Timeline for Higgs mechanism and neutral fields
Current License: CC BY-SA 3.0
3 events
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| Apr 18, 2014 at 10:55 | comment | added | Robin Ekman | The gauge group does not always contain global gauge transformations, or example in the Dirac magnetic monopole there is no global choice of $U(1)$ gauge. This is true generally for monopole and instanton gauge fields. The global $U(1)$ symmetry for e.g. the electron field in the Dirac Lagrangian is strictly speaking unrelated to gauge symmetry. Formally the Dirac field takes values in $S \otimes \mathbb C$ where $S$ is the space of Dirac spinors. The gauge symmetry acts on the latter factor, the global $U(1)$ symmetry on the former. | |
| Apr 17, 2014 at 10:51 | comment | added | MrLee | What is your definition of a scalar field $\phi$ being charged under a gauge field $A$? I thought: If say U(1) is the (local) gauge group of your system then this gauge group always containts also a "global" symmetry. This global symmetry is then used to define the charge. Isn't the charge due to a local gauge transformation trivially (i.e. independent of the equations of motion) conserved? | |
| Apr 17, 2014 at 10:10 | history | answered | innisfree | CC BY-SA 3.0 |