Understanding Chiral Theory & Its Significance

[alphaone]

Could somebody please tell me a workable definition of the term "chiral theory" , and also explain its significance? As far as I know, in a chiral theory not all the fermions obtain a mass but whether this is a definition or a derived result is not clear to me. Thanks in advance

 

[Ruslan_Sharipov]

As to me, the term "chiral" is associated with spinors. There are 2-spinors and 4-spinors. 2-spinors are also known as Weyl spinors or chiral spinors. 4-spinors are composed of 2-spinors and their Hermitian conjugates. 4-spinors are also known as Dirac spinors. See more details in my papers

http://arxiv.org/abs/math/0602359
http://arxiv.org/abs/math/0601262

 

[nrqed]

Could somebody please tell me a workable definition of the term "chiral theory" , and also explain its significance? As far as I know, in a chiral theory not all the fermions obtain a mass but whether this is a definition or a derived result is not clear to me. Thanks in advance

The basic idea is the following. For spin 1/2 fermions, you may define separately left-handed and right-handed states. What I mean by this is that those are well-defined representations of the Lorentz group so they can be used as "building blocks" of a theory. A theory that treats differently the left-handed and right-handed states of the fermions is said to be chiral. By "treating" differently I mean that the terms in the lagrangian are not symmetric under exchanging the left and right handed spinors.