content_image/336018.jpg content_image/336019.jpg content_image/336017.jpg content_image/336016.jpg content_image/336020.jpg
and a similar term would occur in the right-hand part of equation (4b). This contradicts our initial assumption that the electromagnetic field generated by electrical charges and the electromagnetic field generated by magnetic charges are described independently and, hence, with varying potentials A$_{e}$ and B$_{µ}$ we should not vary the terms of full action, containing the effective potentials. The source-containing terms of equations (4b), (15b) make no sense to quantization of a free electromagnetic field in relativistic quantum field theory. 

## III. MAGNETIC MONOPOLE IN RELATIVISTIC QUANTUM FIELD THEORY 

Since a distinction between action (23) and an ordinary action without magnetic charges is not important, from viewpoint of relativistic quantum field theory, the Feynman rules for the calculation of the interaction cross-sections for elementary particles interacting with electrical or magnetic charges can be formulated by generalizing the known results of rela- tivistic quantum field theory for an electromagnetic field without magnetic charges (see, for example, [8], § 24). 

Operator S ( S -matrix), which relates amplitudes of the initial Φ ( −∞ ) and the final Φ ( ∞ ) states: 

– can be expressed via chronological exponent 

where L$_{I}$ ( x ) is Lagrangian of interaction 

and 

<img src='content_image/336018.jpg'>

<img src='content_image/336019.jpg'>

<img src='content_image/336017.jpg'>

<img src='content_image/336016.jpg'>

For the charged particle propagator we have an ordinary expression in terms of function D $^{c}$( x − y ) for scalar particle of mass m$_{n}$ – compare with [8], (15.17), (22.9): 

<img src='content_image/336020.jpg'>

