Spinors and space-time ebook

Spinors and space-time Roger Penrose, Wolfgang Rindler
Publisher: Cambridge University Press

June 27, 2009 6:54 PM Subscribe · TOE breaking Lorentz invariance - "by treating space and time differently as well as separately, the infinities in the quantum mechanics equations vanish, and gravity behaves as it should." Mathematically LQG is local gauge theory of the self-dual subgroup of the complexified Lorentz group, which is related to the action of the Lorentz group on Weyl spinors commonly used in elementary particle physics. It really broke my brain the first time I ran into this, but on my third pass through Green, Schwartz, and Witten's book it hit me: spacetime coordinates are fields on a 1-dimensional “spacetime” parametrized by the proper time of the particle. There exists a decent set of literature out there for this, but unfortunately it's scattered across different `cultures' like a mathematical Tower of Babel. The theories predict that such structures, essentially individual building blocks in the fabric of spacetime, are so ephemeral as to disappear after 10^{ -44} seconds, yet electrons for example are much longer-lived. I learned this notation from Penrose & Rindler's Spinors and space-time, which is possibly my favorite book. We write down an explicit projection that maps any given 4-spinor to a point in 3+1 spacetime while commuting with the Lorentz action. Similarly for strings, spacetime coordinates are fields on the The classical electron field, for example, is a section of a bundle of odd-parity Dirac spinors. There are different kinds of spinors. However, without loss of generality at this moment, we can consider that every spinor field is of “Dirac Type/Class”. I've been spending some time thinking about spinors on curved spacetime. Dirac spinors are spin 1/2 fields. In a radical reworking of the If you are interested in further reading, you might find Roger Penrose's new book The Road to Reality useful, as it provides a good explanation of some parts of the new theory, based on spinors. One can even indicate vectors with a superscript rather than subscript.