Abstract:
A study is made of Feynman path integrals and some similar integrals which are used to solve
the initial-value problem for the Schrödinger equation. The S matrix and the partition function
are found. The relationship between these integrals and operator symbols is found. In
particular, it is shown that functional integrals of this kind depend strongly on the adopted
approximations of finite multiplicity. The relation between the Feynman integral and the Wick
formula is discussed.
This publication is cited in the following 124 articles:
S. V. Dzhenzher, V. Zh. Sakbaev, “Quantum Law of Large Numbers for Banach Spaces”, Lobachevskii J Math, 45:6 (2024), 2485
D. Bonocore, A. Kulesza, J. Pirsch, “Classical and quantum gravitational scattering with Generalized Wilson Lines”, J. High Energ. Phys., 2022:3 (2022)
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Borisov L.A., Orlov Y.N., “Generalized Evolution Equation of Wigner Function For An Arbitrary Linear Quantization”, Lobachevskii J. Math., 42:1 (2021), 63–69
L. A. Borisov, Yu. N. Orlov, “On the Inversion Formula of Linear Quantization and the Evolution Equation for the Wigner Function”, Proc. Steklov Inst. Math., 313 (2021), 17–26
J. E. Gough, Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Random quantization of Hamiltonian systems”, Dokl. Math., 103:3 (2021), 122–126
Orlov Yu.N., Sakbaev V.Zh., Shmidt E.V., “Operator Approach to Weak Convergence of Measures and Limit Theorems For Random Operators”, Lobachevskii J. Math., 42:10, SI (2021), 2413–2426
Borisov L.A., Orlov Yu.N., “On the Generalization of Moyal Equation For An Arbitrary Linear Quantization”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 24:1 (2021), 2150003
Lasha Berezhiani, Michael Zantedeschi, “Evolution of coherent states as quantum counterpart of classical dynamics”, Phys. Rev. D, 104:8 (2021)
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Yana A. Butko, Springer Proceedings in Mathematics & Statistics, 325, Semigroups of Operators – Theory and Applications, 2020, 19
Evgenii Kochetov, “Comment on “Coherent-state path integrals in the continuum””, Phys. Rev. A, 99:2 (2019)
Yu. N. Orlov, V. Zh. Sakbaev, “Feynman–Chernoff iterations and their applications in quantum dynamics”, Proc. Steklov Inst. Math., 301 (2018), 197–206
J. L. M. Assirati, D. M. Gitman, “Covariant quantizations in plane and curved spaces”, Eur. Phys. J. C, 77:7 (2017)
Fiorenzo Bastianelli, Olindo Corradini, Edoardo Vassura, “Quantum mechanical path integrals in curved spaces and the type-A trace anomaly”, J. High Energ. Phys., 2017:4 (2017)
Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Unbounded random operators and Feynman formulae”, Izv. Math., 80:6 (2016), 1131–1158
Butko Ya.A., Grothaus M., Smolyanov O.G., “Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions”, J. Math. Phys., 57:2 (2016), 023508
L. A. Borisov, Yu. N. Orlov, “Analyzing the dependence of finite-fold approximations of the harmonic oscillator equilibrium density matrix and of the Wigner function on the quantization prescription”, Theoret. and Math. Phys., 184:1 (2015), 986–995
L. A. Borisov, Yu. N. Orlov, V. Zh. Sakbaev, “Formuly Feinmana dlya usredneniya polugrupp, porozhdaemykh operatorami tipa Shredingera”, Preprinty IPM im. M. V. Keldysha, 2015, 057, 23 pp.
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