When we perform a organic reaction without any addtional catalyst except that the reaction is carried out under microwave condition we can accelerate this reaction in comparison with one under heating only. So, microwaves can be considered a form of catalysis according to the concept of reaction kinetics?
Here is an example of an entire online GoogleBook dedicated to the topic Microwave Assisted Organic Synthesis, apparently based on some 2,000 papers.
On page 3 of the cited reference, notes to quote:
Interaction between microwave radiation and solutions of polar molecule polar molecules may be adequately described using classical models, which may be derived from Maxwell's equations.
Although this analysis has concentrated on the oscillating components of the electromagnetic field of the microwave radiation, it is also possible to get interaction between the oscillating magnetic field and the magnetic dipoles in the sample. The high-heating rates for Fe304 may be attributed to such interactions.
With respect to benefits, per page 23 to quote:
Reaction rates are generally very high and yields in many cases can be greatly improved, as competing side reactions can be minimized...
I would also add that the use of microwave-based dielectric heating is, at times, more than just fast and efficient and heating, as it can, in the presence of activated carbon, for example, introduce surface-based radicals into the reaction mix. See, for example, Generation of hydroxyl radical in aqueous solution by microwave energy using activated carbon as catalyst and its potential in removal of persistent organic substances.
As such, I described the general use of this new heating technology as microwave-assisted synthesis, and not per se, as catalytic, albeit depending on the reaction mix, it can be (per last cited reference).
If you look at the Arrhenius equation for reaction rates,
we see that the rate is dependent on collision frequency (A) and the portion of molecules with sufficient energy to overcome the activation energy barrier ($E_a$) .
By heating the solution with microwaves, we are increasing T, therefore, increasing the portion of molecules with enough energy to overcome the $E_a$.
Catalysts lower the $E_a$ or provide a different mechanism with a lower $E_a$. This is not how microwaves increase reaction rate as irradiation does not change the activation energy.
Some studies suggest that non-thermal effects are present (i.e. interactions between the EMR field and dipole moment of molecules) however it is still under debate whether they actually exist. A recent article publish in 2018 suggests that a majority of research disputes the existence of non thermal effects or suggest that non thermal effects arise from enhanced diffusion.
Either way, microwaves aren’t a catalyst.