Physics – Quantum Physics
Scientific paper
2006-03-10
Phys.Lett. A357 (2006) 177-180
Physics
Quantum Physics
9 pages, slightly revised published version with updated references
Scientific paper
10.1016/j.physleta.2006.04.045
Analytic continuation of the classical dynamics generated by a standard Hamiltonian, H = p^2/2m + v(x), into the complex plane yields a particular complex classical dynamical system. For an analytic potential v, we show that the resulting complex system admits a description in terms of the phase space R^4 equipped with an unconventional symplectic structure. This in turn allows for the construction of an equivalent real description that is based on the conventional symplectic structure on R^4, and establishes the equivalence of the complex extension of classical mechanics that is based on the above-mentioned analytic continuation with the conventional classical mechanics. The equivalent real Hamiltonian turns out to be twice the real part of H, while the imaginary part of H plays the role of an independent integral of motion ensuring the integrability of the system. The equivalent real description proposed here is the classical analog of the equivalent Hermitian description of unitary quantum systems defined by complex, typically PT-symmetric, potentials.
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