Effects of Non-Locality in Gravity and Quantum Theory

Introduction 11.1 Why non-locality? 1.2 Historical aspects 1.3 Non-local form factors and kernel representations 1.4 On-shell vs. off-shell properties 1.5 Remarks on non-locality and the variational principle 1.6 Initial value problem 1.7 Recent work 1.8 Overview of thesis
2 Green functions in non-local theories 2.1 Introduction 2.2 Green functions in classical field theory 2.3 Green functions in quantum field theory 2.4 Causality from analyticity: local case 2.5 Asymptotic causality condition on Green functions 2.6 Causality from analyticity: non-local case 2.7 Non-local Green function contributions: some results 2.8 Static Green functions 2.9 Concluding remarks
3 Static and stationary solutions in weak-field gravity 3.1 Weak-field limit of non-local gravity3.2 Staticity and stationarity 3.3 Gravitational sources 3.4 Point particles 3.5 Friedel oscillations around point particles 3.6 Extended objects: p-branes 3.7 Geometry of a cosmic string in non-local gravity3.8 Stationary rotating objects (general solution)3.9 Angular momentum in higher dimensions3.10 Spinning point particles 3.11 Spinning strings and p-branes 3.12 Concluding remarks
4 Ultrarelativistic objects 4.1 The Aichelburg{Sexl metric and the Penrose limit 4.2 Gyratons 4.3 Gyratonic p-branes 4.4 Concluding remarks
5 Quantum-mechanical scattering 5.1 Introduction 5.2 A non-local scalar field in quantum mechanics 5.3 Lippmann{Schwinger method 5.4 Transmission and reflection coefficients for a -potential 5.5 Quasinormal modes 5.6 Multiple -potentials 5.7 Concluding remarks
6 Vacuum polarization and the uctuation-dissipation theorem 6.1 Introduction 6.2 A model of a non-local scalar quantum field 6.3 Vacuum uctuations around a -potential 6.4 Stability properties of non-local QFT 6.5 Thermal uctuations around a -potential 6.6 Fluctuation-dissipation theorem 6.7 Concluding remarks
7 Black holes, generalized Polyakov action, and Hawking radiation 7.1 Introduction 7.2 2D conformal anomaly and the Polyakov action 7.3 Ghost-free modication of the Polyakov action 7.4 Black hole entropy 7.5 Hawking ux 7.6 Example: two-dimensional dilaton black hole 7.7 Concluding remarks
8 Conclusions 8.1 Summary of key results 8.2 Open problems A Calculational details A.1 Retarded Green function two dimensions A.2 Two-dimensional massive Green functions A.3 Proof of Eq. (6.46) A.4 G! in GF2 theory B Two-dimensional ghost-free modication of the Polyakov action 187B.1 General relations for static geometries B.2 Energy-momentum tensor B.3 Spectral representation of F(s;R) Bibliography