# Why does gauge fixing break gauge symmetry?

#### TimeRip496

By fixing a gauge (thus breaking orspending the gauge symmetry), the model becomes something easier to analyse mathematically, such as a system of partial differential equations (in classical gauge theories) or a perturbative quantum field theory (in quantum gauge theories), though the tractability of the resulting problem can be heavily dependent on the choice of gauge that one fixed.
https://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/

What do you mean by this? As in why does gauge fixing made the model easier to analyse? Isnt gauge fixing something like choosing a coordinate?

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#### mfb

Mentor
Isnt gauge fixing something like choosing a coordinate?
Right, and choosing a coordinate system can make things easier. As an example from classical mechanics, you can reduce the six position variables of the Kepler problem (three coordinates per object) to two variables by going to the center of mass system and choosing one coordinate to be orthogonal to the motion of the objects.

Gauge symmetry is not a real symmetry. A symmetry relates different states, gauge invariance allows you to identify states being related by a gauge transformation as the same state. You choose the gauge which is easiest to work with, for example in electrostatics we always use Coulomb gauge because Lorenz gauge would just make everything incredibly complicated.

There are no physics manifestations of your gauge choice. However, there are physical manifestations of gauge invariance. It appears in systems with nontrivial topology and results in quantization of things like magnetic charge and the hall conductance. You can use topological invariants to look at these systems.

#### TimeRip496

Gauge symmetry is not a real symmetry. A symmetry relates different states, gauge invariance allows you to identify states being related by a gauge transformation as the same state. You choose the gauge which is easiest to work with, for example in electrostatics we always use Coulomb gauge because Lorenz gauge would just make everything incredibly complicated.

There are no physics manifestations of your gauge choice. However, there are physical manifestations of gauge invariance. It appears in systems with nontrivial topology and results in quantization of things like magnetic charge and the hall conductance. You can use topological invariants to look at these systems.
When you say state, what do you really mean? Do you mean description of a system like rotation, translation, etc? And what do you mean by symmetry relate different state?

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