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Bernard Meurer

11:05 PM

That's some security right there

David Z

@EmilioPisanty True. But not on arXiv.

Emilio Pisanty

@DavidZ precisely.

Emilio Pisanty

11:29 PM

potentially relevant?

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Mew

11:43 PM

halo

Emilio Pisanty

also, c.c. Mr. Noise a.k.a. @DanielSank, nature.com/nphys/journal/v12/n12/abs/nphys3870.html

Mew

sup @heather

@EmilioPisanty If I have a continuous single parameter lie group, what is the infintisimal expansion of F(A)F(B)?

ACuriousMind

@Mew ...wat.

Mew

well suppose F(A) means rotate A units

ACuriousMind

How is anyone supposed to know what F,A,B stand for there if you don't define them?

Mew

11:52 PM

F is the function of the single parameter

ACuriousMind

What has the "continuous single-parameter Lie group" to do with rotations (rotations are three parameters in 3D)?

Mew

@ACuriousMind in 2D rotations have a single parameter no?

ACuriousMind

Sure

Mew

but anyway rotation or not is irrelevant

I'm wondering inthe general case

ACuriousMind

So $A$ and $B$ are real numbers and $F(A),F(B)$ are elements of the group?

Mew

11:53 PM

yep

ACuriousMind

Then, assuming you chose an intelligent parametrization, one would have $F(A)F(B) = F(A+B)$.

Mew

ok always?

I mean obviously that's the case for 2d rotation

ACuriousMind

Well, of course it depends on the function $F$.

But if one takes a "one parameter Lie group" and then writes elements as $F(A)$, one usually assumes that $F$ is a Lie group homomorphism $\mathbb{R}\to G$.

Which it is if you make the natural choice for $F$ as the exponential function.

Mew

So is F(A)F(B) always equal to F(B)F(A) then?

lie groups always commute?

lie groups are always albelian?

ACuriousMind

One-parameter Lie groups are always Abelian, yes.

Mew

11:56 PM

oh k

and how do you work out for 2 parameter

say F(A,B)F(C,D)