Invariants, Projection Operators and $SU(N)\times SU(N)$ Irreducible Schwinger Bosons

Abstract

We exploit SU(N) Schwinger bosons to construct and analyze the coupled irreducible representations of $SU(N)\times SU(N)$ in terms of the invariant group. The corresponding projection operators are constructed in terms of the invariant group generators. We also construct $SU(N)\times SU(N)$ irreducible Schwinger bosons which directly create these coupled irreducible states. The SU(N) Clebsch Gordan coefficients are computed as the matrix elements of the projection operators.

24 pages, 2 figures

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• Mass gap in the weak coupling limit of $(2+1)$ SU(2) lattice gauge theory
• Addition of SU(3) generators and its Singlet Hilbert space
• Bosonic randomized benchmarking with passive transformations