Tdec

Description

Tdec[{q,mu}, {p}]; Tdec[{{qi, mu}, {qj, nu}, ...}, {p1, p2, ...}] or Tdec[exp, {{qi, mu}, {qj, nu}, ...}, {p1, p2, ...}] calculates the tensorial decomposition formulas. The more common ones are saved in TIDL.

Options[Tdec]

See also:  TID, TIDL, OneLoopSimplify.

Examples

Check that ∫(d^D) f(p, q) 
            (q^μ) =  ((p^μ)/(p^2)) ∫(d^D) f(p, q) 
              p·q

Tdec[{q, μ}, {p}]

%[[2]] /. %[[1]]

This calculates integral transformation for any \(TraditionalForm\`∫\(d\^D\) \(q\_1\) \(d\^D\) \(q\_2\) \(d\^D\) q\_3\) f(p, (Subscript[q, 1,]) (Subscript[q, 2]), 
          (Subscript[q, 3])) (Subscript[q, 1]^μ) (Subscript[q, 2]^ν) (Subscript[q, 3]^ρ).

t = 
      Tdec[{{(Subscript[q, 1]), μ}, {(Subscript[q, 2]), ν}, {(Subscript[q, 3]), ρ}}, {p}];

t[[2]] /. t[[1]]

Contract[% FVD[p, μ] FVD[p, ν] FVD[p, ρ]] // 
      Factor

Clear[t];