Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Introduction
- Part I General Properties of Fields; Scalars and Gauge Fields
- Part II Solitons and Topology; Non-Abelian Theory
- Part III Other Spins or Statistics; General Relativity
- 33 Chern–Simons Terms: Emergent Gauge Fields, the Quantum Hall Effect (Integer and Fractional), Anyonic statistics
- 34 Chern–Simons and Self-Duality in Odd Dimensions, Its Duality to Topologically Massive Theory and Dualities in General
- 35 Particle–Vortex Duality in Three Dimensions, Particle–String Duality in Four Dimensions, and p-Form Fields in Four Dimensions
- 36 Fermions and Dirac Spinors
- 37 The Dirac Equation and Its Solutions
- 38 General Relativity: Metric and General Coordinate Invariance
- 39 The Einstein Action and the Einstein Equation
- 40 Perturbative Gravity: Fierz-Pauli Action, de Donder Gauge and Other Gauges, Gravitational Waves
- 41 Nonperturbative Gravity: The Vacuum Schwarzschild Solution
- 42 Deflection of Light by the Sun and Comparison with General Relativity
- 43 Fully Linear Gravity: Parallel Plane (pp) Waves and Gravitational Shock Wave Solutions
- 44 Dimensional Reduction: The Domain Wall, Cosmic String, and BTZ Black Hole Solutions
- 45 Time-Dependent Gravity: The Friedmann-Lemaître-Robertson-Walker (FLRW) Cosmological Solution
- 46 Vielbein-Spin Connection Formulation of General Relativity and Gravitational Instantons
- References
- Index
37 - The Dirac Equation and Its Solutions
from Part III - Other Spins or Statistics; General Relativity
Published online by Cambridge University Press: 04 March 2019
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Introduction
- Part I General Properties of Fields; Scalars and Gauge Fields
- Part II Solitons and Topology; Non-Abelian Theory
- Part III Other Spins or Statistics; General Relativity
- 33 Chern–Simons Terms: Emergent Gauge Fields, the Quantum Hall Effect (Integer and Fractional), Anyonic statistics
- 34 Chern–Simons and Self-Duality in Odd Dimensions, Its Duality to Topologically Massive Theory and Dualities in General
- 35 Particle–Vortex Duality in Three Dimensions, Particle–String Duality in Four Dimensions, and p-Form Fields in Four Dimensions
- 36 Fermions and Dirac Spinors
- 37 The Dirac Equation and Its Solutions
- 38 General Relativity: Metric and General Coordinate Invariance
- 39 The Einstein Action and the Einstein Equation
- 40 Perturbative Gravity: Fierz-Pauli Action, de Donder Gauge and Other Gauges, Gravitational Waves
- 41 Nonperturbative Gravity: The Vacuum Schwarzschild Solution
- 42 Deflection of Light by the Sun and Comparison with General Relativity
- 43 Fully Linear Gravity: Parallel Plane (pp) Waves and Gravitational Shock Wave Solutions
- 44 Dimensional Reduction: The Domain Wall, Cosmic String, and BTZ Black Hole Solutions
- 45 Time-Dependent Gravity: The Friedmann-Lemaître-Robertson-Walker (FLRW) Cosmological Solution
- 46 Vielbein-Spin Connection Formulation of General Relativity and Gravitational Instantons
- References
- Index
Summary
We consider first Lorentz invariant Lagrangians for spinors, Dirac, Majorana, and Weyl. The Dirac Lagrangian leads to the Dirac equation, whose solutions we study.We find the solutions u(p) and v(p) and calculate their normalizations.
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- Information
- Classical Field Theory , pp. 347 - 355Publisher: Cambridge University PressPrint publication year: 2019