Why is it interesting?

Elitzur demonstrated that a spontaneous breaking of a local symmetry is not possible.

https://journals.aps.org/prb/pdf/10.1103/PhysRevB.72.045137

Layman

Student

Researcher

See: https://journals.aps.org/rmp/pdf/10.1103/RevModPhys.51.659

. In particular, zero- or one-dimensional theories with short-range interactions cannot exhibit a phase transition at any finite temperature. Additionally, the Mermin-Wagner theorem1 states that a continuous symmetry cannot be spontaneously broken at any finite temperature for two-dimensional theories with finite range interactions. On the other hand, Elitzur2 demonstrated that a spontaneous breaking of a local symmetry is not possible. Below, we will show that Elitzur’s theorem is a consequence of a reduction to zero of the effective dimension of the gauge invariant theory. Moreover, we will show that from the point of view of the noninvariant gauge fields, the presence of a “d-dimensional gauge
or gaugelike symmetry”
see definition below reduces the effective dimension of the theory from D to d. The dimension d is intermediate between local symmetries
d=0 and global symmetries
d=D. Ho https://journals.aps.org/prb/pdf/10.1103/PhysRevB.72.045137

Common Question 1

Common Question 2

Examples

Example1

Example2:

History