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In this article we apply algebraic operator ordering property of the basicatom and field operators to construct and prove conservation of the excitationnumber operator of the anti-rotating (anti-Jaynes-Cummings) component of thequantum Rabi model. The corresponding U(1) and parity symmetry operators havealso been derived in explicit form.

Conserved excitation number and U(1)-symmetry operator for the anti-rotating (anti-Jaynes-Cummings) term of the Rabi Hamiltonian