Measurements and electroweak gauge invariance/transformations

In summary, most gauge transformations in the standard model do not result in measurable changes. This includes coordinate transformations, SU(3) quark colours, and U(1) phase rotations for charged particles. However, this does not apply to SU(2) rotations in electroweak theory, where the interchangeable nature of quarks, flavours, electrons, and neutrinos is affected by the broken symmetry and Higgs field. In the unitary gauge, the Higgs field acquires a VeV and only one component of the left-handed lepton doublet gets a mass term. In an arbitrary gauge, the mass term can be diagonalized and the massive component is referred to as an electron by convention. It is possible to SU(
  • #1
Michael Price
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TL;DR Summary
Gauge transforms have no effect on measurements, so how can an electroweak SU(2) rotation transform an electron into a neutrino and not be observed?
Most gauge transformations in the standard model are easy to see are measurement invariant. Coordinate transformations, SU(3) quark colours, U(1) phase rotations for charged particles all result in no measurable changes. But how does this work for SU(2) rotations in electroweak theory, where quarks flavours, and electrons and neutrinos, are interchangeable? My guess is that this involves the broken nature of the symmetry and the Higgs field. Is this correct?
 
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In the unitary gauge the Higgs field acquires a VeV only in one of its components and so only one component of the left-handed lepton doublet get a mass term from the Higgs-Lepton Yukawa interaction. So I suppose in arbitrary gauge, we can always diagnolize the mass term and the massive component just gets called an electron by convention.

I suppose you could SU(2) rotate the electron into the neutrino and vice versa even after SSB, but then the Higgs field and all the Gauge fields would all get transformed and the new "neutrino" you end up with will have all the same propeties as the electron.
 
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  • #3
HomogenousCow said:
In the unitary gauge the Higgs field acquires a VeV only in one of its components and so only one component of the left-handed lepton doublet get a mass term from the Higgs-Lepton Yukawa interaction. So I suppose in arbitrary gauge, we can always diagnolize the mass term and the massive component just gets called an electron by convention.

I suppose you could SU(2) rotate the electron into the neutrino and vice versa even after SSB, but then the Higgs field and all the Gauge fields would all get transformed and the new "neutrino" you end up with will have all the same properties as the electron.
Thanks, that does indeed work. Whatever a particle gets transformed into has the properties of the original particle.
 

1. What is the significance of measurements in science?

Measurements are crucial in science as they allow us to quantify and understand the physical world around us. They provide us with accurate and objective data that can be used to make predictions, test hypotheses, and develop theories.

2. What is electroweak gauge invariance/transformations?

Electroweak gauge invariance/transformations refer to the mathematical framework used to describe the interactions between particles and their associated fields. It is based on the principle of gauge invariance, which states that the laws of physics should remain unchanged under certain transformations.

3. How does electroweak gauge invariance/transformations relate to the Standard Model of particle physics?

The Standard Model is a theory that describes the fundamental particles and their interactions. Electroweak gauge invariance/transformations are a key component of this model, as they are used to explain the behavior of the weak nuclear force and the electromagnetic force.

4. Why is gauge invariance important in electroweak interactions?

Gauge invariance is important in electroweak interactions because it ensures that the laws of physics are consistent and do not depend on the specific reference frame or gauge chosen. This allows for more accurate predictions and a deeper understanding of the underlying principles of nature.

5. How are measurements and electroweak gauge invariance/transformations connected?

Measurements play a crucial role in testing the predictions of the Standard Model, which is based on electroweak gauge invariance/transformations. By comparing experimental results to theoretical calculations, we can validate the accuracy of these concepts and further our understanding of the fundamental forces and particles in the universe.

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