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Lapidus
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Why is there no gauge symmetry for spin-1/2 fields?
Has gauge symmetry to be related to spin-1 fields/ particles?
thanks
Has gauge symmetry to be related to spin-1 fields/ particles?
thanks
Last edited:
Well, that's true. The massive spin 1/2 field doesn't possesses gauge invariance, just global U(1) invariance.Lapidus said:Thanks for the answering so far.
I assumed that there is no gauge symmetry for spin-1/2 fields, since it is never mentioned in the textbooks.
Lapidus said:Gauge symmetry just always comes into play when spin-1 particles/fields are introduced.
That's wrong!dextercioby said:Well, that's true. The massive spin 1/2 field doesn't possesses gauge invariance, just global U(1) invariance.
tom.stoer said:That's wrong!
I said that this has nothing to do with the mass of the fermion fields.dextercioby said:The massive spin 1/2 field doesn't possesses gauge invariance, just global U(1) invariance.
Yes, as I said, you have to introduce the covariant derivative.dextercioby said:I've just addressed this post I assumed that there is no gauge symmetry for spin-1/2 fields, since it is never mentioned in the textbooks. Gauge symmetry just always comes into play when spin-1 particles/fields are introduced.
Could you agree?dextercioby + tom said:The kinetic term of the spin 1/2 field doesn't possesses gauge invariance (just a global invariance) w/o introducing spin 1 gauge fields.
tom.stoer said:What about the following:
The kinetic term of the spin 1/2 field doesn't possesses gauge invariance (just a global invariance) w/o introducing spin 1 gauge fields.
Could you agree?
No, the mass term already has local gauge invariance, but of course this is useless w/o the kinetic term. Or let's say it the other way round: introducing local gauge invariance changes the kinetic term, but not the mass term.dextercioby said:the same can be said about a mass term.
tom.stoer said:No, the mass term already has local gauge invariance, but of course this is useless w/o the kinetic term.
tom.stoer said:Or let's say it the other way round: introducing local gauge invariance changes the kinetic term, but not the mass term.
Gauge symmetry for spin 1/2 fields is a fundamental concept in quantum field theory. It refers to the mathematical framework used to describe the behavior of spin 1/2 particles, such as electrons, in a quantum field. Essentially, it means that the physical laws governing these particles are unchanged if certain transformations, known as gauge transformations, are applied to them. This symmetry is crucial in understanding the behavior of elementary particles and the forces between them.
The Standard Model is the most widely accepted theory for describing the fundamental particles and forces in our universe. It is built upon the principles of gauge symmetry, specifically the principles of local gauge invariance. This means that the laws of physics are the same at every point in space and time, and that the particles and forces interact through the exchange of gauge bosons, which are particles associated with the various symmetries in the model.
Gauge symmetry is important because it provides a framework for understanding the fundamental interactions between particles and the forces that govern their behavior. It allows us to describe the behavior of particles in a consistent and mathematically elegant way. Additionally, it has been crucial in the development of the Standard Model and other theories in particle physics.
While gauge symmetry plays a fundamental role in our understanding of particle physics, it is not considered to be a fundamental symmetry of the universe. This is because it is a mathematical concept used to describe the behavior of particles, rather than an inherent property or law of the universe itself. However, its importance in our current understanding of the universe cannot be overstated.
The principles of gauge symmetry have been applied in a wide range of fields, including quantum mechanics, electromagnetism, and particle physics. In addition to its theoretical importance, gauge symmetry has also led to practical applications such as the development of technologies like transistors and lasers. It also plays a crucial role in the development of new materials with unique properties, such as superconductors and topological insulators.