Suppose we have a real field, S(x,y,z,t), that satisfies E^2 = P^2 + m^2. Here the tangent space could be R^1? Say we can expand the tangent space and let it be R^3 but make the restriction that "movement" of the field in the tangent space was restricted to some orbit about the origin of the tangent space, and further, the orbit is contained in some arbitrarily oriented plane that contained the origin of the tangent space. If so then consider how we might graph this field, S, at a point in spacetime (X,t). As the movement is restricted to a plane let the length of a vector represent the magnitude of the fields displacement (the distance from the origin of the tangent space) and let the direction of the vector represent the normal to the orbit plane. An additional unit vector in the orbit plane gives the angular position in the orbit plane. This representation of the "state" of the field S at a point in spacetime smells of spinors, is this the case? If not spinor like can things be tweaked to make it so?(adsbygoogle = window.adsbygoogle || []).push({});

I refer to a paper by W. T. Payne:

http://adsabs.harvard.edu/abs/1952AmJPh..20..253P

In the paper by Payne a spinor is represented as an ax with the end of its handle at the origin. With this we get a direction, a magnitude, and an angle.

Thanks for any help.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Real field and spinors?

**Physics Forums | Science Articles, Homework Help, Discussion**