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References
Bellisard, J., Quantized fields in interaction with external fields. Comm. Math. Phys. 41, 235–266 (1975).
Bongaarts, P.J.M., The electron-positron field coupled to external electromagnetic potentials as an elementary C*-algebra theory. Ann. Physics 56, 108–139 (1970).
Bongaarts, P.J.M., Linear fields according to I. E. Segal, in Mathematics of Contemporary Physics (R.F. Streater, Ed.), 187–208. New York: Academic Press 1972.
Brauer, R., & H. Weyl, Spinors in n dimensions. Amer. J. of Math. 57, 425–449 (1935).
Cook, J., The mathematics of second quantization. Trans. Am. Math. Soc. 74, 222–245 (1953).
Gross, L., Existence and uniqueness of physical ground states. J. Functional Analysis 10, 52–109 (1972).
Kato, T., Perturbation Theory for Linear Operators. Berlin Heidelberg New York: Springer 1966.
Foldy, L.L., & S.A. Wouthuysen, On the Dirac theory of spin 1/2 particles and its non relativistic limit. Phys. Rev. 78, 29–36 (1950).
Klein, A., & J. Rafelski, Quantum electrodynamics of spin 1/2 and spin 0 particles in external electrostatic fields of arbitrary strength. AIP conference proceeding no. 23, Particles and Fields (subseries 10), 356 (1975).
Labonti, G., On the nature of “strong” Bogoliubov transformations for fermions. Comm. Math. Phys. 36, 59 (1974)
Manuceau, J., & A. Verbeure, The theorem on unitary equivalence of Fock representations. Ann. Inst. Poincaré 16, 87–91 (1971).
Palmer, J., Symplectic groups and the Klein-Gordon field. J. Functional Anal. 27, 308–336 (1978).
Palmer, J., Scattering automorphisms of the Dirac field. J. Math. Anal, and Applications 64, 189–215 (1978).
Palmer, J., Euclidean Fermi fields, preprint.
Ruijsenaars, S. N. M., Charged particles in external fields, Commun. Math. Phys. 52, 267–294 (1971).
Segal, I. E., Foundations of the theory of dynamical systems of infinitely many degrees of freedom I. Mat. Fys. Medd. Dansk. Vid. Selsk. 12 (1959).
Segal, I. E., Foundations of the theory of dynamical systems of infinitely many degrees of freedom II. Can. J. Math. 13, 1–18 (1961).
Segal, I. E., Distributions in Hilbert space and canonical systems of operators. Trans. Amer. Math. Soc. 88, 12–41 (1958).
Seiler, R., Quantum theory of particles with spin 0 and 1/2 in external fields. Comm. Math. Phys. 25, 127–151 (1972).
Seiler, R., Particles with spin s≦1 in an external field, preprint, Freie Universität Berlin.
Shale, D., & F. Stinespring, Spinor representations of infinite orthogonal groups. J. Math. Mech. 14, 315 (1965).
Reed, M., & B. Simon, Methods of Modern Mathematical Physics II, Fourier Analysis and Self-Adjointness. New York-London: Academic Press 1975.
von Neumann, J., On infinite products. Composite Math., 6, 1–77 (1938).
Weinless, M., Existence and uniqueness of the vacuum for linear quantized fields. J. Functional Anal., 4, 350–379 (1969).
Wightman, A., Relativistic wave equations as singular hyperbolic systems, in Partial Differential Equations. Proc. Symp. Pure Math. XXIII, A.M.S., (1973).
Greiner, W., & J. Reinhardt, Quantum electrodynamics of strong fields. Rep. Prog. Phys. 40, 219–295 (1977).
Popov, V., Collapse to the center at Z>137 and critical nuclear charge, Soviet J. Nuc. Phys. 12, no. 2, 235–243 (1971).
Cook, J., Complex hilbertian structures on stable linear systems. J. Math. Mech., 16, 339–349 (1966).
van Daele, A., & A. Verbeure, Unitary equivalence of Fock representations on the Weyl algebra. Comm. Math. Phys. 20, 268–278 (1971).
Wightman, A.S. On the localizability of quantum mechanical systems. Rev. Mod. Phys. 34, 845–872 (1962).
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Communicated by G. Strang
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Palmer, J. Complex structures and external fields. Arch. Rational Mech. Anal. 75, 31–49 (1980). https://doi.org/10.1007/BF00284619
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DOI: https://doi.org/10.1007/BF00284619