# Can the lorentz group be covered by single-parameter subgroups?

1. Sep 11, 2010

### wdlang

we all know the lorentz group is of four disconnected components

about the component connected to the unit element,

is it coverable with single-parameter subgroups?

put it in another way

are all the elements in this component of the form exp(A)?

i am studying relativistic quantum mechanics, and i find that most textbooks take this to be guaranteed.

2. Sep 12, 2010

### chrispb

No; the Lorentz algebra is six-dimensional. Yes, you can write any element in the connected-to-the-identity part of the Lorentz group in the form e^{i theta^a T^A}.