformations freely change it.

There's little influence of electromagnetic fields on radioactive decay because, at our scales, the electroweak interaction is broken into the electromagnetic and weak force. The electroweak scale where they begin to merge again lies somewhere on the order of hundreds of $\textrm{GeV}$, and I'm pretty sure you don't reach an energy scale like that just by applying "strong" magnetic fields - afaik, the only processes this highly energetic are incoming cosmic rays and our own particle colliders.

In conclusion, I think there is, on the level of the quantities you mention, no useful analogy between the electromagnetic and the weak or electroweak force.

    Bounty Ended with 50 reputation awarded by WalyKu
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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 massive bosons is exponentially suppressed by their mass, and the W and Z bosons are quite heavy. You don't notice it as an actual classical force at scales where you could meaningfully talk about "flux" or "current".

However, the concepts of "charge" and "voltage", in some way, generalize. Voltage is just the (difference in the) potential of the electric field, and thus, relativistically, the spatial parttime-component of the four-potential of electrodynamics. The concept of four-potential immediately generalizes to the weak force, where it then is no longer real-number-valued, but $\mathrm{SU}(2)$-matrix-valued. Much like the electromagnetic four-potential contains the creation operators for photons, the weak four-potential contains the creation operators for W and Z bosons.

"Charge", instead of being a positive or negative multiple of the elementary charge of quarks, would be more akin to spin (since both spin and weak numbers arise from the representation theory of the symmetry group $\mathrm{SU}(2)$), and hence you get particles with "half-integer total weak charge" and "directional weak charges" which can, in any spatial direction, take a value between + and - their total weak charge.

However, much like color is not an observable, this directional weak charge would likewise be unobservable because the weak gauge transformations freely change it.

There's little influence of electromagnetic fields on radioactive decay because, at our scales, the electroweak interaction is broken into the electromagnetic and weak force. The electroweak scale where they begin to merge again lies somewhere on the order of hundreds of $\textrm{GeV}$, and I'm pretty sure you don't reach an energy scale like that just by applying "strong" magnetic fields - afaik, the only processes this highly energetic are incoming cosmic rays and our own particle colliders.

In conclusion, I think there is, on the level of the quantities you mention, no useful analogy between the electromagnetic and the weak or electroweak force.

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 massive bosons is exponentially suppressed by their mass, and the W and Z bosons are quite heavy. You don't notice it as an actual classical force at scales where you could meaningfully talk about "flux" or "current".

However, the concepts of "charge" and "voltage", in some way, generalize. Voltage is just the (difference in the) potential of the electric field, and thus, relativistically, the spatial part of the four-potential of electrodynamics. The concept of four-potential immediately generalizes to the weak force, where it then is no longer real-number-valued, but $\mathrm{SU}(2)$-matrix-valued. Much like the electromagnetic four-potential contains the creation operators for photons, the weak four-potential contains the creation operators for W and Z bosons.

"Charge", instead of being a positive or negative multiple of the elementary charge of quarks, would be more akin to spin (since both spin and weak numbers arise from the representation theory of the symmetry group $\mathrm{SU}(2)$), and hence you get particles with "half-integer total weak charge" and "directional weak charges" which can, in any spatial direction, take a value between + and - their total weak charge.

However, much like color is not an observable, this directional weak charge would likewise be unobservable because the weak gauge transformations freely change it.

There's little influence of electromagnetic fields on radioactive decay because, at our scales, the electroweak interaction is broken into the electromagnetic and weak force. The electroweak scale where they begin to merge again lies somewhere on the order of hundreds of $\textrm{GeV}$, and I'm pretty sure you don't reach an energy scale like that just by applying "strong" magnetic fields - afaik, the only processes this highly energetic are incoming cosmic rays and our own particle colliders.

In conclusion, I think there is, on the level of the quantities you mention, no useful analogy between the electromagnetic and the weak or electroweak force.

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 massive bosons is exponentially suppressed by their mass, and the W and Z bosons are quite heavy. You don't notice it as an actual classical force at scales where you could meaningfully talk about "flux" or "current".

However, the concepts of "charge" and "voltage", in some way, generalize. Voltage is just the (difference in the) potential of the electric field, and thus, relativistically, the time-component of the four-potential of electrodynamics. The concept of four-potential immediately generalizes to the weak force, where it then is no longer real-number-valued, but $\mathrm{SU}(2)$-matrix-valued. Much like the electromagnetic four-potential contains the creation operators for photons, the weak four-potential contains the creation operators for W and Z bosons.

"Charge", instead of being a positive or negative multiple of the elementary charge of quarks, would be more akin to spin (since both spin and weak numbers arise from the representation theory of the symmetry group $\mathrm{SU}(2)$), and hence you get particles with "half-integer total weak charge" and "directional weak charges" which can, in any spatial direction, take a value between + and - their total weak charge.

However, much like color is not an observable, this directional weak charge would likewise be unobservable because the weak gauge transformations freely change it.

There's little influence of electromagnetic fields on radioactive decay because, at our scales, the electroweak interaction is broken into the electromagnetic and weak force. The electroweak scale where they begin to merge again lies somewhere on the order of hundreds of $\textrm{GeV}$, and I'm pretty sure you don't reach an energy scale like that just by applying "strong" magnetic fields - afaik, the only processes this highly energetic are incoming cosmic rays and our own particle colliders.

