Effects of Non-Locality in Gravity and Quantum Theory

ISBN-13: 9783030829124 / Angielski / Miękka / 2022

Jens Boos

Opis

This thesis is devoted to the systematic study of non-local theories that respect Lorentz invariance and are devoid of new, unphysical degrees of freedom. Such theories are attractive for phenomenological applications since they are mostly unconstrained by current experiments. Non-locality has played an increasingly important role in the physics of the last decades, appearing in effective actions in quantum field theory, and arising naturally in string theory and non-commutative geometry. It may even be a necessary ingredient for quantum theories of gravity. It is a feature of quantum entanglement, and may even solve the long-standing black hole information loss problem. “Non-locality” is a broad concept with many promising and fruitful applications in theoretical and mathematical physics. After a historical and pedagogical introduction into the concept of non-locality the author develops the notion of non-local Green functions to study various non-local weak-field problems in quantum mechanics, quantum field theory, gravity, and quantum field theory in curved spacetime. This thesis fills a gap in the literature by providing a self-contained exploration of weak-field effects in non-local theories, thereby establishing a “non-local intuition” which may serve as a stepping stone for studies of the full, non-linear problem of non-locality.

Spis treści

Introduction 1

1.1 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 gravity

3.2 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 gravity

3.8 Stationary rotating objects (general solution)

3.9 Angular momentum in higher dimensions

3.10 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 187

B.1 General relations for static geometries  

B.2 Energy-momentum tensor  

B.3 Spectral representation of F(s;R)  

Bibliography 

O autorze

Jens obtained his Bachelor’s and Master’s at RWTH Aachen and the University of Cologne in Germany with a focus on black hole physics and obtained a second Master’s at Perimeter Institute/University of Waterloo in Canada in 2015. Upon completion he was awarded a doctoral recruitment scholarship by the University of Alberta and went on to do his PhD in the Alberta gravity group with Prof. Valeri Frolov (supervisor) and Prof. Don Page (committee), where he was later awarded a Canada Vanier Graduate Scholarship. Presently he is a postdoctoral research associate in high energy physics at William & Mary in the United States.