S-matrix at spatial infinity

Abstract

We provide a new method to construct the S-matrix in quantum field theory. This method implements crossing symmetry manifestly by erasing the a priori distinction between in- and out-states. It allows the description of processes where the interaction weakens with distance in space, but remains strong in the center at all times. It should also be applicable to certain spacetimes where the conventional method fails due to lack of temporal asymptotic states.Comment: 4 pages, LaTeX + revtex4; v2: normalization factors corrected; v3: two paragraphs added, minor corrections and enhancements, reference list updated; v4: references corrected/update

States and amplitudes for finite regions in a two-dimensional Euclidean quantum field theory

“…We have thus shown that this is also true quantum mechanically. Note that this is analogous to what happens in Klein-Gordon theory for hypercylinders in Minkowski space [11][12][13].…”

“…In [12,13] coherent states have been an essential tool for the computation of asymptotic amplitudes. This is equally the case in the present paper.…”

“…We will, however, be able to infer this amplitude indirectly. It is a map ρ [τ 1 ,τ 2 ,R] : The concept of such an isomorphism is familiar from [12,13], where a similar situation occurs. There, an isomorphism between the tensor product of an initial and final state space (similar to H 1 ⊗H * 2 here) and the state space on a hypercylinder (similar to H R here) is constructed in Klein-Gordon theory.…”

“…Nevertheless, a consistent probability interpretation was demonstrated. Perturbatively interacting QFT was treated in [12,13] showing that an interacting asymptotic amplitude can be defined from the large radius limit of the hypercylinder. Moreover, it was demonstrated that this amplitude is equivalent to the usual S-matrix when both can be defined.…”

Semiclassical regime of Regge calculus and spin foams

“…The starting point for this progress was the suggestion by Rovelli [8,9] of a procedure for computing the graviton propagator from Loop Quantum Gravity (LQG) [1,10,11] with the dynamics implemented covariantly in terms of a spin foam model. On the calculational side, the key ingredients are a boundary semiclassical spin network state peaked on large spins and an analytic expression for the large spin asymptotics of the spin foam vertex amplitude [12]; on the conceptual side, the framework is the boundary state formalism discussed in [1] and in [13,14,15,16,17], which prescribes how to compute observables in the boundary of a spacetime region with a path integral over the interior region only. IfÔ 1 ,Ô 2 are local boundary geometry observables (such as areas, dihedral angles, 3-volumes or lengths [18,19,20,21,22,23]) acting on a space of spin networks s , then the expectation value for their correlation in a boundary geometry q is given in the boundary state formalism by…”