zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

81S05Commutation relations (quantum theory)
81S40Path integrals in quantum mechanics
70H03Lagrange’s equations
70H20Hamilton-Jacobi equations (mechanics of particles and systems)
Full Text: DOI
[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.