- #1

- 238

- 6

x[itex]^{\lambda}_{,\mu}[/itex]x[itex]^{\mu}_{,\nu}[/itex]=g[itex]^{\lambda}_{\nu}[/itex]

Shouldn't that have a 4 on the right side?

x[itex]^{\lambda}_{,\mu}[/itex]x[itex]^{\mu}_{,\nu}[/itex]=(4?)g[itex]^{\lambda}_{\nu}[/itex]

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- Thread starter exmarine
- Start date

- #1

- 238

- 6

x[itex]^{\lambda}_{,\mu}[/itex]x[itex]^{\mu}_{,\nu}[/itex]=g[itex]^{\lambda}_{\nu}[/itex]

Shouldn't that have a 4 on the right side?

x[itex]^{\lambda}_{,\mu}[/itex]x[itex]^{\mu}_{,\nu}[/itex]=(4?)g[itex]^{\lambda}_{\nu}[/itex]

- #2

- 1,948

- 200

x[itex]^{\lambda}_{,\mu}[/itex]x[itex]^{\mu}_{,\nu}[/itex]=g[itex]^{\lambda}_{\nu}[/itex]

Shouldn't that have a 4 on the right side?

x[itex]^{\lambda}_{,\mu}[/itex]x[itex]^{\mu}_{,\nu}[/itex]=(4?)g[itex]^{\lambda}_{\nu}[/itex]

Nope. let me open the expression for you

[itex]\Sigma _ \mu \frac{\partial x^ \lambda}{\partial x ^ \mu} \frac{\partial x^ \mu}{\partial x ^ \nu}=\delta ^ \lambda _ \nu = g ^ \lambda _ \nu [/itex]

- #3

- 1,948

- 200

[itex]

\Sigma _ \mu \frac{\partial x^ \lambda}{\partial x ^ \mu} \frac{\partial x^ \mu}{\partial x ^ \nu}=\Sigma _ \mu \delta ^ \lambda _ \mu \delta ^ \mu _ \nu =\delta ^ \lambda _ \nu = g ^ \lambda _ \nu [/itex]

- #4

- 238

- 6

[itex]\frac{\partial x^{0}}{\partial x^{0'}}[/itex][itex]\frac{\partial x^{0'}}{\partial x^{0}}[/itex]+[itex]\frac{\partial x^{0}}{\partial x^{1'}}[/itex][itex]\frac{\partial x^{1'}}{\partial x^{0}}[/itex]+[itex]\frac{\partial x^{0}}{\partial x^{2'}}[/itex][itex]\frac{\partial x^{2'}}{\partial x^{0}}[/itex]+[itex]\frac{\partial x^{0}}{\partial x^{3'}}[/itex][itex]\frac{\partial x^{3'}}{\partial x^{0}}[/itex]=4?

And all the off-diagonals be 0 of course.

- #5

Bill_K

Science Advisor

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