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synoe

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In summary, when considering spontaneous symmetry breaking in the standard model, only terms containing scalar fields are included in the Lagrangian. This is because including spinor or vector fields with nonzero expectation values would violate rotational (and Lorentz) invariance of the vacuum state. Additionally, while the vacuum expectation value of the propagator may vanish, the propagator itself does not necessarily vanish due to the presence of Lorentz indices or spinor indices.

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synoe

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Bill_K

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If a spinor or vector had a nonzero expectation value, it would single out a preferred direction. The vacuum state must be rotationally invariant (Lorentz invariant too) so this is not possible.synoe said:Why don't we have to contain spinors and vectors? I think it's related to Lorentz invariance.

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synoe

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Could you explan more formally or mathematically by using language of quantum theory?

I would like to proof [itex] \langle 0|\psi_\alpha|0\rangle=0[/itex] from Lorentz invariance of the vacuum. Your explanation seems that the vacuum expectation vales is supposed to be Lorentz invariant but I think Lorentz invariance means [itex] U^\dagger(\Lambda)|0\rangle=|0\rangle[/itex].

And another question occurred. Your explanation seems that the propagator, the vacuum expectation value of two point function also vanishes. Why propagators don't vanish even if they have Lorentz indices or spinor indices?

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samalkhaiat

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synoe said:

Could you explan more formally or mathematically by using language of quantum theory?

I would like to proof [itex] \langle 0|\psi_\alpha|0\rangle=0[/itex] from Lorentz invariance of the vacuum. Your explanation seems that the vacuum expectation vales is supposed to be Lorentz invariant but I think Lorentz invariance means [itex] U^\dagger(\Lambda)|0\rangle=|0\rangle[/itex].

And another question occurred. Your explanation seems that the propagator, the vacuum expectation value of two point function also vanishes. Why propagators don't vanish even if they have Lorentz indices or spinor indices?

See post#35 in

www.physicsforums.com/showthread.php?t=172461

Sam

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Bill_K

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Which directly is: https://www.physicsforums.com/showthread.php?p=1398896#post1398896samalkhaiat said:See post#35 in

www.physicsforums.com/showthread.php?t=172461

Spontaneous symmetry breaking in the standard model is a phenomenon where the symmetries of a physical system are broken at a certain critical point, leading to the emergence of new properties and behaviors. In the context of the standard model of particle physics, this refers to the breaking of a symmetry between the electromagnetic and weak forces, resulting in the acquisition of mass by certain particles.

In the standard model, spontaneous symmetry breaking occurs through the Higgs mechanism. This involves the Higgs field, a scalar field that permeates all of space, interacting with certain particles and giving them mass. As the temperature of the universe cooled after the Big Bang, the Higgs field settled into its lowest energy state, breaking the symmetry between the electromagnetic and weak forces.

Spontaneous symmetry breaking is crucial for the standard model to accurately describe the behavior of particles and forces in the universe. Without it, particles would not have mass and the theory would not be able to explain certain phenomena, such as the weak force's short range and the differences in mass between particles.

Yes, spontaneous symmetry breaking has been experimentally observed through the discovery of the Higgs boson at the Large Hadron Collider in 2012. This confirmed the existence of the Higgs field and its role in giving particles mass through the Higgs mechanism.

Yes, spontaneous symmetry breaking occurs in various physical systems, such as in magnets and crystals. It also plays a role in the formation of patterns and structures in nature, such as in snowflakes and spiral galaxies.

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