Geodesic
Path integral in the energy representation in quantum mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 1, pp. 92-111 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider an alternative path integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is the Laplace transform of the evolution operator) in a form that has the meaning of “the sum over paths” but is much better defined than the usual functional integral. We investigate this representation from different standpoints and compare such an approach to quantum mechanics with the standard approaches.
Keywords: path integral, quantum mechanics, instanton. 
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P. A. Putrov. Path integral in the energy representation in quantum mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 1, pp. 92-111. http://geodesic.mathdoc.fr/item/TMF_2008_156_1_a4/

[1] R. Feinman, A. Khibbs, Kvantovaya mekhanika i integraly po traektoriyam, Mir, M., 1968 | MR | Zbl

[2] L. D. Landau, E. M. Livshits, Kvantovaya mekhanika. Nerelyativistskaya teoriya, Nauka, M., 1989 | MR | MR | Zbl

[3] S. Coleman, “Uses of instantons”, The Whys of Subnuclear Physics, Proceedings of the International School of Subnuclear Physics (Trapani, Sicily, July 23 – August 10, 1977), ed. A. Zichichi, Plenum, New York, 1979, 805 | DOI | MR

[4] V. A. Novikov, M. A. Shifman, A. I. Vainshtein, V. I. Zakharov, “ABC of instantons”, ITEP Lectures on Particle Physics and Field Theory, v. 1, World Sci. Lecture Notes Phys., 62, ed. M. A. Shifman, World Scientific, Singapore, 1999, 201–299 | DOI | MR | Zbl

[5] A. Polyakov, 2D Quantum Gravity and SC at high $T_c$, Elsevier Science Publishers B.V., 1989

[6] A. M. Polyakov, Kalibrovochnye polya i struny, ITF, Chernogolovka, 1995 | MR | Zbl