Bisolutions to the Klein-Gordon equation and quantum field theory on two-dimensional cylinder spacetimes

Fewster, Christopher J.

doi:10.1088/0264-9381/16/3/010

Cited by 7 publications

(8 citation statements)

References 22 publications

(82 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where µ > 0 is the constant appearing in (3). The Noether Theorem associates with every vector field X a conserved current * T X :…”

Section: Classical Fields On De Sitter Spacementioning

confidence: 99%

“…which may be interpreted as the total energy for the classical P(ϕ) 2 model on the Einstein universe [3], [4], i.e., the space-time of the form S 1 ×R with the metric induced from the ambient Minkowski space R 1+2 . However, the quantity on the left hand side of the inequality in (7) is not a conserved quantity on de Sitter space and therefore should be disregarded.…”

Section: Classical Fields On De Sitter Spacementioning

confidence: 99%

“…2 Due to Lorentz invariance, the geodesic KMS condition applies to any wedge W = ΛW 1 , Λ ∈ SO 0 (1, 2), with the relevant boosts t → Λ W (t) now given by Λ W (t) . = ΛΛ 1 (t)Λ −1 , t ∈ R. 3 Uniqueness of the vacuum state for free scalar field on the de Sitter space has been established by several authors using different but equivalent characterisations of the vacuum. If one uses the geodesic KMS condition to characterise the vacuum state, this very condition fixes the free 2-point function.…”

Section: Interacting Quantum Fieldsmentioning

confidence: 99%

See 2 more Smart Citations

Canonical interacting quantum fields on two-dimensional de Sitter space

Jäkel

Mund

2017

Physics Letters B

View full text Add to dashboard Cite

We present the P(ϕ) 2 model on de Sitter space in the canonical formulation. We discuss the role of the Noether theorem and we provide explicit expressions for the energy-stress tensor of the interacting model. * 1 Due to an unfortunate choice of coordinates (which was adopted due to the formulation of Osterwalder-Schrader positivity used in [6]) the absence of infrared singularities was not visible in the non-perturbative treatment of the P(ϕ) 2 model by Figari, published in 1975.

show abstract

“…where µ > 0 is the constant appearing in (3). The Noether Theorem associates with every vector field X a conserved current * T X :…”

Section: Classical Fields On De Sitter Spacementioning

confidence: 99%

Section: Classical Fields On De Sitter Spacementioning

confidence: 99%

Section: Interacting Quantum Fieldsmentioning

confidence: 99%

See 1 more Smart Citation

Canonical interacting quantum fields on two-dimensional de Sitter space

Jäkel

Mund

2017

Physics Letters B

View full text Add to dashboard Cite

show abstract

“…which may be interpreted as the energy density for the classical P(ϕ) 2 model on the Einstein universe (see, e.g., [55] [56]), i.e., the space-time of the form S 1 × R.…”

