spinor love

# spinor

## Definitions

### from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A mathematical object associated with group representations, often used in theoretical physics to model certain topological properties of space. Spinors resemble vectors but change sign (that is, they are multiplied by −1) when rotated 360 degrees.

• noun algebra An element of the fundamental representation of a Clifford algebra

## Etymologies

### from The American Heritage® Dictionary of the English Language, 4th Edition

[spin + –or (on the model of tensor and vector).]

## Examples

• As spinor is a variable which has algebraic properties identical to that of angular momentum or spin.

• I have ideas that the D-branes have spinor structure similar to electrons which constrain some of that structure in ways.

• As such the position spinor x is related to the momentum spinor p by a "motion," similar to x = x0 + vt.

• Now we consider the primary species of dark matter as the neutralino, which might be a Majorana spinor field and act as its own anti-matter.

• A twistor is a pair of spinors well what's a spinor?

• For gravity I turn to the Weyl tensor C_ {abcd}, which is the traceless component of Riemann curvature tensor for spacetime, and in spinor form this may be written as

Dark Matter: Still Dark. Julianne 2008

• The spinor solutions of the Dirac equation have positive and negative solutions, just as the quadratic equation often has positive and negative solutions.

Dark Matter: Still Dark. Julianne 2008

• The mass which couples the two equations is due to the Higgs field with the Yukawa Lagrangian L = bar-psi H psi which in spinor components is

Dark Matter: Still Dark. Julianne 2008

• But then you take the commutator of two covariant derivatives acting on this spinor field and get a relation involving the Riemann tensor.

• Being that the supersymmetry variation of the gravitino is the covariant derivative of the local spinor parameterizing the supersymmetry transformation, this would seem to always imply that the condition for supersymmetry is that there must exist a covariantly constant spinor field.