Relativistic Quantum Invariance

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