Non-Dynamical Fields: Definition & Interpretations

[fhenryco]

Hello,

May be i have a wrong idea about what is the definition of a non dynamical field. I recently read that it's a field without any kinetic term in the action (first interpretation). But previously i thought that it could be a field with any kind of Lagrangien except that it was not considered dynamical in the sense that it was not to be varied in the action to get it's own equations of motion (second interpretation). In this last sense this field would need to be fixed by another constraint imposed before considering the action where only other fields coupling to it would be dynamical: for instance a flat non dynamical metric g_munu could be fixed a priori by requiring Riem (g)=0.
Another way could be to let the non dynamical field in one action S_1 , actually play it's dynamics in another action S_2, and only enter S_1 as a spectator field, still in the sense that it is not varied to extremize S1 as the other fields in S1.
What is wrong with this second interpretation of what is a non dynamical field : i don't remember any paper where there are non dynamical fields in this sense, so i don't actually know why i have this in mind.
thanks in advance for helpful comments

 

[fhenryco]

Hello,

May be i have a wrong idea about what is the definition of a non dynamical field. I recently read that it's a field without any kinetic term in the action (first interpretation). But previously i thought that it could be a field with any kind of Lagrangien except that it was not considered dynamical in the sense that it was not to be varied in the action to get it's own equations of motion (second interpretation). In this last sense this field would need to be fixed by another constraint imposed before considering the action where only other fields coupling to it would be dynamical: for instance a flat non dynamical metric g_munu could be fixed a priori by requiring Riem (g)=0.
Another way could be to let the non dynamical field in one action S_1 , actually play it's dynamics in another action S_2, and only enter S_1 as a spectator field, still in the sense that it is not varied to extremize S1 as the other fields in S1.
What is wrong with this second interpretation of what is a non dynamical field : i don't remember any paper where there are non dynamical fields in this sense, so i don't actually know why i have this in mind.
thanks in advance for helpful comments

and a third way would be to impose some isometries to a metric entering in an action which can be done rigorously and in a covariant way in the language of killing vectors, not only to fix the form of the metric but even to freeze some modes or elements of the metric which should not be varied anymore leading to less equations than usual ... why not ?