# What is Spontaneous symmetry breaking: Definition and 41 Discussions

Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.

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1. ### Non quadratic potentials and quantization in QFT (home exercise)

I noticed that ##V(\phi)## has nonzero minima, therefore I found the stationary points as ##{{\partial{V}}\over{\partial\phi}}=0##, and found the solutions: $$\phi^0_{1,2}=-{{m}\over{\sqrt{\lambda}}}\quad \phi^0_3={{2m}\over{\sqrt{\lambda}}}$$ of these, only ##\phi^0_3## is a stable minimum...

7. ### I Lorentz Invarience and Spontaneous Symmetry Breaking

Spontaneous symmetry breakingI’m not sure if I understand spontaneous symmetry breaking.In the context of the Mexican hat (and marble) example, wouldn’t the actual path of the marble down the Mexican hat from the top be determined by several small factors that one would normally not consider...

11. ### A How can gauge symmetry be broken?

Hello, I was reading about the Higgs mechanism and I must say that I did not really follow the argument of how the gauge symmetry is broken. I think that my problem has to do with the more general question of how does a gauge symmetry get broken in general? Thanks!

20. ### Topological phase and spontaneous symmetry breaking coexist?

As we know topological phases cannot be explained using spontaneous symmetry breaking and order parameter. But can they coexist? Suppose there is a system which is undergoing quantum phase transition to a anti-ferromagnetic phase from a disordered phase. So in the anti-ferromagnetic phase...
21. ### Wilson Loop and spontaneous symmetry breaking.

I would like to ask about the case of: ##SU(2)\otimes U(1) \rightarrow U(1)\otimes U(1),## spontaneous symmetry breaking. It is given that the Wilson Loop: ##W \equiv exp[ig \oint dy H T^1]= diag(−1,−1,1).## Where ##y## is the ##S^1/Z^2## fifth/extra dimension, ##H = \frac{1}{g R}## and...
22. ### Spontaneous symmetry breaking in SHO

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...
23. ### Spontaneous symmetry breaking and the photon/baryon ratio

Hi, I am looking into symmetry breaking and how it (may have) affected the photon/baryon ratio in the primordial universe. I found this wonderful encyclopaedia of cosmology which relates the grand unified theory to an orthorhombic crystal, making analogies for symmetry, spontaneous symmetry...
24. ### Understanding Inflation: Effects of Spontaneous Symmetry Breaking on Gravity

I'm trying to understand inflation (in the cosmic sense). I know that ultimately that's a subject that involves both quantum field theory and General Relativity, but I'm wondering to what extent it can be understood from the point of view of classical (non-quantum) GR. If you have a classical...
25. ### Spontaneous symmetry breaking in the standard model

In the standard model, the Lagrangian contains scalar and spinor and vector fields. But when we consider spontaneous symmetry breaking, we only account for the terms contain only scalar fields, " the scalar potential", in the Lagrangian. And if the scalar fields have vacuum expectation value...
26. ### Understanding Spontaneous Symmetry Breaking in Quantum Field Theory

Is there a reason why we have to expand a field ψ about the true vacuum |Ω>? Can't we just do field theory about ψ=0 instead of about ψ=<Ω|ψ|Ω>? Also, I'm a bit confused about other fields. For the E&M potential, under the true vacuum, wouldn't we need to expand about A=<Ω|A|Ω> instead of...
27. ### Spontaneous symmetry breaking: How can the vacuum be infinitly degener

Spontaneous symmetry breaking: the vacuum be infinitly degenerate? In classical field theories, it is with no difficulty to imagine a system to have a continuum of ground states, but how can this be in the quantum case? Suppose a continuous symmetry with charge Q is spontaneously broken, that...
28. ### Spontaneous symmetry breaking. Ferromagnet.

I'm not sure what people meant about this. Heisenberg hamiltonian is ##O(3)## invariant. H=-J\sum_{\langle i,j \rangle} \vec{S}_i \cdot \vec{S}_j ##\langle \rangle## denotes nearest neighbors. It has ##O(3)## symmetry. If I understand well ground state is infinitely degenerate. But system...
29. ### Spontaneous Symmetry Breaking -Conceptual Question

what is the relationship between unstable equilibria and spontaneous symmetry breaking? Would this qualify as an example of spontaneous symmetry breaking? Take a (perfectly round and unlabeled) pencil standing upright on its eraser so there is a U(1) symmetry on its original position...
30. ### Is the Higgs mechanism really a spontaneous symmetry breaking?

