Abstract
Guided by a diagonalized form of the classical field-energy we construct a time-dependent canonical pair of Schrödinger fields Φ t (x) and Π t (x) which diagonalizes the field-HamiltonianH t . These Schrödinger fields in general belong to inequivalent representations of the canonical commutation relations for differentt's.
The Heisenberg field is constructed by solving the Heisenberg equation of motion and its time-evolution turns out to be governed by a unitary operator, i.e. the Heisenberg fields at different times are unitarily equivalent.
Scattering theory (including eventual incoming and/or outgoing bound-states) is finally constructed.
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References
Heisenberg, W., Pauli, W.: Zeitschrift für Physik56, 1 (1929).
Schnyder, H., Weinberg, J.: Phys. Rev.57, 307 (1940).
Moses, H.E.: Phys. Rev.89, 115 (1953),95, 237 (1954).
Bongaarts, P.J.M.: Ann. of Phys.56, 108 (1970).
Lehmann, H., Symanzik, K., Zimmermann, W.: Nuovo Cimento1, 425 (1955).
Feynmann, R.P.: Phys. Rev.76, 749 (1949).
Dyson, F.J.: Phys. Rev.75, 486 (1949).
Salam, A., Matthews, P.T.: Phys. Rev.90, 690 (1953).
Schwinger, J.: Phys. Rev.93, 615 (1954).
Capri, A.Z.: Journ. Math. Phys.10, 575 (1969).
Schroer, B., Seiler, R., Swieca, J.A.: Phys. Rev. D,2, 2929 (1970).
Ekstein, H.: Phys. Rev. D,5, 5 (1972).
Labonté, G., Capri, A.Z.: Nuovo Cimento B10, 583 (1972).
Lundberg, L.-E.: Commun. math. Phys.31, 243–257 (1973).
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Lundberg, LE. Relativistic quantum theory for charged spinless particles in external vector fields. Commun.Math. Phys. 31, 295–316 (1973). https://doi.org/10.1007/BF01646491
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DOI: https://doi.org/10.1007/BF01646491