Bosonic/Fermionic Tensor Network Diagram and Normal Ordering Super-Fock Space

Tensor network diagrams and Feynman diagrams are both widely used in many-body physics, and they are originated from the concept of the tensor category, which provides an intuitive way to understand quantum physics through information theory. But Feynman diagrams only deal with scattering problems, while tensor networks focus on product spaces; they are not intended to explain how many-body systems work. In this talk, a generalization of tensor network diagram, called bosonic/fermionic tensor network diagram, is introduced, which captures the exchange symmetry of Fock spaces, and provides an intuitive view of interactions in many-body systems. As an analogy for Fock spaces, symmetric/antisymmetric tensor algebras for open systems, called normal ordering super-Fock space, are also established. In this formulation, the master equation of the system can be easily derived, and the boundary between dissipation and fluctuation is surprisingly clear.