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Commutation rules and spurious eigenstates in soluble field theories

Norton, R. E. and Watson, W. K. R. (1959) Commutation rules and spurious eigenstates in soluble field theories. Physical Review, 116 (6). pp. 1597-1603. ISSN 0031-899X. doi:10.1103/PhysRev.116.1597.

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A study is made of the exactly soluble field theories which are characterized by Hamiltonians quadratic in the field variables. As an example of such a theory, a model describing the electric dipole interaction of photons and a nonrelativistic, harmonically bound electron is studied explicitly. For the cases when the cutoff is sufficiently large to admit the "runway solutions," it is necessary in order to obtain consistency and a sensible physical interpretation that the theory be reformulated by a unique modification of the equaltime commutation rules of the field operators. The problems which arise here in connection with the "run-away solutions" are closely related to the troubles of ghost states and negative transition "probabilities" which have been demonstrated or suggested to exist in other theories. It is hoped, therefore, that the procedure of reformulation required here may be a guide for the eventual resolution of the ghost-state problem should it be demonstrated that such problems actually exist in the physical, relativistic field theories.

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Additional Information:©1959 The American Physical Society. Received 13 April 1959; revised 31 August 1959. One of us (R.E.N.) would like to express his gratitude to the California Institute of Technology for the Richard C. Tolman postdoctoral research fellowship which he held during the course of this work. Both of us wish to thank Professors R. Feynman and M. Gell-Mann for many illuminating discussions; and also Mr. Sidney Coleman for a number of enjoyable and helpful conversations.
Issue or Number:6
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6117
Deposited By: Tony Diaz
Deposited On:25 Nov 2006
Last Modified:08 Nov 2021 20:31

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