Timeline for What gauge is used in the Lagrangian for a non-relativistic point particle in an electromagnetic potential
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| May 11, 2011 at 13:34 | vote | accept | Larry Harson | ||
| May 11, 2011 at 4:38 | comment | added | Luboš Motl | Thanks, Qmechanic, but nope. $A_\mu$ may be treated as a background but even with this Lagrangian, it may be perfectly dynamical as well, so that the charged fields influence the electromagnetic field and vice versa. It's exactly how physics was supposed to work throughout the 19th century. The Lagrangian is that of ordinary electrodynamics so why should the key field be non-dynamical? Of course, there should also be $(E^2-B^2)/2$ in the Lagrangian which is gauge-invariant, too. Again, there is no need to gauge-fix it - don't get confused. Gauge symmetry is a virtue not vice. | |
| May 10, 2011 at 22:44 | comment | added | Qmechanic♦ | Good answer. It should probably be stressed that the $A_{\mu}$ field in the Lagrangian $L$ mentioned in the question is not dynamically active, but just an electromagnetic background, which is required to satisfy Maxwell's eqs. (The dynamically active variable is the position of the point charge.) To make $A_{\mu}$ dynamically active as well, we should first introduce the standard $F_{\mu\nu}^2$ term, and secondly, gauge-fixing terms. | |
| May 10, 2011 at 19:38 | history | edited | Luboš Motl | CC BY-SA 3.0 |
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| May 10, 2011 at 17:55 | history | edited | Luboš Motl | CC BY-SA 3.0 |
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| May 10, 2011 at 17:45 | history | edited | Luboš Motl | CC BY-SA 3.0 |
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| May 10, 2011 at 17:39 | history | answered | Luboš Motl | CC BY-SA 3.0 |