SplitSymbolicPowers
SplitSymbolicPowers
is an option for FCFeynmanParametrize
and other functions. When set to True
, propagator powers containing symbols will be split into a nonnegative integer piece and the remaining piece. This leads to a somewhat different form of the resulting parametric integral, although the final result remains the same. The default value is False
.
See also
Overview, FCFeynmanParametrize.
Examples
(p2−m2+iη)−r−2
v1 = FCFeynmanParametrize[SFAD[{p, m^2, r - 1}], {p}, Names -> x, FCReplaceD -> {D -> 4 - 2 Epsilon}]
{1,Γ(r−1)m6(−1)r−1(m2)−ε−rΓ(ε+r−3),{}}
v2 = FCFeynmanParametrize[SFAD[{p, m^2, r - 1}], {p}, Names -> x, FCReplaceD -> {D -> 4 - 2 Epsilon},
SplitSymbolicPowers -> True]
{1,Γ(r)m6(−1)r−1(r−1)(m2)−ε−rΓ(ε+r−3),{}}
Both parametrizations lead to the same results (as expected)
Series[v1[[2]], {Epsilon, 0, 1}] // Normal
Series[v2[[2]], {Epsilon, 0, 1}] // Normal
% - %% // Simplify // FunctionExpand
Γ(r−1)εm6(−1)r(m2)−rΓ(r−3)(log(m2)−ψ(0)(r−3))−Γ(r−1)m6(−1)r(m2)−rΓ(r−3)
Γ(r)εm6(−1)r(r−1)(m2)−rΓ(r−3)(log(m2)−ψ(0)(r−3))−Γ(r)m6(−1)r(r−1)(m2)−rΓ(r−3)
0