Spontaneous symmetry breaking in SHO

Click For Summary
SUMMARY

Spontaneous symmetry breaking is a concept primarily rooted in quantum mechanics (QM) rather than classical mechanics. In the context of the Simple Harmonic Oscillator (SHO), while its Lagrangian is time translationally invariant, the periodic nature of its solutions does not constitute spontaneous symmetry breaking. This phenomenon occurs when the ability to form superpositions of solutions with different symmetries is lost, which is not applicable to the SHO. Instead, spontaneous symmetry breaking is relevant in systems of infinite extent, such as magnets composed of numerous spins.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with Lagrangian mechanics
  • Knowledge of superposition in quantum systems
  • Concept of infinite systems in physics
NEXT STEPS
  • Study the implications of spontaneous symmetry breaking in quantum field theory
  • Explore the role of symmetry in phase transitions
  • Investigate the behavior of infinite systems in statistical mechanics
  • Learn about the applications of spontaneous symmetry breaking in condensed matter physics
USEFUL FOR

Physicists, particularly those specializing in quantum mechanics and condensed matter physics, as well as students seeking to deepen their understanding of symmetry concepts in physical systems.

Shadumu
Messages
2
Reaction score
0
Spontaneous symmetry breaking refers to the solution of a system loses some symmetry in its Lagrangian. Consider a Simple Harmonic Oscillator, its lagrangian is time translationally invariant but its solution is periodic in time, thus not time-translational invariant. Is this Spontaneous symmetry breaking?
 
Physics news on Phys.org
No, it is not. The concept of spontaneous symmetry breaking is a concept from quantum mechanics (QM) rather than classical mechanics. The point is that in QM, you can usually form superpositions of solutions of the equations of motion and they will be solutions again. In the case of the harmonic oscillator, you can form any superpositions of the different solutions which aren't completely symmetric. The point of spontaneous symmetry breaking is that this possibility to form superpositions of solutions of different symmetry is no longer possible. For an harmonic oscillator, this is not possible. Rather, it requires systems of infinite extent, like for example a magnet which is built up of an infinite number of spins.
 

Similar threads

Undergrad Could the Lorentz symmetry be theoretically broken in vacuum?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Non commutator of symmetries giving rise to a gauge symmetry
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Understanding Symmetry Breaking to Everyday Examples
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Metric Ansatz For Unifying All Forces In 11D?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate What would it mean if symmetries in physics would not be fundamental?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Spontaneous Symmetry Breaking and quantum mechanics
  • · Replies 15 ·
Replies
15
Views
3K
Graduate Question about S(3) spontaneous symmetry breaking in Peskin & Schroeder
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Lorentz Invarience and Spontaneous Symmetry Breaking
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Why isn't the Lagrangian invariant under ##\theta## rotations?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate High energy symmetry breaking and laws of physics?
  • · Replies 2 ·
Replies
2
Views
2K