Conservation laws in quantum field theory on graphs
arXiv:1809.05945
Abstract
It is shown that expected values of free scalar and vector quantum fields on graphs satisfy the same conservation laws as the classic fields. It is demonstrated that a modified version of conservation laws is satisfied for Villain action. The proofs are based on the consideration of multidimensional normal distribution.
The main result turned out to be known. It is derived analogously to the Schwinger-Dyson equation and the Ward identities