What happens when particle-antiparticle pairs annihilate in MWI? The many-worlds interpretation of quantum physics is built around a configuration space, where the position of a particle is three components of the position of that universe.
What happens with particle-antiparticle creation or annihilation? It can't just change the number of dimensions, can it?
 A: In the many-worlds interpretation of quantum mechanics, there is at all times just one state vector for the entire Universe. It is a vector in a certain (infinite-dimensional) vector space, and that vector space is always the same. So there's nothing in the theory whose dimension changes when the number of particles in the Universe changes.
To be a bit more precise, the space in which the state vector of the Universe lives is (something like) a Fock space. Vectors in that space include states with all possible different numbers of particles, as well as superpositions containing different numbers of particles. So if a particle-antiparticle pair is created, the state vector simply "wanders" from one part of that space to another; the space itself needn't get any bigger.
A: As I look upon the MWI: every event is a branch point of a particular universe (i.e. the universe before the event) to a set of universes after the event. Every universe in the set has another outcome of the event as it's start point. All universes are to be considered as objectively real, all outcomes of the event do occur, all in another universe and the different universes cannot interact.
You descrive an event with one particular outcome: the annihilation of a particle-antiparticle pair. The MWI is not related to this situation, your universe is the same before and after this event because you do not consider different outcomes of the event, you assume an event with only one result (annililation).
Some further remarks: 
1) Your phrase "position of the universe" does not make sense, because position is measured ín some universe. For a universe to have a position we have to consider another universe that contains it.
2) The MWI is extremley absurd. When there are 10^80 paricles in the universe and each particle has 10^40 events per second, then after 10^17 seconds there are (10^80^40^17 = 10^54400) universes. MWI defies common sense also in other respects.
