Path integrals and stationary-phase approximations
Abstract
The general formalism for path integrals expressed in terms of an arbitrary continuous representation (generalized coherent states) is applied to give $c$-number formulations for the canonical algebra and for the spin algebra, and is used to derive meaningful stationary-phase approximations for these two cases. Some clarification of a recent discussion by Jevicki and Papanicolaou for the spin case is given.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The spin-orbit Lagrangian has the form of the Coriolis term in systems with intrinsic angular momentum.
“This Lagrangian has the form of the Coriolis term in systems with intrinsic angular momentum [64 -67].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [64]
Cites
Quantum Mechanics and Path Integrals
Miguel Blasco, L. D. (1966) · Students Quarterly Journal · doi:10.1049/sqj.1966.0063 · Cited by 9,884 · see citing works
Coherent and Incoherent States of the Radiation Field
Glauber, R. J. (1963) · Physical Review · doi:10.1103/physrev.131.2766 · Cited by 6,742 · see citing works
Generalized Hamiltonian Dynamics
Dirac, P. A. M. (1950) · Canadian Journal of Mathematics · doi:10.4153/cjm-1950-012-1 · Cited by 2,079 · see citing works
On a Hilbert space of analytic functions and an associated integral transform part I
Bargmann, V. (1961) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160140303 · Cited by 1,830 · see citing works
Periodic Orbits and Classical Quantization Conditions
Gutzwiller, M. C. (1971) · Journal of Mathematical Physics · doi:10.1063/1.1665596 · Cited by 1,536 · see citing works
Atomic Coherent States in Quantum Optics
Arecchi, F. T., Courtens, E., Gilmore, R., & Thomas, H. (1972) · Physical Review A · doi:10.1103/physreva.6.2211 · Cited by 1,491 · see citing works
Some properties of coherent spin states
Radcliffe, J. M. (1971) · Journal of physics. A, Proceedings of the Physical Society. General · doi:10.1088/0305-4470/4/3/009 · Cited by 916 · see citing works
Fundamentals of quantum optics
L.R. (1969) · Nuclear Physics A · doi:10.1016/0375-9474(69)90295-4 · Cited by 904 · see citing works
Phase-Integral Approximation in Momentum Space and the Bound States of an Atom
Gutzwiller, M. C. (1967) · Journal of Mathematical Physics · doi:10.1063/1.1705112 · Cited by 765 · see citing works
Dashen, R. F., Hasslacher, B., & Neveu, A. (1974) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.10.4114 · Cited by 530 · see citing works
Dashen, R. F., Hasslacher, B., & Neveu, A. (1974) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.10.4130 · Cited by 521 · see citing works
The action option and a Feynman quantization of spinor fields in terms of ordinary c-numbers
Klauder, J. R. (1960) · Annals of Physics · doi:10.1016/0003-4916(60)90131-7 · Cited by 508 · see citing works
Self-citationEnergy Spectrum According to Classical Mechanics
Gutzwiller, M. C. (1970) · Journal of Mathematical Physics · doi:10.1063/1.1665328 · Cited by 475 · see citing works
Continuous-Representation Theory. II. Generalized Relation between Quantum and Classical Dynamics
Klauder, J. R. (1963) · Journal of Mathematical Physics · doi:10.1063/1.1704035 · Cited by 358 · see citing works
Self-citationPhase-Integral Approximation in Momentum Space and the Bound States of an Atom. II
Gutzwiller, M. C. (1969) · Journal of Mathematical Physics · doi:10.1063/1.1664927 · Cited by 322 · see citing works
Quantum Kinematics and Dynamics
Schwinger, J. (2018) · CRC Press eBooks · doi:10.1201/9780429497933 · Cited by 292 · see citing works
The Hamiltonian Form of Field Dynamics
Dirac, P. A. M. (1951) · Canadian Journal of Mathematics · doi:10.4153/cjm-1951-001-2 · Cited by 268 · see citing works
Dashen, R. F., Hasslacher, B., & Neveu, A. (1974) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.10.4138 · Cited by 228 · see citing works
Non-Wiener functional integrals
Berezin, F. A. (1971) · Theoretical and Mathematical Physics · doi:10.1007/bf01036576 · Cited by 141 · see citing works
Schweber, S. S. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1724296 · Cited by 95 · see citing works
Classical theory of a rigid magnetic continuum
Valenti, C. F., & Lax, M. D. (1977) · Physical review. B, Solid state · doi:10.1103/physrevb.16.4936 · Cited by 7 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Albash, T., & Lidar, D. A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015002 · Cited by 1,546 · see citing works
Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
Bliokh, K. Y. (2009) · Journal of Optics A: Pure and Applied Optics · doi:10.1088/1464-4258/11/9/094009 · Cited by 217 · see citing works
On the emerging potential of quantum annealing hardware for combinatorial optimization
Tasseff, B., Albash, T., Morrell, Z., Vuffray, M., Lokhov, A. Y., Misra, S., & Coffrin, C. (2024) · Journal of Heuristics · doi:10.1007/s10732-024-09530-5 · Cited by 42 · see citing works
Geometric Canonical Phase Factors and Path Integrals
Kuratsuji, H. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.1687 · Cited by 43 · see citing works
Dynamical Meaning of Quantum Adiabatic Phase: The Case of a Noncanonical System
Kuratsuji, H., & Iida, S. (1986) · Physical Review Letters · doi:10.1103/physrevlett.56.1003 · Cited by 41 · see citing works
- Authors
- Klauder, J. R.
- Corresponding author
- Klauder, John R.
- ORCID
- Klauder, John R.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1979-04-15
- Volume
- 19
- Issue
- 8
- Pages
- 2349-2356
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2110564246
- Cited by
- 327
- References
- 21
- Citations by year
- 2026: 5 · 2025: 3 · 2024: 4 · 2023: 2 · 2022: 7 · 2021: 9 · 2020: 7 · 2019: 7 · 2018: 6 · 2017: 7 · 2016: 7 · 2015: 7 · 2014: 11 · 2013: 6 · 2012: 6
- FWCI
- 5.09
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- path integral, stationary phase method, generalized coherent states, canonical algebras, spin algebra
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
