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A nonzero vector v=(v_0,v_1,...,v_(n-1)) in n-dimensional Lorentzian space R^(1,n-1) is said to be positive lightlike if it has zero (Lorentzian) norm and if its first ...

A nonzero vector v=(v_0,v_1,...,v_(n-1)) in n-dimensional Lorentzian space R^(1,n-1) is said to be positive timelike if it has imaginary (Lorentzian) norm and if its first ...

The Lie derivative of a spinor psi is defined by L_Xpsi(x)=lim_(t->0)(psi^~_t(x)-psi(x))/t, where psi^~_t is the image of psi by a one-parameter group of isometries with X ...

Spinor fields describing particles of zero rest mass satisfy the so-called zero rest mass equations. Examples of zero rest mass particles include the neutrino (a fermion) and ...

Lorentzian n-space is the inner product space consisting of the vector space R^n together with the n-dimensional Lorentzian inner product. In the event that the (1,n-1) ...

A functor F is called covariant if it preserves the directions of arrows, i.e., every arrow f:A-->B is mapped to an arrow F(f):F(A)-->F(B).

A dual number is a number x+epsilony, where x,y in R and epsilon is a matrix with the property that epsilon^2=0 (such as epsilon=[0 1; 0 0]).

A function between categories which maps objects to objects and morphisms to morphisms. Functors exist in both covariant and contravariant types.

A hom-set of a category C is a set of morphisms of C.

A natural transformation Phi={Phi_C:F(C)->D(C)} between functors F,G:C->D of categories C and D is said to be a natural isomorphism if each of the components is an ...