I was wondering if the universal wave function can be thought of using a path integral approach? And if so, does each path correspond to a "branch" of the MWI of QM? Or have I misunderstood what is meant by a MWI branch?
Quantum Mechanics – Universal Path Integral & the Many-Worlds Interpretation
path-integralquantum mechanicsquantum-interpretations
Best Answer
Branches in the MWI are coarse-grained emergent things, and their number cannot be precisely quantified (see https://oxford.universitypressscholarship.com/view/10.1093/acprof:oso/9780199546961.001.0001/acprof-9780199546961-chapter-4 ). Depending on how finely you coarse-grain worlds and how the measurement is performed, more or less paths in the path integral may contribute significantly to each branch.
If you work only at the level of "individual" paths and define each path as a branch, like some sort of quantum Laplace's demon, then you must be very comfortable with some of your branches interfering with each other indefinitely rather than decohering into approximately separate worlds. By refusing to coarse-grain, you haven't really isolated any branching structure at all.