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We give a brief introduction to the physics goals of Tensor Field Theory (for a recent review see arXiv:2010.06539).
We show that standard identities and theorems for lattice models with U(1) symmetry get re-expressed discretely in the tensorial formulation.
We explain the geometrical analogy between the continuous lattice equations of motion and the discrete selection rules of the tensors.
We construct a gauge-invariant transfer matrix in arbitrary dimensions. We show the equivalence with its gauge-fixed version in a maximal temporal gauge and explain how a discrete Gauss's law is always enforced. We propose a noise-robust way to implement Gauss's law in arbitrary dimensions.
We reformulate Noether's theorem for global, local, continuous or discrete Abelian symmetries: for each given symmetry, there is one corresponding tensor redundancy (this is the main message of Phys. Rev. D 102, 014506 (2020)). If time permits, we will discuss semi-classical approximations for classical solutions and implications for quantum computing.