Effects of the Pauli principle for nucleons in a classical phase space

Operators in Bargmann-Hilbert space are dequantized by associating with them a classical function on phase space. Three types of classical functions are considered. They are defined as expectation values between coherent states, symmetrized coherent states and antisymmetrized coherent states. Classical equations of motion are derived through the time-dependent variational principle. For symmetric and antisymmetric dequantization the solutions are given by pairs of trajectories. The method is applied to the relative motion of two nucleons with an effective Gaussian interaction. In a one-dimensional model, the lines of constant energy on phase space show the strong non-local contributions to the interaction. According to the time-dependent variation principle, the trajectories of the solutions must coincide with these lines. The Pauli principle has the following effect: antisymmetric dequantization yields a significant repulsion whereas symmetric dequantization yields additional attraction, compared with the dequantization through coherent states.