The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>S</mml:mi></mml:math>-matrix in Schrödinger representation for curved spacetimes in general boundary quantum field theory

Colosi, Daniele; Dohse, Max

doi:10.1016/j.geomphys.2016.11.023

Cited by 5 publications

(21 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As in [4], we suppose that the spacetime region M admits a foliation whose leaves are hypersurfaces, described in terms of a smooth coordinate system (τ, x). The leaves Σ τ of the foliation are parametrized by the coordinate τ ∈ I (1) ⊆ R, while the coordinates on each leaf are denoted by x = (x 1 , x 2 , x 3 ) ∈ I (3) ⊆ R 3 .…”

Section: Classical Theorymentioning

confidence: 99%

“…Next, we introduce mode decompositions for the Klein-Gordon solutions and for the boundary field configurations, see [4] for their properties. With k denoting the set of three parameters (momenta) labeling the modes, we assume that there is a set of complex modes {U k (x)}, which has the reflection property U −k = U k and forms a complete orthonormal basis in the space of field configurations on the hypersurfaces Σ τ , and also in momentum space, namely:…”

Section: Interval Regions Mmentioning

confidence: 99%

“…Therein, X a (τ ) and X b (τ ) are commuting, linear operators from the space of real-valued data Y a , Y b to solutions on hypersurfaces at fixed values of τ . 4 In particular each X a,b (τ ) act as operators on a mode decomposition of Y a,b (x) respectively as in (6), and we use the notation X a,b k (τ ) for the real eigenvalues of the corresponding operator when acting on a mode of momentum k:…”

Section: Interval Regions Mmentioning

confidence: 99%

“…The coefficients (φ a k , φ b k ) of the real expansion determine the solution φ(τ, x) and can be recovered directly from initial data φ(T, x), (∂ τ φ)(T, x) on a hypersurface Σ τ =T , see Section II.A in [4]. In calculations, we often need the following Wronskians, which never vanish (making them invertible) due to the linear independence of X a and X b :…”

Section: Interval Regions Mmentioning

confidence: 99%

See 3 more Smart Citations

Complex Structures and Quantum Representations for Scalar QFT in Curved Spacetimes

Colosi

Dohse

2017

Int J Theor Phys

Self Cite

View full text Add to dashboard Cite

We confirm the equivalence of the Schrödinger representation and the holomorphic one, based on previous results of the General Boundary Formulation (GBF) of quantum field theory. 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 vacuum (which determines this representation) and for the corresponding complex structure on the space of classical solutions (which determines the holomorphic representation). 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. We also transcribe the complex structure to phase space and show that it agrees with earlier results. CONTENTS

show abstract

Section: Classical Theorymentioning

confidence: 99%

Section: Interval Regions Mmentioning

confidence: 99%

Section: Interval Regions Mmentioning

confidence: 99%

Section: Interval Regions Mmentioning

confidence: 99%

See 2 more Smart Citations

Complex Structures and Quantum Representations for Scalar QFT in Curved Spacetimes

Colosi

Dohse

2017

Int J Theor Phys

Self Cite

View full text Add to dashboard Cite

show abstract

“…The asymptotic amplitude arises when the radius of the sphere is sent to infinity [59]. Of particular interest are applications in curved spacetime [60,61], especially when there are obstructions to constructing the standard S-matrix such as in Anti-deSitter spacetime [62]. This has also lead to new investigations of the Unruh effect [63,64].…”

Section: Towards Operationalism -Boundary Measurementsmentioning

confidence: 99%

A local and operational framework for the foundations of physics

Oeckl

2016

Preprint

View full text Add to dashboard Cite

We discuss a novel framework for physical theories that is based on the principles of locality and operationalism. It generalizes and unifies previous frameworks, including the standard formulation of quantum theory, the convex operational framework and Segal's approach to quantum field theory. It is capable of encoding both classical and quantum (field) theories, implements spacetime locality in a manifest way and contains the complete modern notion of measurement in the quantum case. Its mathematical content can be condensed into a set of axioms that are similar to those of Atiyah and Segal. This is supplemented by two basic rules for extracting probabilities or expectation values for measurement processes. The framework, called the positive formalism, is derived in three completely different ways. One derivation is from first principles, one starts with classical field theory and one with quantum field theory. The latter derivation arose previously in the programme of the general boundary formulation of quantum theory. As in the convex operational framework, the difference between classical and quantum theories essentially arises from certain partially ordered vector spaces being either lattices or anti-lattices. If we add the ad hoc ingredient of imposing anti-lattice structures, the derivation from first principles may be seen as a reconstruction of quantum theory. Among other things, the positive formalism suggests a statistical approach to classical field theories with dynamical metric, provides a common ground for quantum information theory and quantum field theory, introduces a notion of local measurement into quantum field theory, and suggests a new perspective on quantum gravity by removing the incompatibility with general relativistic principles. The positive formalism as a framework for quantum theory is in conflict with various interpretations or modifications of quantum theory, including physical collapse theories, manyworlds interpretations, and non-local hidden variable theories.

show abstract

Canonical Quantization of Yang-Mills Theory in Curved Space-time

2023

PSBJ

View full text Add to dashboard Cite

show abstract

The S-matrix in Schrödinger representation for curved spacetimes in general boundary quantum field theory

Cited by 5 publications

References 17 publications

Complex Structures and Quantum Representations for Scalar QFT in Curved Spacetimes

Complex Structures and Quantum Representations for Scalar QFT in Curved Spacetimes

A local and operational framework for the foundations of physics

Canonical Quantization of Yang-Mills Theory in Curved Space-time

Contact Info

Product

Resources

About