http://blogsearch.google.com/ping/RPC2? sitemap/http://www.impunv.blogspot.com google71a594b9a41d2ae0.html impunv: Dirac's equation

Monday, November 26, 2007

Dirac's equation

Why does Dirac’s equation hold? Despite an all too prevalent belief it is not some strange property of nature. It is a trivial property of geometry. Considering only space transformations, ignoring interactions and internal symmetry, objects (thus free) belong to states of the Poincaré group. This has two invariants (like the rotation group has one, the total angular momentum). For a massive object these are the mass and spin in the rest frame. Knowing these the object is completely determined. Thus two equations, not one, are needed to determine an object. For spin- 1/2 , only, these two can be replaced by one, Dirac’s equation. Why is this? The momentum, p_µ is a four-vector. There is another four-vector, g_ µ. Thus µpµ is an invariant. It is a property of the object, and we give that property the name mass. Thus g_µp_µ = m, (1) which is Dirac’s equation. It gives the mass of the object, and the spin, 1/2 . This is only possible because of the g_µ’s. These form a Clifford algebra and there is (up to inversions) only one for each dimension. This is then the reason for Dirac’s equation, and only for a single spin.1/2

4 comments:

visachris322 said...

oh, your post is so great. I like it very much.I love oakley sunglasses cheap very much and concern on discount oakley sunglasses review, discount ray ban sunglasses are highly recommended.

linchunxia said...

Of which utterly a fantastic site,these individuals priced at could protect the application , thanks for your time typically the bloger£¬I believe that you can fascinating in D&G Snapback Hats
Diamond Snapback Hats. this is each of our site : http://www.wholesalehatsandcaps.com.

Unknown said...

Why does Dirac’s equation hold? Despite an all too prevalent belief it is not some strange property of nature. It is a trivial property of geometry. Considering only space transformations, ignoring interactions and internal symmetryguild wars 2 gold
buy guild wars 2 gold
cheap guild wars 2 gold
cheapest guild wars 2 gold
guild wars 2 gold for sale

Unknown said...

But even before the envelope is opened, the first impression the guest has of the invitation is what’s on the outside.swtor gold
buy swtor gold
cheap swtor gold
tor credits
buy tor credits
cheap tor credits