- #1
cianfa72
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- TL;DR
- About notation employed for inverse Lorentz transform
Hi, reading again this old thread about Index notation for inverse Lorentz transform, I believe there is a missing ##\hat{L}## in the following, namely
$$(\hat{\eta} \hat{L} \hat{\eta})^{\text{T}} \hat{L}=\hat{\eta} \hat{L}^{\text{T}} \hat{\eta} = \mathbb{1} \; \Rightarrow \; \hat{L}^{-1} = \hat{\eta} \hat{L}^{\text{T}} \hat{\eta}$$ should actually be $$(\hat{\eta} \hat{L} \hat{\eta})^{\text{T}} \hat{L}=(\hat{\eta} \hat{L}^{\text{T}} \hat{\eta}) \hat{L}= \mathbb{1} \; \Rightarrow \; \hat{L}^{-1} = \hat{\eta} \hat{L}^{\text{T}} \hat{\eta}.$$
Does it make sense ? Thanks.
$$(\hat{\eta} \hat{L} \hat{\eta})^{\text{T}} \hat{L}=\hat{\eta} \hat{L}^{\text{T}} \hat{\eta} = \mathbb{1} \; \Rightarrow \; \hat{L}^{-1} = \hat{\eta} \hat{L}^{\text{T}} \hat{\eta}$$ should actually be $$(\hat{\eta} \hat{L} \hat{\eta})^{\text{T}} \hat{L}=(\hat{\eta} \hat{L}^{\text{T}} \hat{\eta}) \hat{L}= \mathbb{1} \; \Rightarrow \; \hat{L}^{-1} = \hat{\eta} \hat{L}^{\text{T}} \hat{\eta}.$$
Does it make sense ? Thanks.