Talk:Conformal symmetry

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Conventions

Where do the forms of the generators come from? According to me they aren't the conventional forms. It should rather be:

M_{\mu \nu }\equiv i(x_{\mu }\partial _{\nu }-x_{\nu }\partial _{\mu }),

P_{\mu }\equiv -i\partial _{\mu },

D\equiv -ix_{\mu }\partial ^{\mu },

K_{\mu }\equiv i(x^{2}\partial _{\mu }-2x_{\mu }x_{\nu }\partial ^{\nu }),

For example if we take a function $f(x_{\mu })$ and we dilate it, we get

f((1+\epsilon )x_{\mu })\approx f(x_{\mu })+\epsilon x_{\mu }\partial ^{\mu }f(x_{\mu })

which should be the same as

e^{i\epsilon D}f(x_{\mu })\approx f(x_{\mu })+i\epsilon Df(x_{\mu })

Greets, David 08:39, 8 June 2007 (UTC)[reply]

I've cleaned it all up myself. MuDavid (talk) 12:22, 13 October 2009 (UTC)[reply]

Errors in commutation relations

The definition of P is wrong, should be

P_{\mu }=i\partial _{\mu }

See L.H. Ryder, "Quantum Field Theory", 2nd ed. Antimatter33 (talk) 03:35, 25 December 2010 (UTC)[reply]

What is Conformal symmetry

Because it is mentioned every now and then in physics; "I can't read this it's in Greek!" This article needs a tag for improvement or to notify the user opening the page it is not meant to be understood by the layman. There might as well not be any text on this page and just equations; one blue link after another after another after another... Wikipedia is here to define and document things NOT to be a search engine! Lazy!

 — Preceding unsigned comment added by 162.219.204.36 (talk) 03:05, 13 July 2016 (UTC)[reply]

Biquaternions

The hyperbolic angle is essential in relativity as it expresses rapidity and is preserved in a Lorentz boost. The circular angle is also important as being respected by spatial rotations. The Lorentz group includes transformations of each of these angles and hence is a subgroup of the conformal group of spacetime. To see both angles respected, view the article biquaternion. There a 4-space found as a subspace and subject to algebraic motions expressing both circular and hyperbolic rotation. Traditionally the references have been Ludwik Silberstein (1914) and Cornelius Lanczos (1949). Rgdboer (talk) 23:29, 27 August 2024 (UTC)[reply]