Summary
Recent experimental measurements at HERA of the Structure Functions in lepton-hadron inelastic scattering started to bridge the gap between the hard and the soft regimes of strong interactions. In this scenario the Complex Angular Momentum (CAM) theory, which plays a relevant role in describing soft processes, which are intrinsically non-perturbative, is widely adopted as a phenomenological model. It is therefore of some interest to explore up to what extent one can give a theoretical foundation to CAM methods, starting from the basic axiomatic principles of Quantum Field Theory (QFT). In this review we shall try to expose the main results obtained recently on this topic.
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References
B. Barone and E. Predazzi: High-energy particle diffraction. Springer, Berlin, Heidelberg, New York, 2002.
J. Bros: Some analyticity properties implied by the two-particle structure of Green’s functions in general quantum field theory. In: Analytic methods in mathematical physics (R.P. Gilbert and R.G. Newton, eds.). Gordon and Breach, New York, 1970.
J. Bros and M. Lassalle: Analiticity properties and many-particle structure in general quantum field theory. III. Two-particle irreducibility in a single channel. Comm. Math. Phys. 54:33–62 (1977).
J. Bros and M. Lassalle: Analiticity properties and many-particle structure in general quantum field theory. IV. Two-particle structural equations for the four, five and six-points functions. Ann. Inst. H. Poincaré 27:279–317 (1977).
J. Bros and D. Pesenti: Fredholm theory in complex manifolds with complex parameters: Analyticity properties and Landau singularities of the resolvent. J. Math. Pures. Appl. 59:375–401 (1980).
J. Bros and D. Pesenti: Fredholm resolvents of meromorphic kernels with complex parameters: A Landau singularity and the associated equations of type U in a non-holonomic case. J. Math. Pures. Appl. 62:215–252 (1983).
J. Bros and G.A. Viano: Connection between the algebra of kernels on the sphere and the Volterra algebra on the one-sheeted hyperboloid: holomorphic perikernels. Bull. Soc. Math. France 120:169–225 (1992).
J. Bros and G.A. Viano: Connection between the harmonic analysis on the sphere and the harmonic analysis on the one-sheeted hyperboloid: an analytic continuation viewpoint. I. Forum Math. 8:621–658 (1996). II. Forum Math. 8:659–722 (1996). III. Forum Math. 9:165–191 (1997).
J. Bros and G.A. Viano: Complex angular momentum in general quantum field theory. Ann. Henri Poincaré 1:101–172 (2000).
J. Bros and G.A. Viano: Complex angular momentum diagonalization of the Bethe-Salpeter structure in general quantum field theory. Ann. Henri Poincaré 4:85–126 (2003).
P.D.B. Collins: An introduction to Regge theory and high energy physics. Cambridge University Press, Cambridge, 1977.
A. Donnachie and P.V. Landshoff: Total cross sections. Phys. Lett. B 296:227–232 (1992).
J. Faraut and G.A. Viano: Volterra algebra and the Bethe-Salpeter equation. J. Math. Phys. 27:840–848 (1986).
S. Helgason: Lie groups and symmetric spaces. In: Battelle Rencontres. 1967 lectures in mathematics and physics (C.M. DeWitt and J.A. Wheeler, eds.). Benjamin, New York Amsterdam, 1967.
J. Hilgert and G. Olafsson: Causal symmetric spaces, geometry and harmonic analysis. Academic Press, San Diego, 1997.
L.N. Lipatov: Pomeron in quantum cromodynamics. In: Perturbative quantum cromodynamics (A.H. Mueller, ed.). World Scientific, Singapore, 1989.
S. Mandelstam: Cuts in angular momentum plane. I. Nuovo Cimento 30:1127–1147 (1963). II. Nuovo Cimento 30:1148–1162 (1963).
M. Toller: Group-theoretical techniques for the construction of Regge and multi-Regge models. Riv. Nuovo Cimento 1:403–437 (1969).
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Viano, G.A. (2007). Complex Angular Momentum Analysis and Diagonalization of the Bethe-Salpeter Structure in Axiomatic Quantum Field Theory. In: de Monvel, A.B., Buchholz, D., Iagolnitzer, D., Moschella, U. (eds) Rigorous Quantum Field Theory. Progress in Mathematics, vol 251. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7434-1_22
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