Does Schroedinger Eat Goldstone too?

[waterfall]

Note the wave function in the Schroedinger Equation has phase freedom from 0 to 360 degrees.

Imagine the Mexican Hat thing or potential well.
http://www.nature.com/nphys/journal/v7/n1/images/nphys1874-f1.jpg

When a double slit emitter is shut off. The phase is at the center of the hat or well.
When it turns on. The phase chooses a value (akin to falling to the ground state of the hat). This means wave functions are example of spontaneous symmetry breaking. So where is the goldstone boson in QM?

Please give another example in quantum mechanics where the concept of spontaneous symmetry breaking is used. Goldstone Theorem says that whenever a symmetry breaks, goldstone bosons appear. In the wave functions, the phases are the degrees of freedom that breaks from the symmetry.

Also perhaps one can consider a particle as the symmetry or at the center of the hat or well. When it turns to wave, there is a phase degrees of freedom. Has anyone heard of this before, if so, please share papers or references about it. Thanks.

 

[eljose79]

Thank you for your interesting post about the phase freedom in the Schrödinger equation and the concept of spontaneous symmetry breaking in quantum mechanics.

One example in quantum mechanics where spontaneous symmetry breaking is used is in the Higgs mechanism. This is a fundamental concept in the Standard Model of particle physics, which explains the origin of mass in elementary particles. The Higgs mechanism breaks the symmetry between the weak and electromagnetic interactions, resulting in the appearance of the Higgs boson as the Goldstone boson.

Another example is in the theory of superconductivity, where the spontaneous breaking of gauge symmetry leads to the appearance of the Goldstone boson known as the Cooper pair. This boson is responsible for the phenomenon of superconductivity, where certain materials can conduct electricity with zero resistance.

Regarding your question about the relationship between particles and symmetry breaking, there have been several studies on this topic in the field of quantum field theory. One example is the concept of "dynamical symmetry breaking", where the particles themselves are considered as the symmetry, and their interactions lead to the breaking of this symmetry. This has been studied in the context of the electroweak theory and the strong interactions.

I hope this helps answer your question and provides some additional examples of spontaneous symmetry breaking in quantum mechanics. For further reading, I would recommend looking into books or articles on the Higgs mechanism, superconductivity, and dynamical symmetry breaking. Thank you for your contribution to the discussion on quantum mechanics.