The Higgs mechanism is often explained (both here at PF and in many physics sites including wikipedia) as an example of spontaneous symmetry breaking, but the Nobel winner physicist 't Hooft says in his "for laymen" book about particle physics, "In search of the ultimate building blocks", that...
31. ### Spontaneous symmetry breaking, Higgs mech, and particles getting masses?

I'm trying to get a basic picture in my head of particles having mass. I always seem to come across the ridiculously vague statement that "the Higgs mechanism gives particles mass", and a passing mention of "spontaneous symmetry breaking". There is a lot of stuff confusing me at the minute so...
32. ### Electric charge and spontaneous symmetry breaking

Hi, If I have a Lagrangian of complex scalar field (just U(1) local invariance). And I know that phi^star describes field with -e electric charge and phi describes field with e electric charge. How do I apply "charge issue" when I write Lagrnangian after spontaneous symmetry breaking in...
33. ### Spontaneous Symmetry Breaking of SU(3)

Homework Statement The generators of SU(3) are the Gell Mann matrices, \lambda_a. Consider symmetry breaking of an SU(3) theory generated by a triplet of complex scalar fields \Phi = \left(\phi_1, \phi_2, \phi_3\right). Assuming the corresponding potential has a minimum at \Phi_0 =...
34. ### Why can't there be spontaneous symmetry breaking in finite volume?

Hello everyone, I'm a bit confused by something I've read as have been unable to find resources to clarify it. Here is the statement that confused me, from Binetruy's Supersymmetry textbook (p.26): It is well-known that [in the case of ordinary continuous symmetries] no possibility of...
35. ### Spontaneous symmetry breaking of gauge symmetries

hello all gauge symmetries are redundencies of the description of a situation. Therefore they are not real symmetries. So in what sense does it mean to spontaneously break a gauge symmetry? ian
36. ### What is Spontaneous Symmetry Breaking?

Hi: What is Spontaneous symmetry breking ? and when does it happen.? Regards
37. ### Did Exponential Expansion Trigger Early Spontaneous Symmetry Breaking?

Was the early spontaneous symmetry breaking caused by exponential expansion in the first instant of standard theory? Is that the reason that the early Big Bang universe is thought to have contained equal amounts of matter and anti-matter (produced by spontaneous symmetry breaking)? Does...
38. ### On spontaneous symmetry breaking and Higgs’s mechanism of mass production

On spontaneous symmetry breaking and Higgs’s mechanism of mass production From lectures: L. Peak and K. Varvell. The Physics of the Standard Model. Full Lagrangian for fermion and photon Combine the gauge-invariant Lagrangian density describing a fermion field in the presence of an...
39. ### Spontaneous symmetry breaking in the SM

\mathcal{L} = \frac{1}{2}(\partial_{\mu}\underline{\phi}).(\partial^{\mu}\underline{\phi}) + \frac{1}{2}\mu^{2}\underline{\phi}.\underline{\phi} - \frac{\lambda}{4}(\underline{\phi}.\underline{\phi})^{2} + \bar{\psi}(i\gamma . \partial )\phi - g\bar{\psi}(\phi_{1}+i\gamma^{5}\phi_{2})\psi...
40. ### How Does Spontaneous Symmetry Breaking Explain Particle Masses?

I often have this problem when reading physics books (the kind I can understand) where, because I'm only in High school math, the author explains only in analogies, and the analogies sometimes don't make logical sense. I'm reading Steven Weinberg's "Dreams of a Final Theory" and I got to the...
41. ### Question on Spontaneous Symmetry Breaking in QFT Final

Hello. I've got a QFT final tomorrow, and one question is still bothering me. Consider two lagrangians. The first one is L = \frac{1}{2} D_{\mu} \vec{\phi}.D^{\mu} \vec{\phi} + \frac{m^{2}}{2} \vec{\phi}.\vec{\phi} - \frac{\lambda}{4} \left(\vec{\phi}.\vec{\phi}\right)^{2} The second...