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Canonical quantization of higher-order Lagrangians. (English) Zbl 1226.81098
Summary: After reducing a system of higher-order regular Lagrangians into first-order singular Lagrangians using a constrained auxiliary description, the Hamilton-Jacobi function is constructed. Besides, the quantization of the system is investigated using the canonical path integral approximation.

MSC:
81S05Commutation relations (quantum theory)
81S40Path integrals in quantum mechanics
70H03Lagrange’s equations
70H20Hamilton-Jacobi equations (mechanics of particles and systems)
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References:
[1] P. A. M. Dirac, “Generalized Hamiltonian dynamics,” Canadian Journal of Mathematics, vol. 2, pp. 129-148, 1950. · Zbl 0036.14104 · doi:10.4153/CJM-1950-012-1
[2] P. A. M. Dirac, Lectures on Quantum Mechanics, vol. 2, Belfer Graduate School of Science, Yeshiva University, New York, NY, USA, 1967. · Zbl 0161.20704
[3] E. M. Rabei and Y. Guler, “Hamilton-Jacobi treatment of second-class constraints,” Physical Review A, vol. 46, no. 6, pp. 3513-3515, 1992. · doi:10.1103/PhysRevA.46.3513
[4] C. Carathéodory, Calculus of Variations and Partial Differential Equations of the First Order, Holden-Day, San Francisco, Calif, USA, 1967. · Zbl 0152.31602
[5] B. M. Pimentel and R. G. Teixeira, “Hamilton-Jacobi formulation for singular systems with second-order Lagrangians,” Il Nuovo Cimento B, vol. 111, no. 7, pp. 841-854, 1996. · doi:10.1007/BF02749015
[6] B. M. Pimentel and R. G. Teixeira, “Generalization of the Hamilton-Jacobi approach for higher-order singular systems,” Il Nuovo Cimento B, vol. 113, no. 6, pp. 805-817, 1998.
[7] S. Muslih and Y. Güler, “The Feynman path integral quantization of constrained systems,” Il Nuovo Cimento B, vol. 112, no. 1, pp. 97-107, 1997.
[8] E. M. Rabei, “On the quantization of constrained systems using path integral techniques,” Il Nuovo Cimento B, vol. 115, no. 10, pp. 1159-1165, 2000.
[9] S. I. Muslih, “Quantization of singular systems with second-order Lagrangians,” Modern Physics Letters A, vol. 17, no. 36, pp. 2383-2391, 2002. · Zbl 1083.81008 · doi:10.1142/S0217732302009027
[10] S. I. Muslih, “Path integral formulation of constrained systems with singular-higher order Lagrangians,” Hadronic Journal, vol. 24, no. 6, pp. 713-720, 2001. · Zbl 1154.70333
[11] E. M. Rabei, K. I. Nawafleh, and H. B. Ghassib, “Quantization of constrained systems using the WKB approximation,” Physical Review A, vol. 66, no. 2, pp. 024101/1-024101/4, 2002. · Zbl 1081.81524
[12] M. V. Ostrogradski, Mémoires de l’Académie de Saint Peters Bourg, vol. 6, p. 385, 1850.
[13] J. Govaerts, Hamiltonian Quantization and Constrained Dynamics, Leuven University Press, Leuven, Belgium, 1991. · Zbl 0736.65015
[14] J. M. Pons, “Ostrogradski’s theorem for higher-order singular Lagrangians,” Letters in Mathematical Physics, vol. 17, no. 3, pp. 181-189, 1989. · Zbl 0688.70010 · doi:10.1007/BF00401583
[15] K. I. Nawafleh and A. A. Alsoub, “Quantization of higher order regular lagrangians as first order singular lagrangians using path integral approach,” Jordan Journal of Physics, vol. 1, no. 2, pp. 73-78, 2008.