G _ _ _ _ _ _ _ _ _ _ _ _ operator

g is an n-ary operator used to denote a product of gamma matrices contracted with Lorentz four-vectors, in high-energy physics.

syntax:

g(<identifier>,<vector-expr> {,<vector-expr>}*)

<identifier> is a scalar identifier representing a fermion line identifier, <vector-expr> can be any valid vector expression, representing a vector or a gamma matrix.

examples:

vector aa,bb,cc; 

vector a; 

g(line1,aa,bb); 

  AA.BB 


g(line2,aa,a); 

  0 


g(id,aa,bb,cc); 

  0 


g(li1,aa,bb) + k; 

  AA.BB + K 


let aa.bb = m*k; 

g(ln1,aa)*g(ln1,bb); 

  K*M 


g(ln1,aa)*g(ln2,bb); 

  0

The vector A is reserved in arguments of g to de note the special gamma matrix gamma_5. It must be declared to be a vector before you use it.

Gamma matrix expressions are associated with fermion lines in a Feynman diagram. If more than one line occurs in an expression, the gamma matrices involved are separate (operating in independent spin space), as shown in the last two example lines above. A product of gamma matrices associated with a single line can be entered either as a single g command with several vector arguments, or as products of separate g commands each with a single argument.

While the product of vectors is not defined, the product, sum and difference of several gamma expressions are defined, as is the product of a gamma expression with a scalar. If an expression involving gamma matrices includes a scalar, the scalar is treated as if it were the product of itself with a unit 4 x 4 matrix.

Dirac expressions are evaluated by computing the trace of the expression using the commutation algebra of gamma matrices. The algorithms used are described in articles by J. S. R. Chisholm in <Il Nuovo Cimento X,> Vol. 30, p. 426, 1963, and J. Kahane, <Journal of Mathematical Physics>, Vol. 9, p. 1732, 1968. The trace is then divided by 4 to distinguish between the trace of a scalar and the trace of an expression that is the product of a scalar with a unit 4 x 4 matrix.

Trace calculations may be prevented over any line identifier by declaring it to be nospur. If it is later desired to evaluate these trace s, the declaration can be undone with the spur declaration.

The notation of Bjorken and Drell, <Relativistic Quantum Mechanics,> 1964, is assumed in all operations involving gamma matrices. For an example of the use of g in a calculation, see the <REDUCE User's Manual>.