In conclusion, I think there is, on the level of the quantities you mention, no useful analogy between the electromagnetic and the weak or electroweak force.

2 silly typo
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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 massive bosons is exponentially suppressed by their mass, and the W and Z bosons are quite heavy. You don't notice it as an actual classical force at scales where you could meaningfully talk about "flux" or "current".

However, the concepts of "charge" and "voltage", in some way, generalize. Voltage is just the (difference in the) potential of the electric field, and thus, relativistically, the spatial part of the four-potential of electrodynamics. The concept of four-potential immediately generalizes to the weak force, where it then is no longer real-number-valued, but $\mathrm{SU}(2)$-matrix-valued. Much like the electromagnetic four-potential contains the creation operators for photons, the weak four-potential contains the creation operators for W and Z bosons.

"Charge", instead of being a positive or negative multiple of the elementary charge of quarks, would be more akin to spin (since both spin and weak numbers arise from the representation theory of the symmetry group $\mathrm{SU}(2)$), and hence you get particles with "half-integer total weak charge" and "directional weak charges" which can, in any spatial direction, take a value between + and - their total weak charge.

However, much like color is not an observable, this directional weak charge would likewise be unobservable because the weak gauge transformations freely change it.

There's little influence of electromagnetic fields on radioactive decay because, at our scales, the electroweak interaction is broken into the electromagnetic and strongweak force. The electroweak scale where they begin to merge again lies somewhere on the order of hundreds of $\textrm{GeV}$, and I'm pretty sure you don't reach an energy scale like that just by applying "strong" magnetic fields - afaik, the only processes this highly energetic are incoming cosmic rays and our own particle colliders.

In conclusion, I think there is, on the level of the quantities you mention, no useful analogy between the electromagnetic and the weak or electroweak force.

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 massive bosons is exponentially suppressed by their mass, and the W and Z bosons are quite heavy. You don't notice it as an actual classical force at scales where you could meaningfully talk about "flux" or "current".

However, the concepts of "charge" and "voltage", in some way, generalize. Voltage is just the (difference in the) potential of the electric field, and thus, relativistically, the spatial part of the four-potential of electrodynamics. The concept of four-potential immediately generalizes to the weak force, where it then is no longer real-number-valued, but $\mathrm{SU}(2)$-matrix-valued. Much like the electromagnetic four-potential contains the creation operators for photons, the weak four-potential contains the creation operators for W and Z bosons.

"Charge", instead of being a positive or negative multiple of the elementary charge of quarks, would be more akin to spin (since both spin and weak numbers arise from the representation theory of the symmetry group $\mathrm{SU}(2)$), and hence you get particles with "half-integer total weak charge" and "directional weak charges" which can, in any spatial direction, take a value between + and - their total weak charge.

However, much like color is not an observable, this directional weak charge would likewise be unobservable because the weak gauge transformations freely change it.

There's little influence of electromagnetic fields on radioactive decay because, at our scales, the electroweak interaction is broken into the electromagnetic and strong force. The electroweak scale where they begin to merge again lies somewhere on the order of hundreds of $\textrm{GeV}$, and I'm pretty sure you don't reach an energy scale like that just by applying "strong" magnetic fields - afaik, the only processes this highly energetic are incoming cosmic rays and our own particle colliders.

In conclusion, I think there is, on the level of the quantities you mention, no useful analogy between the electromagnetic and the weak or electroweak force.

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 massive bosons is exponentially suppressed by their mass, and the W and Z bosons are quite heavy. You don't notice it as an actual classical force at scales where you could meaningfully talk about "flux" or "current".

However, the concepts of "charge" and "voltage", in some way, generalize. Voltage is just the (difference in the) potential of the electric field, and thus, relativistically, the spatial part of the four-potential of electrodynamics. The concept of four-potential immediately generalizes to the weak force, where it then is no longer real-number-valued, but $\mathrm{SU}(2)$-matrix-valued. Much like the electromagnetic four-potential contains the creation operators for photons, the weak four-potential contains the creation operators for W and Z bosons.

"Charge", instead of being a positive or negative multiple of the elementary charge of quarks, would be more akin to spin (since both spin and weak numbers arise from the representation theory of the symmetry group $\mathrm{SU}(2)$), and hence you get particles with "half-integer total weak charge" and "directional weak charges" which can, in any spatial direction, take a value between + and - their total weak charge.

However, much like color is not an observable, this directional weak charge would likewise be unobservable because the weak gauge transformations freely change it.

There's little influence of electromagnetic fields on radioactive decay because, at our scales, the electroweak interaction is broken into the electromagnetic and weak force. The electroweak scale where they begin to merge again lies somewhere on the order of hundreds of $\textrm{GeV}$, and I'm pretty sure you don't reach an energy scale like that just by applying "strong" magnetic fields - afaik, the only processes this highly energetic are incoming cosmic rays and our own particle colliders.

In conclusion, I think there is, on the level of the quantities you mention, no useful analogy between the electromagnetic and the weak or electroweak force.

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