Section: Conservation Lawsmentioning

confidence: 99%

The ${\mathscr P}(φ)_2$ Model on the de Sitter Space

Barata,

Jäkel,

Mund

2013

Preprint

View full text Add to dashboard Cite

List of Symbols viiPreface xiii Part 1. De Sitter Space Chapter 1. De Sitter Space as a Lorentzian Manifold 1.1. The metric and the isometry group 1.2. The causal structure 1.3. Geodesics and geodesic distances 1.4. Wedges and double cones 1.5. Finite speed of propagation Chapter 2. Space-time symmetries 2.1. The group O(1, 2) 2.2. Horospheres 2.3. The complex Lorentz group 2.4. The Cartan decomposition of SO 0 (1, 2) 2.5. The Iwasawa decomposition of SO 0 (1, 2) 2.6. The Hannabuss decomposition of SO 0 (1, 2) 2.7. Homogeneous spaces, cosets and orbits 2.8. Invariant measures Part 2. Harmonic Analysis Chapter 3. Induced Representations for the Lorentz Group 3.1. The general case 3.2. Induced representations for SO 0 (1, 2) 3.3. Unitary representations on a circle on the light cone 3.4. Unitary representations on the mass shell Chapter 4. Harmonic Analysis on the Hyperboloid 4.1. Tuboids 4.2. Plane waves 4.3. The Fourier-Helgason transformation 4.4. The Plancherel theorem on the hyperboloid iii iv CONTENTS Part 3. Classical Fields Chapter 5. Classical Field Theory 5.1. The classical equations of motion 5.2. Conservation Laws 5.3. The covariant classical dynamical system 5.4. The restriction of the KG equation to a (double) wedge 5.5. The canonical classical dynamical system Part 4. Free Quantum Fields Chapter 6. One-Particle Hilbert Spaces 6.1. The covariant one-particle Hilbert space 6.2. The canonical one-particle Hilbert space 6.3. Time-symmetric and time-antisymmetric test-functions Chapter 7. Quantum One-Particle Structures 7.1. The covariant one-particle structure 7.2. One-particle structures with positive and negative energy 7.3. One-particle KMS structures 7.4. The canonical one-particle structure Chapter 8. Second Quantization 8.1. De Sitter vacuum states 8.2. The canonical free field 8.3. Analyticity properties of the correlation functions Part 5. Euclidean Quantum Fields Chapter 9. The Euclidean Sphere 9.1. The symmetry group of the sphere 9.2. Geographical and path-space coordinates Chapter 10. Gaussian Measures 10.1. The definition of the measure 10.2. Properties of the covariance 10.3. Sobolev spaces 10.4. Conditional expectations 10.5. Sharp-time fields 10.6. Foliation of the Euclidean field Chapter 11. Non-Gaussian Measures 11.1. Wick ordering of random variables 11.2. Sharp-time interactions 11.3. Foliations of the interaction Part 6. The Osterwalder-Schrader Reconstruction Chapter 12. The Reconstruction of Free Quantum Fields CONTENTS v 12.1. Reflection positivity 12.2. The reconstruction of the Hilbert space 12.3. Generalised path spaces 12.4. Path-spaces on the sphere 12.5. Local symmetric semigroups 12.6. Tomita-Takesaki modular theory 12.7. Multi-analyticity of the correlation functions 12.8. The interacting vacuum vector Chapter 13. The Reconstruction of Interacting Quantum Fields 13.1. The Hilbert space for the interacting measure 13.2. Virtual representations 13.3. A unitary representation of the Lorentz group 13.4. Perturbation theory of generalised path spaces Part 7. Interacting Quantum...

show abstract

“…(These ideas also underpin Shannon-type theorems in signal processing (see, e.g., [6].) As mentioned above, an application of Theorem 1.1 to quantum field theory on cylinder spacetimes will appear elsewhere [2,3].…”

Section: Introductionmentioning

confidence: 99%

A unique continuation result for Klein-Gordon bisolutions on a two-dimensional cylinder

Fewster

1999

Class. Quantum Grav.

Self Cite

View full text Add to dashboard Cite

We prove a novel unique continuation result for weak bisolutions to the massive Klein-Gordon equation on a 2-dimensional cylinder M . Namely, if such a bisolution vanishes in a neighbourhood of a 'sufficiently large' portion of a 2-dimensional surface lying parallel to the diagonal in M ×M , then it is (globally) translationally invariant. The proof makes use of methods drawn from Beurling's theory of interpolation. An application of our result to quantum field theory on 2-dimensional cylinder spacetimes will appear elsewhere. *

show abstract

Bisolutions to the Klein-Gordon equation and quantum field theory on two-dimensional cylinder spacetimes

Cited by 7 publications

References 22 publications

Canonical interacting quantum fields on two-dimensional de Sitter space

Canonical interacting quantum fields on two-dimensional de Sitter space

The ${\mathscr P}(φ)_2$ Model on the de Sitter Space

A unique continuation result for Klein-Gordon bisolutions on a two-dimensional cylinder

Contact Info

Product

Resources

About