What is action: Definition and 7 Discussions

I just need a hint to get started, and then I reckon the rest will follow... We consider a theory where matter is a covector field ##\omega_a## which is described by a diffeomorphism-invariant action ##S_m##. Define:$$E^{a} = \frac{1}{\sqrt{-g}} \frac{\delta S_m}{\delta \omega_a}$$Also, ##T^{ab}...

Dirac derives Einstein's field equations from the action principle ##\delta I=0## where $$I=\int R\sqrt{-g} \, d^4x$$ (##R## is the Ricci scalar). Using partial integration, he shows that $$I=\int L\sqrt{-g} \, d^4x$$ where ##L## involves only ##g_{\mu\nu}## and its first derivatives, unlike...

Under the RELATIVISTIC definition of Action, is the Action for a beam of light always zero? Thanks in advance.

Here is an action for a theory which couples gravity to a field in this way:$$S = \int d^4 x \ \sqrt{-g} e^{\Phi} (R + g^{ab} \Phi_{;a} \Phi_{;b})$$I determine\begin{align*} \frac{\partial L}{\partial \phi} &= \sqrt{-g} e^{\Phi} (R + g^{ab} \Phi_{;a} \Phi_{;b}) \\ \nabla_a \frac{\partial...

I am stuck at the final part where one is supposed to show that the derivative of the second term of the action gives the mass term in the Majorana equation. For $$\chi^T\sigma^2\chi = -(\chi^\dagger\sigma^2\chi^*)^*$$ we get $$\frac{\delta}{\delta\chi^\dagger}(\chi^\dagger\sigma^2\chi^*)^*$$...

How and/or why does the existence of the quantum of action (Planck's constant) cause indeterminism?

Here is the action: ##S = \frac{1}{16\pi} \int d^4 x \sqrt{-g} (R\phi - \frac{\omega}{\phi} g^{ab} \phi_{,a} \phi_{,b} + 16\pi L_m)## the ordinary matter is included via ##L_m##. Zeroing the variation ##\delta/\delta g^{\mu \nu}## in the usual way gives ##\frac{\delta}{\delta g^{\mu \nu}}[R\phi...