Product Representations and the Quantization of Constrained Systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 212-222 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study special systems with infinitely many degrees of freedom with regard to dynamical evolution and fulfillment of constraint conditions. Attention is focused on establishing a meaningful functional framework, and for that purpose, coherent states and reproducing kernel techniques are heavily exploited. Several examples are given.
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J. R. Klauder. Product Representations and the Quantization of Constrained Systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 212-222. http://geodesic.mathdoc.fr/item/TM_1999_226_a16/

[1] Klauder J. R., McKenna J., “Continuous-representation theory. V: Construction of a class of scalar boson field continuous representation”, J. Math. Phys., 6 (1965), 68–87 | DOI | MR | Zbl

[2] Klauder J. R., McKenna J., Woods E. J., “Direct-product representations of the canonical commutation relation”, J. Math. Phys., 7 (1966), 822–828 | DOI | MR | Zbl

[3] Klauder J. R., Skagerstam B.-S., Coherent states, World Sci., Singapore, 1985 | MR | Zbl

[4] Klauder J. R., Ann. Phys., 254 (1997), 419 | DOI | MR | Zbl

[5] Shabanov S., “Path integral in golomorphic representation without gauge fixation”, Path integrals: Theory and applications (Dubna, May 1996), eds. V. S. Yarunin, M. A. Smondyrev, Joint Inst. Nucl. Res., Dubna, 1996, 133–138 | MR

[6] Aronszajn N., “La théorie des noyaux reproduisants et ses applications, I”, Proc. Cambridge Phil. Soc., 39 (1943), 133–153 | DOI | MR

[7] Aronszajn N., “Theory of reproducing kernels”, Trans. Amer. Math. Soc., 68 (1950), 337–404 | DOI | MR | Zbl

[8] von Neumann J., “On infinite direct products”, Compos. math., 6 (1938), 1–77

[9] Haag R., “On quantum field theories”, Danske Vid. Selsk. Mat.-Fys. Medd., 29:12 (1955), 37 | MR | Zbl