Abstract:
A study is made of the classical mechanics and canonical quantization of systems with commuting and anticommuting variables (mixed systems). Boson and fermion dual strings with internal spin are second quantized. A representation of the propagator of the spin string in terms of a path integral with respect to commuting and anticommuting variables is considered and a rule for matching such integrals is obtained.
Citation:
N. V. Borisov, M. V. Ioffe, M. I. Eides, “Second quantization of field systems on a Grassmann Algebra dual string with internal spin”, TMF, 29:1 (1976), 25–41; Theoret. and Math. Phys., 29:1 (1976), 906–916
\Bibitem{BorIofEid76}
\by N.~V.~Borisov, M.~V.~Ioffe, M.~I.~Eides
\paper Second quantization of field systems on a~Grassmann Algebra dual string with internal spin
\jour TMF
\yr 1976
\vol 29
\issue 1
\pages 25--41
\mathnet{http://mi.mathnet.ru/tmf3428}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=475402}
\transl
\jour Theoret. and Math. Phys.
\yr 1976
\vol 29
\issue 1
\pages 906--916
\crossref{https://doi.org/10.1007/BF01093462}
Linking options:
https://www.mathnet.ru/eng/tmf3428
https://www.mathnet.ru/eng/tmf/v29/i1/p25
This publication is cited in the following 5 articles:
Andrianov A.A. Ioffe M.V., “Nonlinear Supersymmetric Quantum Mechanics: Concepts and Realizations”, J. Phys. A-Math. Theor., 45:50 (2012), 503001
M.V. Ioffe, J. Mateos Guilarte, P.A. Valinevich, “Two-dimensional supersymmetry: From SUSY quantum mechanics to integrable classical models”, Annals of Physics, 321:11 (2006), 2552
A. G. Izergin, V. S. Kapitonov, N. A. Kitanin, “Equal-time temperature correlators of the one-dimensional Heisenberg XY chain”, J. Math. Sci. (New York), 100:2 (2000), 2120–2140
N. V. Borisov, K. N. Ilinski, “Supersymmetry on noncompact manifolds and complex geometry”, J. Math. Sci. (New York), 85:1 (1997), 1605–1618
N. V. Borisov, P. P. Kulish, “Path integral in superspace for a relativistic spinor particle in an external gauge field”, Theoret. and Math. Phys., 51:3 (1982), 535–540
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