A. H. VGlkel, Phys. Rev. D 1, 3377 (19701. 'A. H . Volkel, Phys. Rev. D 3, 917 (1971). 3~o r the sake of fairness we should mention that this i s denied by some physicists (H. Kleinert and B. Hamprecht, private communication). 4~. Renner, Current ,llgebras and their Applications (Pergamon, New York, 1968). %. L. Adler and R. F. Dashen, Current Algebras and Applications t o Particle Physics (Benjamin, Amsterdam, 19fi8). 6~h e distribution and use of indices a t the currents throughout this paper a r e a s follows: (i) Upper Greek indices p , v , A . . . = 0 , 1, 2, 3 to the left of the argument(s) indicate tensor properties with respect to the Lorentz group, the corresponding Latin indices k , I , Y . . . -1 , 2 , 3 their restriction to the space parts. (ii) Louver Latin indices a , b , c = V , A to the right of the argument(s) differentiate between vectors ( V ) and axial vectors ( A ) . In the commutation relations we have the connection a # bc = A and a = bc = V . (iii) Lower Greek indices a , 8 , y to the left of the a rg u m e n t (~) r e f e r to the internal broken-symmetry group with structure constants E~, ,~~Y .The usual summation convention for double indices i s used. The hfinkowski metric i s (+I, -1, -1, -1).IFurther restrictions on the c l a s s of admitted 6 s equences like cp(xo) 0, etc., would not influence our r esults.8~. F. Streater and A. S. Wightman, P C T , Spin and Statzstics a n d A l l That (Benjamin, New York, 1964). 9~. Girding and A. S. Wightman, Arkiv Fysik 28, 129 (1964).'k. J o s t , The General Theory 01-Quantzaed Fields (American Mathematical Society, Providence, R . I., 1965). "B. Schroer and P. Stichel, Commun. Math. Phys. 3, 258 (1966). l2v. Volkel and A. H. Volkel, Nuovo Cimento @, 203 (1969). 1 3~. Schwartz, ThSorie des Distributions (Hermann. P a r i s , 1959), Vol. II. 14From the work of Schroer and Stichel (Ref. 11) i t follows that this i s very probably not a new and s e v e r e a ssumption beyond the existence of equal-time commutat o r s .l5watch that the form factors depend a l s o on the isospin quantum numbers of the nucleon s t a t e s , which we have not written out explicitly. Therefore, in the following formulas, a summation over s o m e of these quantum numb e r s i s to be understood. 1 6~. Schildknecht. DESY Report No. 69/41, 1969 (unpublished).'?we want to point out that the one-pion pole in the t channel does not contribute to the invariant function
A1-The general properties of analyticity, covariance, and unitarity a r e studied in quantum field theories regularized by finite-mass, indefinite-norm states. After reviewing the genera l status of indefinite-metric theories, a relativistic s c a l a r model i s analyzed for covariance and analyticity. This model shows that a commonly accepted prescription for treating the negative-norm states i s not covariant, and more sophisticated methods a r e required. The technique of shadow states developed elsewhere i s reviewed a d applied to this problenl.