- #1
dyn
- 773
- 61
Hi.
The book I am using gives the following equations for the the Lorentz transformations of contravariant and covariant vectors
x/μ = Λμν xν ( 1 )
xμ/ = Λμν xv ( 2 )
where the 2 Lorentz transformation matrices are the inverses of each other. I am trying to get equation 2 from equation 1 but if I lower the index on the LHS of (1) using the metric gρμ and apply it to both sides of (1) I get
xρ/ = Λρν x ν
Then I'm stuck because how can I lower the ν on xν as ν is already repeated twice on the RHS and so I can't use a metric with ν in it ?
Thanks
The book I am using gives the following equations for the the Lorentz transformations of contravariant and covariant vectors
x/μ = Λμν xν ( 1 )
xμ/ = Λμν xv ( 2 )
where the 2 Lorentz transformation matrices are the inverses of each other. I am trying to get equation 2 from equation 1 but if I lower the index on the LHS of (1) using the metric gρμ and apply it to both sides of (1) I get
xρ/ = Λρν x ν
Then I'm stuck because how can I lower the ν on xν as ν is already repeated twice on the RHS and so I can't use a metric with ν in it ?
Thanks