Quick question, index notation, alternating tensor.

[binbagsss]

Q) I am using index notation to show that ε^{0123}=-1 given that ε_{0123}=1.

The soluton is:

ε^{0123}=g^{00}g^{11}g^{22}g^{33}ε_{0123}=-ε_{0123}

where g_{\alpha\beta} is the metric tensor.

I am struggling to understand the last equality.

Many thanks for any assistance.

 

[Dick]

Q) I am using index notation to show that ε^{0123}=-1 given that ε_{0123}=1.

The soluton is:

ε^{0123}=g^{00}g^{11}g^{22}g^{33}ε_{0123}=-ε_{0123}

where g_{\alpha\beta} is the metric tensor.

I am struggling to understand the last equality.

Many thanks for any assistance.

Look up the definition of the metric tensor you are using and insert the values of the g components.

 

[HallsofIvy]

If you are using the standard metric tensor for relativity then g^{11}= g^{22}= g{33}= -1 while g^{00}= 1.