Structure and Decay in the QED Vacuum
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Structure and Decay in the QED Vacuum Item Type text; Electronic Dissertation Authors Labun, Lance Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 04/10/2021 14:30:11 Link to Item http://hdl.handle.net/10150/203491 STRUCTURE AND DECAY IN THE QED VACUUM by Lance Andrew Labun A Dissertation Submitted to the Faculty of the DEPARTMENT OF PHYSICS In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 2011 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dis- sertation prepared by Lance Andrew Labun entitled Structure and Decay in the QED Vacuum and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy. Date: 16 November 2011 Johann Rafelski Date: 16 November 2011 Sumitendra Mazumdar Date: 16 November 2011 Michael Shupe Date: 16 November 2011 Shufang Su Date: 16 November 2011 Ubirajara van Kolck Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. Date: 16 November 2011 Dissertation Director: Johann Rafelski 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: Lance Andrew Labun 4 ACKNOWLEDGMENTS Prof. Johann Rafelski, my mentor, has been a continuous source of ideas, energy and wisdom. The deep and broad foundation I now have in the scholarly pursuit of physics is a credit to his teaching. I am indebted to Prof. Keith Dienes for bringing me to Arizona and providing early guidance. I would like to thank Prof. Berndt Mueller for encouragement and insightful discussion over the past four years. I am very grateful to my dissertation committee who granted patience, under- standing and helpful advice in the completion of this dissertation. Many more have supported and contributed to the work constituting this dis- sertation. The limits of this page leave insufficient space to individually thank each professor, colleague and friend who has enriched my education over the course of the past four years, though even the smallest element is essential to the final composition presented here. 5 DEDICATION I dedicate this work to my parents, Lance C. Labun, Ph.D, and Patricia A. Labun, Ph.D. 6 TABLE OF CONTENTS LIST OF FIGURES................................8 ABSTRACT....................................9 CHAPTER 1 Introduction .......................... 11 1.1 Strong Field QED: New Tools and Observations............ 11 1.2 Units and Notation............................ 13 1.3 External Fields and Vacuum Structure................. 13 1.4 The Euler-Heisenberg Effective Potential................ 15 1.5 Instability and Decay of the Electromagnetic Field........... 18 1.5.1 Vacuum Expectation of the Current............... 19 1.5.2 Imaginary Part of Veff ...................... 21 1.5.3 Decay of the Electric Field by Tunneling............ 22 CHAPTER 2 Key Findings .......................... 26 2.1 Energy-Momentum Tensor of Nonlinear Electromagnetism...... 26 2.1.1 4-Momentum and Mass...................... 27 2.1.2 Rest Frame of an Electromagnetic Field............ 29 2.2 Time Constant for Decay of Electromagnetic Field Mass....... 30 2.3 Energy of Particles from Laser-Induced Vacuum Decay........ 31 2.4 The Energy-momentum Trace...................... 34 κ 2.4.1 Fermi Condensate in Vacuum and Tκ .............. 36 κ 2.4.2 Astrophysical Effects of Tκ .................... 37 2.4.3 Modified Lorentz Force...................... 38 2.5 Comparison of Modifications of the Maxwell T µν ............ 40 2.6 Dark Energy due to a Metastable Vacuum State............ 42 2.7 Summary and Conclusions........................ 43 REFERENCES................................... 45 APPENDIX A Energy of the Dirac Vacuum.................. 48 APPENDIX B Vacuum Decay Time in Strong External Fields........ 50 APPENDIX C Dark Energy Simulacrum in Nonlinear Electrodynamics... 55 APPENDIX D QED Energy-momentum Trace as a Force in Astrophysics.. 72 7 TABLE OF CONTENTS { Continued APPENDIX E Strong Field Physics: Probing Critical Acceleration and Inertia with Laser Pulses and Quark-Gluon Plasma............. 79 APPENDIX F Vacuum Structure and Dark Energy.............. 104 APPENDIX G Spectra of Particles from Laser-Induced Vacuum Decay.... 110 8 LIST OF FIGURES 1.1 Photon-photon scattering........................ 11 1.2 Diagrammatic representation of the effective potential......... 16 1.3 Example diagrams not included in the effective potential....... 18 9 ABSTRACT This thesis is a guide to a selection of the author's published work that connect and contribute to understanding the vacuum of quantum electrodynamics in strong, prescribed electromagnetic fields. This theme is elaborated over the course of two chapters: The first chapter sets the context, defining the relevant objects and con- ditions of the study and reviewing established knowledge upon which this study builds. The second chapter organizes and explains important results appearing in the published work. The papers 1.(Labun and Rafelski, 2009) \Vacuum Decay Time in Strong External Fields" 2.(Labun and Rafelski, 2010a) \Dark Energy Simulacrum in Nonlinear Electro- dynamics" 3.(Labun and Rafelski, 2010b) \QED Energy-Momentum Trace as a Force in Astrophysics" 4.(Labun and Rafelski, 2010c) \Strong Field Physics: Probing Critical Acceler- ation and Inertia with Laser Pulses and Quark-Gluon Plasma" 5.(Labun and Rafelski, 2010d) \Vacuum Structure and Dark Energy" 6.(Labun and Rafelski, 2011) \Spectra of Particles from Laser-Induced Vacuum Decay" are presented in their published format as appendices. Related literature is cited throughout the body where it directly supports the content of this overview; more extensive references are found within the attached papers. This study begins with the first non-perturbative result in quantum electro- dynamics, a result obtained by Heisenberg and Euler(1936) for the energy of a 10 zero-particle state in a prescribed, long-wavelength electromagnetic field. The re- sulting Euler-Heisenberg effective potential generates a nonlinear theory of electro- magnetism and exhibits the ability of the electrical fields to decay into electron- positron pairs. Context for phenomena arising from the Euler-Heisenberg effective potential is established by considering the energy-momentum tensor of a general nonlinear electromagnetic theory. The mass of a field configuration is defined, and I discuss two of its consequences pertinent to efforts to observe vacuum decay. I de- velop a method for non-perturbative evaluation of a trace component of the energy- momentum tensor and discuss its significance and consequences. I study the effect of the energy-momentum trace as part of a Euler-Heisenberg-generated modification to the Lorentz force. Modifications of the energy-momentum tensor from the Maxwell theory are evaluated numerically and compared to those arising from Born-Infeld electromagnetism and the Euler-Heisenberg effective potential for a scalar electron. Finally, I explore how this study guides investigation into how vacuum structure can generate the cosmological dark energy. 11 CHAPTER 1 Introduction 1.1 Strong Field QED: New Tools and Observations Quantum electrodynamics (QED) exhibits rich dynamics even in the state empty of real electrons or positrons, the vacuum. An electromagnetic field excites virtual electron-positron pairs, and this polarization of the vacuum leads to an effective interaction permitting the scattering of photons. Shown diagrammatically in Fig. 1.1 for two incident photons, the interaction potential was computed in the low photon- energy limit by Euler and Kockel(1935). In electric fields where the potential difference exceeds the rest mass of a pair 2mc2, the electron and positron can become real particles, as recognized by Sauter(1931). photon e− photon e+ Figure 1.1: Two-photon scattering mediated by a virtual electron-positron pair fluctuation in the vacuum. The photon scattering and pair-creation processes are complementary aspects of polarization of the electron-positron pair fluctuations by the external electro- magnetic field. Considering the exactly-solvable case of a constant prescribed field, Heisenberg and Euler(1936) unified these aspects in a non-perturbative effective potential for the electromagnetic field, which incorporates all quantum