Quantum Scattering Theory in the light of an exactly solvable model with rearrangement collisions

We present an exactly solvable quantum field theory which allows rearrangement collisions. We solve the model in the relevant sectors and demonstrate the orthonormality and completeness of the solutions, and construct the S-matrix. In the light of the exact solutions constructed, we discuss various issues and assumptions in quantum scattering theory, including the isometry of the M\"oller wave matrix, the normalization and completeness of asymptotic states, and the non-orthogonality of basis states. We show that these common assertions do not obtain in this model. We suggest a general formalism for scattering theory which overcomes these, and other, shortcomings and limitations of the existing formalisms in the literature.Comment: 74 pages, uuencoded postscript fil

The Influence of Quantum Critical Fluctuations of Circulating Current Order Parameters on the Normal State Properties of Cuprates

We study a model of the quantum critical point of cuprates associated with the "circulating current" order parameter proposed by Varma. An effective action of the order parameter in the quantum disordered phase is derived using functional integral method, and the physical properties of the normal state are studied based on the action. The results derived within the ladder approximation indicate that the system is like Fermi liquid near the quantum critical point and in disordered regime up to minor corrections. This implies that the suggested marginal Fermi liquid behavior induced by the circulating current fluctuations will come in from beyond the ladder diagrams.Comment: 7pages, 1 figure included in RevTex file. To appear in Phys. Rev.