U(1), SU(2), SU(3) are symmetry of what?

In summary, the Standard Model symmetries of U(1), SU(2), and SU(3) are symmetries of the action, or equivalently, the Lagrangian. They are not symmetries of spacetime. These symmetries are expected to survive in both special and general relativity as they are gauge symmetries that are independent of the underlying spacetime. There is a diffeomorphic invariant version of the path integral for particle physics that uses these symmetry groups, where the Lagrangian remains the same but with the substitution of the spacetime metric.
  • #1
friend
1,452
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The Standard Model symmetries are U(1), SU(2), and SU(3). But I'm not sure whether these are symmetries of the Action intgral or if they are symmetries of the background spacetime.
 
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  • #2
They are symmetries of the action, or equivalently, the Lagrangian. They are not symmetries of spacetime.
 
  • #3
Fredrik said:
They are symmetries of the action, or equivalently, the Lagrangian. They are not symmetries of spacetime.

Are these symmetries expected to survive in GR as well as in SR?
 
  • #4
Yes, they are gauge symmetries that have nothing to do with the underlying spacetime.
 
  • #5
Ben Niehoff said:
Yes, they are gauge symmetries that have nothing to do with the underlying spacetime.

So is there a diffeomorphic invariant version of the path integral for particle physics that uses the U(1), SU(2), and SU(3) symmetry groups?
 
  • #6
friend said:
So is there a diffeomorphic invariant version of the path integral for particle physics that uses the U(1), SU(2), and SU(3) symmetry groups?

The Lagrangian is exactly the same; just replace [itex]\eta_{\mu\nu}[/itex] with [itex]g_{\mu\nu}[/itex].
 

1. What is the significance of U(1), SU(2), and SU(3) in physics?

In physics, U(1), SU(2), and SU(3) are known as gauge symmetries. They describe the fundamental interactions between particles, such as electromagnetism, weak nuclear force, and strong nuclear force. These symmetries are essential in understanding the behavior of particles and the laws of nature.

2. How do U(1), SU(2), and SU(3) relate to the Standard Model of particle physics?

The Standard Model is a theory that describes the fundamental particles and their interactions. U(1), SU(2), and SU(3) are three of the symmetries that are incorporated into the Standard Model to explain the behavior of particles and their interactions. These symmetries are crucial in predicting and understanding the properties of particles.

3. Can you give an example of a system that exhibits U(1) symmetry?

One example of a system that exhibits U(1) symmetry is the behavior of an electron in a magnetic field. The laws of electromagnetism, described by U(1) symmetry, govern the movement and behavior of the electron in the magnetic field.

4. What is the difference between U(1), SU(2), and SU(3) symmetries?

The main difference between U(1), SU(2), and SU(3) symmetries lies in their mathematical structures. U(1) is a 1-dimensional symmetry, SU(2) is a 2-dimensional symmetry, and SU(3) is a 3-dimensional symmetry. They also correspond to different fundamental interactions and have different representations in the Standard Model.

5. Are there any real-world applications of U(1), SU(2), and SU(3) symmetries?

Yes, these symmetries have numerous real-world applications, particularly in the field of particle physics and quantum physics. They are crucial in understanding the behavior of particles and interactions, as well as in the development of new technologies such as particle accelerators and quantum computers.

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