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LoopQG

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Find the Euler – Lagrange Equation when

[itex] L = -1/2 (D_p a_u)(D^p a^u) \sqrt{-g} dx^4[/itex]

Use [itex] g_u_v [/itex] to raise/lower indices

[itex] D_p [/itex] is the covariant derivative

I am very new at this notation and am having a lot of trouble getting anywhere with this.

I know I have to take the action:

[itex] S = \int Ldt [/itex]

and i know the covariant derivative [itex] D_p a^q = d_p a^q + \Gamma_p_h^q a^h [/itex]I honestly have know idea where to start any help would be much appreciated.

[itex] L = -1/2 (D_p a_u)(D^p a^u) \sqrt{-g} dx^4[/itex]

Use [itex] g_u_v [/itex] to raise/lower indices

[itex] D_p [/itex] is the covariant derivative

I am very new at this notation and am having a lot of trouble getting anywhere with this.

I know I have to take the action:

[itex] S = \int Ldt [/itex]

and i know the covariant derivative [itex] D_p a^q = d_p a^q + \Gamma_p_h^q a^h [/itex]I honestly have know idea where to start any help would be much appreciated.

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