 Title Pages
 Dedication
 Prologue

1 Introduction 
2 Relativistic Invariance 
3 The Electromagnetic Field 
4 General Relativity: A Field Theory of Gravitation 
5 The Physical States 
6 Relativistic Wave Equations 
7 Towards a Relativistic Quantum Mechanics 
8 Functional Integrals and Probabilistic Amplitudes 
9 Functional Integrals and Quantum Mechanics: Formal Developments 
10 The Euclidean Functional Integrals 
11 Fermions and Functional Formalism 
12 Relativistic Quantum Fields 
13 Applications 
14 Geometry and Quantum Dynamics 
15 Broken Symmetries 
16 Quantum Field Theory at Higher Orders 
17 A First Glance at Renormalisation and Symmetry 
18 Renormalisation of Yang–Mills Theory and BRST Symmetry 
19 Some Consequences of the Renormalisation Group 
20 Analyticity Properties of Feynman Diagrams 
21 Infrared Singularities 
22 Coherent States and Classical Limit of Quantum Electrodynamics 
23 Quantum Field Theories with a Large Number of Fields 
24 The Existence of Field Theories beyond the Perturbation Expansion 
25 Fundamental Interactions 
26 Beyond the Standard Model 
27 Supersymmetry, or the Defence of Scalars 
Appendix A Tensor Calculus 
Appendix B Differential Calculus 
Appendix C Groups and Lie Algebras 
Appendix D A Collection of Useful Formulae 
Appendix E Extract from Maxwell’s A Treatise on Electricity and Magnetism  Index
Towards a Relativistic Quantum Mechanics
Towards a Relativistic Quantum Mechanics
 Chapter:
 (p.142) 7 Towards a Relativistic Quantum Mechanics
 Source:
 From Classical to Quantum Fields
 Author(s):
Laurent Baulieu
John Iliopoulos
Roland Sénéor
 Publisher:
 Oxford University Press
Towards a relativistic quantum mechanics. Klein–Gordon and the problems of the probability current and the negative energy solutions. The Dirac equation and negative energies. P, C, and T symmetries. Positrons. The Schrödinger equation as the nonrelativistic limit of relativistic equations. Majorana and Weyl equations. Relativistic corrections in hydrogenlike atoms. The Dirac equation as a quantum system with an infinite number of degrees of freedom.
Keywords: relativistic quantum mechanics, Klein–Gordon, Dirac, Majorana, Weyl, CPT symmetry, positron, hydrogenoid atoms
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 Title Pages
 Dedication
 Prologue

1 Introduction 
2 Relativistic Invariance 
3 The Electromagnetic Field 
4 General Relativity: A Field Theory of Gravitation 
5 The Physical States 
6 Relativistic Wave Equations 
7 Towards a Relativistic Quantum Mechanics 
8 Functional Integrals and Probabilistic Amplitudes 
9 Functional Integrals and Quantum Mechanics: Formal Developments 
10 The Euclidean Functional Integrals 
11 Fermions and Functional Formalism 
12 Relativistic Quantum Fields 
13 Applications 
14 Geometry and Quantum Dynamics 
15 Broken Symmetries 
16 Quantum Field Theory at Higher Orders 
17 A First Glance at Renormalisation and Symmetry 
18 Renormalisation of Yang–Mills Theory and BRST Symmetry 
19 Some Consequences of the Renormalisation Group 
20 Analyticity Properties of Feynman Diagrams 
21 Infrared Singularities 
22 Coherent States and Classical Limit of Quantum Electrodynamics 
23 Quantum Field Theories with a Large Number of Fields 
24 The Existence of Field Theories beyond the Perturbation Expansion 
25 Fundamental Interactions 
26 Beyond the Standard Model 
27 Supersymmetry, or the Defence of Scalars 
Appendix A Tensor Calculus 
Appendix B Differential Calculus 
Appendix C Groups and Lie Algebras 
Appendix D A Collection of Useful Formulae 
Appendix E Extract from Maxwell’s A Treatise on Electricity and Magnetism  Index