Symmetry and conservation

In summary: Therefore, the symmetry for the strong force is SU(3).In summary, the connection between symmetry and conservation is that for different forces, there are different conserved quantities and corresponding symmetries. For the electromagnetic force, the conserved quantity is charge and the symmetry is the phase of the wave. For the electroweak force, the conserved quantities are weak isospin and weak hypercharge and the symmetry is invariance under SU(2) \times U(1)_{ Y }. For the strong force, the conserved quantity is the "colour charge" and the symmetry is invariance under SU(3).
  • #1
newphy
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I am trying to understand the connection between symmetry and conservation.

For the electromagnetic force, the conserved quantity is charge, the corresponding symmetry is the phase of the wave and the force carrier is the photon.
For the electroweak force, the conserved quantities are the weak isospin and the weak hypercharge (for the weak and em forces) and the force carriers are the W+, W- and Z0. What is the corresponding symmetry?
Same question for the strong force. The conserved quantity is the Isospin and the force carrier is the gluon. What is the symmetry corresponding to this force?

Thanks
 
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  • #2
newphy said:
I am trying to understand the connection between symmetry and conservation.

For the electromagnetic force, the conserved quantity is charge, the corresponding symmetry is the phase of the wave and the force carrier is the photon.
Which is the invariace under [itex]SO(2)=U(1)[/itex] rotation.

For the electroweak force, the conserved quantities are the weak isospin and the weak hypercharge (for the weak and em forces) and the force carriers are the W+, W- and Z0. What is the corresponding symmetry?
Invariance under [itex]SU(2) \times U(1)_{ Y }[/itex].

Same question for the strong force. The conserved quantity is the Isospin and the force carrier is the gluon. What is the symmetry corresponding to this force?

Thanks

Not Iso-spin. The invariance under "rotation" in the 3-dimensional Colour space, which form the group [itex]SU(3)_{ C }[/itex], leads to 8 conserved quantities (called the colour charges) to which the 8-gluons get coupled.
 

1. What is symmetry?

Symmetry is a concept that refers to a balanced arrangement of parts or elements. In science, symmetry can be found in various forms, such as geometric shapes, molecular structures, and physical laws.

2. How is symmetry related to conservation laws?

Symmetry is closely related to conservation laws in physics. Conservation laws state that certain physical properties, such as energy, momentum, and charge, remain constant in a closed system. Symmetry principles, such as translational symmetry and rotational symmetry, are used to derive and explain these conservation laws.

3. Can symmetry be broken?

Yes, symmetry can be broken in certain situations. This is known as spontaneous symmetry breaking, where a system that appears symmetric at first glance exhibits an asymmetrical behavior. This phenomenon is observed in various physical systems, such as magnets and superconductors.

4. What is the role of symmetry in the laws of nature?

Symmetry plays a crucial role in the laws of nature. Many fundamental laws, such as the laws of thermodynamics, quantum mechanics, and general relativity, are based on symmetry principles. These principles provide insight into the fundamental nature of the universe and help scientists understand and predict its behavior.

5. How does symmetry impact our daily lives?

Symmetry is present in many aspects of our daily lives, from the shapes of objects we encounter to the laws of nature that govern our world. For example, symmetry is important in art and design, as it is often considered aesthetically pleasing. In technology, symmetry is utilized in the design of bridges, buildings, and other structures to ensure structural stability.

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