Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 301 / 2 / b / ii

Table of contents
- Solution ii

Solution

The scalar kinetic operator is proportional in momentum space to

k^{2} (c k^{2} - m^{2})

. Its inverse has the partial-fraction decomposition

\frac{i}{k ^{2} ( c k ^{2} - m ^{2} )} = - \frac{i}{m ^{2}} (\frac{1}{k ^{2}} - \frac{c}{c k ^{2} - m ^{2}}),

up to the overall convention-dependent factor allowed in the question. Thus

c = a + b

. Under the physical relation

b = - a

, one has

c = 0

, so the extra massive pole and its ghost residue disappear.

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version