Is the vectorial representation of the Lorentzian Group unitary?

[IRobot]

I am 99% sure it is not, but I would like to hear that from someone else to be more serene.

 

[The_Duck]

The Lorentz group has no unitary representation of finite dimension, except for the trivial representation (where every group element is represented by 1).

http://en.wikipedia.org/wiki/Representation_theory_of_the_Lorentz_group

The vector representation has dimension 4.

 

[IRobot]

Thanks I already was thinking with that argument, I did the calculation of $\Lambda \Lambda ^\dagger$ for some random Lorentz Matrix. Was just looking for a confirmation.

 

[dextercioby]

It's because the Lorentz group (or its component connected to the identity) is non-compact. It's a classical result, a proof of which can be found in Cornwell's compendium.