- #1
USeptim
- 98
- 5
Hello,
It’s well know that there are some gauge conditions that permit different potential fields to generate the same EM fields, this gauge conditions are:
A'=A+(e/c)∇χ
[itex]\phi[/itex]'=[itex]\phi[/itex]+(∂χ/∂t)
Where χ is any scalar field.
However, it’s also possible to get the potentials at some point integrating the four currents in the space through a Green function and adding a term due the fields in the boundary of the integration region (if this region is infinite, only radiated fields remain as long as charges are confined to some region).
This is well explained at this link:
http://www.phy.duke.edu/~rgb/Class/Electrodynamics/Electrodynamics/node148.html
Without discussing the ways to close the contour, in the next section (node149), the Lienard-Wiechert potentials are derived from the “upwards” contour Green function, and then it comes my qüestion:
Can the “fixed” four potential of a point be determined integrating the Lienard-Wiechert potentials caused by all the charges in the space-time plus a term due to the radiated field in the far past? Or there is some trick or caveat in this approach?
I wonder if it can be determined how can be used techniques as gauge-fixing in QFT which perhaps might affect the evolution of the system…
Sergio
It’s well know that there are some gauge conditions that permit different potential fields to generate the same EM fields, this gauge conditions are:
A'=A+(e/c)∇χ
[itex]\phi[/itex]'=[itex]\phi[/itex]+(∂χ/∂t)
Where χ is any scalar field.
However, it’s also possible to get the potentials at some point integrating the four currents in the space through a Green function and adding a term due the fields in the boundary of the integration region (if this region is infinite, only radiated fields remain as long as charges are confined to some region).
This is well explained at this link:
http://www.phy.duke.edu/~rgb/Class/Electrodynamics/Electrodynamics/node148.html
Without discussing the ways to close the contour, in the next section (node149), the Lienard-Wiechert potentials are derived from the “upwards” contour Green function, and then it comes my qüestion:
Can the “fixed” four potential of a point be determined integrating the Lienard-Wiechert potentials caused by all the charges in the space-time plus a term due to the radiated field in the far past? Or there is some trick or caveat in this approach?
I wonder if it can be determined how can be used techniques as gauge-fixing in QFT which perhaps might affect the evolution of the system…
Sergio