Relativistic Quantum Invariance

Description

This book describes the invariant nature of the relativistic quantum field theories utilizing the idea of interpolating the instant form dynamics and the light-front dynamics. While the light-front dynamics (LFD) based on the light-front time was proposed by Dirac in 1949, there has not yet been a salient review on the connection between the LFD and the instant form dynamics (IFD) based on the ordinary time. By reviewing the connection between LFD and IFD using the idea of interpolating the two different forms of the relativistic dynamics, one can learn the distinguished features of each form and how one may utilize those distinguished features in solving the complicated relativistic quantum field theoretic problems more effectively. With the ongoing 12-GeV Jefferson Lab experiments, the internal structures of the nucleon and nuclei are vigorously investigated in particular using the physical observables defined in the LFD rather than in the IFD. This book offers a clear demonstration on why and how the LFD is more advantageous than the IFD for the study of hadron physics, illustrating the differences and similarities between these two distinguished forms of the dynamics. It aims at presenting the basic first-hand knowledge of the relativistic quantum field theories, describing why and how the different forms of dynamics (e.g., IFD and LFD) can emerge in them, connecting the IFD and the LFD using the idea of the interpolation, and demonstrating explicit examples of the interpolation in quantum electrodynamics and other field theories. While the level of presentation is planned mainly for the advanced undergraduate students and the beginning graduate students, the topics of the interpolation between the IFD and the LFD are innovative enough for even the experts in the field to appreciate its usefulness. Acknowledgements About This Book Contents About the Author 1 Introduction 1.1 Special Relativity 1.2 Four-Vectors and Relativistic Collisions 1.3 Symmetry Properties of Special Relativity 1.4 Poincaré Group 2 Interpolation Between Instant Form Dynamics and Light-Front Dynamics 2.1 Dirac's Proposition 2.2 Interpolating Scattering Amplitudes 2.3 Kinematic Transformations of Particle Momenta 2.4 Application of Transformations on Interpolating Scattering Amplitudes 2.5 Interpolating Scattering Amplitudes in Infinite Momentum Frame 2.6 Conclusions 3 Interpolation of Quantum Electrodynamics 3.1 Introduction 3.2 Formal Derivation of the Interpolation of QED 3.2.1 Scattering Theory 3.2.2 Canonical Field Theory 3.3 Toy Calculation of e+ e- Annihilation Producing Two Scalar Particles 3.3.1 Collinear Scattering/Annihilation, θ= π 3.3.2 Summary of e+ e- rightarrow Two Scalar Particles 3.4 Interpolating Helicity Scattering Probabilities 3.4.1 e+ e- Pair Annihilation into Two Photons 3.4.2 Compton Scattering 3.5 Summary and Conclusion 4 Interpolation of Quantum Chromodynamics in 1+1 Dimension 4.1 Introduction 4.2 The Mass Gap Equation 4.2.1 The Hamiltonian Method 4.2.2 The Feynman Diagram Method 4.2.3 Behavior of the Gap Equation When Approaching the Light-Front 4.3 The Mass Gap Solution 4.4 Chiral Condensate and Constituent Quark Mass 4.4.1 The Chiral Condensate 4.4.2 The Fermion Propagator and Constituent Mass 4.5 The Bound-State Equation 4.6 The Bound-State Solution 4.6.1 Spectroscopy 4.6.2 Wavefunctions 4.6.3 Quasi-PDFs 4.7 Conclusion and Outlook A QED Appendix A.1 Fermion Propagator in the Position Space A.2 Derivation of Interpolating QED Hamiltonian A.3 Sum of the Interpolating Time-Ordered Fermion Propagators A.4 Non-collinear Scattering/Annihilation, ps: [/EMC pdfmark [/Subtype /Span /ActualText (0 less than theta less than pi) /StPNE pdfmark [/StBMC pdfmark0 < θ< πps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark, in ps: [/EMC pdfmark [/Subtype /Span /ActualText (e Superscript plus Baseline e Superscript minus Baseline right arrow) /StPNE pdfmark [/StBMC pdfmarke+ e- rightarrowps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Two Scalar Particles A.5 Boosted ps: [/EMC pdfmark [/Subtype /Span /ActualText (e Superscript plus Baseline e Superscript minus Baseline right arrow gamma gamma) /StPNE pdfmark [/StBMC pdfmarke+ e- toγγps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Interpolating Helicity Amplitudes A.6 Boost Dependence in ps: [/EMC pdfmark [/Subtype /Span /ActualText (e Superscript plus Baseline e Superscript minus Baseline right arrow gamma gamma) /StPNE pdfmark [/StBMC pdfmarke+ e- toγγps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Interpolating Helicity Amplitudes Appendix B QCD1+1 Appendix B.1 Bogoliubov Transformation for the Interpolating Spinors Between IFD and LFD B.2 Minimization of the Vacuum Energy with Respect to the Bogoliubov Angle B.3 Treatment of the ps: [/EMC pdfmark [/Subtype /Span /ActualText (lamda equals 0) /StPNE pdfmark [/StBMC pdfmarkλ= 0ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark (Free) Case Versus the ps: [/EMC pdfmark [/Subtype /Span /ActualText (lamda not equals 0) /StPNE pdfmark [/StBMC pdfmarkλneq0ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark (Interacting) Case with Respect to the Mass Dimension ps: [/EMC pdfmark [/Subtype /Span /ActualText (StartRoot 2 lamda EndRoot) /StPNE pdfmark [/StBMC pdfmarksqrt2λps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark B.4 Mesonic Wavefunctions for ps: [/EMC pdfmark [/Subtype /Span /ActualText (m equals) /StPNE pdfmark [/StBMC pdfmarkm=ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark 0.045, 1.0 and 2.11 in the Unit of ps: [/EMC pdfmark [/Subtype /Span /ActualText (StartRoot 2 lamda EndRoot) /StPNE pdfmark [/StBMC pdfmarksqrt2λps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark B.5 ``Quasi-PDFs'' Corresponding to Mesonic Wavefunctions for ps: [/EMC pdfmark [/Subtype /Span /ActualText (m equals) /StPNE pdfmark [/StBMC pdfmarkm=ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark 0.045, 1.0 and 2.11 in the Unit of ps: [/EMC pdfmark [/Subtype /Span /ActualText (StartRoot 2 lamda EndRoot) /StPNE pdfmark [/StBMC pdfmarksqrt2λps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark B.6 Rest Frame Bound-State Equation and Its Solution