arXiv subjects
Publications and source records attributed to Martin Zika.
We review the notion of homotopy of quantum master actions in geometric Batalin-Vilkovisky formalism. Then we construct new examples of such homotopies, coming from renormalization group flow and non-infinitesimal changes of gauge fixing. Finally, we use the field redefinitions given by these homotopies to construct spans of quantum master actions with isomorphic effective actions.
Quantum $L_\infty$ algebras are higher loop generalizations of cyclic $L_\infty$ algebras. Motivated by the problem of defining morphisms between such algebras, we construct a linear category of $(-1)$-shifted symplectic vector spaces and distributional half-densities, originally proposed by \v{S}evera. Morphisms in this category can be given both by formal half-densities and Lagrangian relations; we prove that the composition of such morphisms recovers the construction of homotopy transfer of quantum $L_\infty$ algebras. Finally, using this category, we propose a new notion of a relation between quantum $L_\infty$ algebras.