@article{8816,
abstract = {Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.},
author = {Runkel, Ingo and Szegedy, Lorant},
issn = {14320916},
journal = {Communications in Mathematical Physics},
number = {1},
pages = {83–117},
publisher = {Springer Nature},
title = {{Area-dependent quantum field theory}},
doi = {10.1007/s00220-020-03902-1},
volume = {381},
year = {2021},
}