[en] Massive quantum electrodynamics of the electron is formulated as an LSZ theory of the electromagnetic field F(μν) and the electron-positron fields PSI. The interaction is introduced with the help of mathematically well defined subsidiary conditions. These are: 1) gauge invariance of the first kind, assumed to be generated by a conserved current j(μ); 2) the homogeneous Maxwell equations and a massive version of the inhomogeneous Maxwell equations; 3) a minimality condition concerning the high momentum behaviour of the theory. The inhomogeneous Maxwell equation is a linear differential equation connecting Fsub(μν) with the current Jsub(μ). No Lagrangian, no non-linear field equations, and no explicit expression of Jsub(μ) in terms of PSI, anti-PSI are needed. It is shown in perturbation theory that the proposed conditions fix the physically relevant (i.e. observable) quantities of the theory uniquely

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[en] We demonstrate in our work, on the special example of dressing the nucleon propagator, that, if ghost poles exist, they lead to ghost cuts, and the ghost cuts generate new ghost cuts. The geometry of the location of these cuts in the complex s plane is fully discussed and analyzed. We found a simple exact parametric representation of the nth ghost cut: s = s/sub g//(1-p) + (nμ)²/p, where p is a real parameter 0 < or = p < or = 1, s/sub g/ is the location of the ghost pole, and μ is the pion mass. When the location of the ghost pole approaches the nucleon pole, the ghost cuts approach the unitarity cut. The renormalization procedure is adopted to the case of a ghost pole appearing on the real axis of s

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[en] We derive the analytical properties of the elastic forward scattering amplitude of two scalar particles from the axioms of the noncommutative quantum field theory. For the case of only space-space noncommutativity, i.e., θ_0i=0, we prove the dispersion relation which is similar to the one in commutative quantum field theory. The proof in this case is based on the existence of the analog of the usual microcausality condition and uses the Lehmann-Symanzik-Zimmermann (LSZ) or equivalently the Bogoliubov-Medvedev-Polivanov (BMP) reduction formalisms. The existence of the latter formalisms is also shown. We remark on the general noncommutative case, θ_0i≠0, as well as on the nonforward scattering amplitude and mention their peculiarities

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[en] The extraction of one-particle singularities from the n-point functions is performed in the framework of L.S.Z. field theory in the case of a single massive scalar field. It is proved that the 'one-particle irreducible' functions thus obtained enjoy the analytic and algebraic primitive structure of general n-point functions (up to a finite number of generalized C.D.D. singularities). Finally under an additional technical assumption, it is shown that the Glaser-Lehmann-Zimmermann relations stating the completeness of asymptotic states yield similar relations satisfied in any given channel by the corresponding one-particle irreducible functions. (orig.)

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[en] An S matrix analog is defined for anti - de Sitter (Ads) space by constructing in and out states that asymptote to the timelike boundary. A derivation parallel to that of the Lehmann-Symanzik-Zimmermann formula shows that this boundary S matrix is given directly by correlation functions in the boundary conformal theory. This provides a key entry in the AdS to conformal field theory dictionary. copyright 1999 The American Physical Society

No abstract available