Symmetry breaking

[1] This collapse is often one of many possible bifurcations that a particle can take as it approaches a lower energy state.

Due to the many possibilities, an observer may assume the result of the collapse to be arbitrary.

This phenomenon is fundamental to quantum field theory (QFT), and further, contemporary understandings of physics.

[2][3] Symmetry breaking and tunneling relate through the collapse of a particle into non-symmetric state as it seeks a lower energy.

[4] Symmetry breaking can be distinguished into two types, explicit and spontaneous.

Roughly speaking there are three types of symmetry that can be broken: discrete, continuous and gauge, ordered in increasing technicality.

There are three possible stationary states for the particle: the top of the hill at

At the bottom, it is no longer invariant under rotations but minimizes its gravitational potential energy.

Furthermore rotations move the particle from one energy minimizing configuration to another.

There is a novelty here not seen in the previous example: from any of the vacuum states it is possible to access any other vacuum state with only a small amount of energy, by moving around the trough at the bottom of the hill, whereas in the previous example, to access the other vacuum, the particle would have to cross the hill, requiring a large amount of energy.

Gauge symmetry breaking is the most subtle, but has important physical consequences.

Spontaneous symmetry breaking was developed to resolve this inconsistency.

The idea is that in an early stage of the universe it was in a high energy state, analogous to the particle being at the top of the hill, and so had full gauge symmetry and all the gauge fields were massless.

As it cooled, it settled into a choice of vacuum, thus spontaneously breaking the symmetry, thus removing the gauge symmetry and allowing mass generation of those gauge fields.

A full explanation is highly technical: see electroweak interaction.

This act of selecting one of the states as the system reaches a lower energy is SSB.

is a functional of quantum fields which is invariant under the action of a symmetry group

However, the vacuum expectation value formed when the particle collapses to a lower energy may not be invariant under

[5] Further, in this context the usage of 'symmetry breaking' while standard, is a misnomer, as gauge 'symmetry' is not really a symmetry but a redundancy in the description of the system.

symmetry of the vacuum is broken, giving a phase transition of the system.

This is essentially the paradigm for perturbation theory in quantum mechanics.

Symmetry breaking can cover any of the following scenarios: One of the first cases of broken symmetry discussed in the physics literature is related to the form taken by a uniformly rotating body of incompressible fluid in gravitational and hydrostatic equilibrium.

Jacobi[6] and soon later Liouville,[7] in 1834, discussed the fact that a tri-axial ellipsoid was an equilibrium solution for this problem when the kinetic energy compared to the gravitational energy of the rotating body exceeded a certain critical value.

The axial symmetry presented by the McLaurin spheroids is broken at this bifurcation point.

Furthermore, above this bifurcation point, and for constant angular momentum, the solutions that minimize the kinetic energy are the non-axially symmetric Jacobi ellipsoids instead of the Maclaurin spheroids.

A ball is initially located at the top of the central hill (C). This position is an unstable equilibrium: a very small perturbation will cause it to fall to one of the two stable wells left (L) or right (R). Even if the hill is symmetric and there is no reason for the ball to fall on either side, the observed final state is not symmetric.
A (black) particle is always driven to lowest energy. In the proposed -Symmetric system, it has two possible (purple) states. When it spontaneously breaks symmetry, it collapses into one of the two states. This phenomenon is known as spontaneous symmetry breaking.
A 3D representation of a particle in a symmetric system (a Higgs Mechanism ) before assuming a lower energy state
Relativistic fine structure corrections (Dirac) to the Bohr model of the hydrogen atom break the symmetries and split the degenerate levels. The Lyman-alpha line (emitted in a transition from n = 2 to n = 1) splits into a doublet.