Daniele Colosi

Spatially asymptotic S matrix from general boundary formulation

We construct a new type of S-matrix in quantum field theory using the general boundary formulation. In contrast to the usual S-matrix the space of free asymptotic states is located at spatial rather than at temporal infinity. Hence, the new S-matrix applies to situations where interactions may remain important at all times, but become negligible with distance. We show that the new S-matrix is equivalent to the usual one in situations where both apply. This equivalence is mediated by an isomorphism between the respective asymptotic state spaces that we construct. We introduce coherent states that allow us to obtain explicit expressions for the new S-matrix. In our formalism crossing symmetry becomes a manifest rather than a derived feature of the S-matrix.

S-matrix at spatial infinity

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.

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

Abstract We quantize the Helmholtz equation (plus perturbative interactions) in two dimensions to illustrate a manifestly local description of quantum field theory. Using the general boundary formulation we describe the quantum dynamics both in a traditional time evolution setting as well as in a setting referring to finite disk (or annulus) shaped regions of spacetime. We demonstrate that both descriptions are equivalent when they should be.

On Unitary Evolution in Quantum Field Theory in Curved Spacetime

We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that maps the state space associated with one hypersurface to the state space associated with the other hypersurface. Working in Klein-Gordon theory, we find that such an evolution is generically unitary given a one-to-one correspondence between classical solutions in neighborhoods of the respective hypersurfaces. This covers the case of pairs of Cauchy hypersurfaces, but also certain cases where hypersurfaces are timelike. The tools we use are the Schroedinger representation and the Feynman path integral.

S-Matrix for AdS from General Boundary QFT

The General Boundary Formulation (GBF) is a new framework for studying quantum theories. After concise overviews of the GBF and Schrodinger-Feynman quantization we apply the GBF to resolve a well known problem on Anti-deSitter spacetime where due to the lack of temporally asymptotic free states the usual S-matrix cannot be defined. We construct a different type of S-matrix plus propagators for free and interacting real Klein-Gordon theory.

Complex Structures and Quantum Representations for Scalar QFT in Curved Spacetimes

We confirm the equivalence of the Schrödinger representation and the holomorphic representation, based on previous results of the General Boundary Formulation (GBF) of Quantum Field Theory (QFT). On a wide class of curved spacetimes, we consider real Klein-Gordon theory in two types of regions: interval regions (consisting e.g. of a time interval times all of space), and rod regions (a solid ball of space extended over all of time). Using mode expansions, we provide explicit expressions for the Schrödinger vacua (choosing a vacuum determines a Schrödinger representation) and for the corresponding complex structures on the space of classical solutions (choosing a complex structure determines a holomorphic representation). That is, we parametrize the space of representations through vacua respectively complex structures. We also transcribe the complex structure to phase space and show that it agrees with earlier results. We explicitly construct the map which determines the isomorphism between the two representations. For both representations we give the corresponding coherent states and calculate the generalized free transition amplitudes of the GBF, which coincide and hence confirm the equivalence of the two representations.