Keywords:
Dirac equation.
;
Electronic books.
Type of Medium:
Online Resource
Pages:
1 online resource (111 pages)
Edition:
1st ed.
ISBN:
9783030148256
Series Statement:
SpringerBriefs in Physics Series
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=5739706
Language:
English
Note:
Intro -- Contents -- 1 Introduction -- References -- 2 The Dirac Equation in Special Relativity -- 2.1 Review of the Dirac Equation -- 2.2 Plane Wave Solutions in the Standard Representation -- 2.3 The Hamiltonian, Energy and Spin Operators -- References -- 3 The Spinorial Covariant Derivative -- 3.1 The Fock-Ivanenko Coefficients -- 3.2 The Dirac Hamiltonian in Curved Spacetime -- 3.3 Transformation Properties of the Spin Operator -- 3.4 The Ricci Rotation Coefficient Approach -- 3.5 The Electromagnetic Interaction -- 3.6 The Newman-Penrose Formalism -- References -- 4 Examples in (3+1) GR -- 4.1 Schwarzschild Spacetime F-I -- 4.2 Schwarzschild Spacetime N-P -- 4.3 Nonfactorizable Metric -- 4.4 de Sitter Spacetime, Fermi Coordinates -- References -- 5 The Dirac Equation in (1+1) GR -- 5.1 Introduction to (1+1) -- 5.2 The Dirac Equation in the Milne Universe -- References -- 6 The Dirac Equation in (2+1) GR -- 6.1 Introduction to (2+1) -- 6.2 The Dirac Equation in the Schrödinger Universe -- References -- 7 Scalar Product -- 7.1 Conservation of j Special Relativity -- 7.2 The Current Density in General Relativity -- 7.3 The Scalar Product in Special Relativity -- 7.4 The Scalar Product in General Relativity -- 7.5 Example: The Closed FRW Universe -- References -- Tetrads -- A.1 The Tetrad Formalism -- A.2 Fermi Tetrad Fields -- A.3 The Cartesian Gauge Tetrad -- A.4 Vielbeins, Spinors and Local Lorentz Transformations -- The Gamma Matrices -- B.1 General Summary -- B.2 The Standard or Dirac-Pauli Representation -- B.3 The Chiral or Weyl Representation -- B.4 The Majorana Representation -- B.5 The Jauch-Rohrlich Representation -- B.6 Gamma Matrices in (1+1) and (2+1) Spacetime -- Metric Signatures, the FI Coefficients, etc. -- C.1 Additional Comments on the Gamma Matrices -- C.2 Signature (-2) -- C.3 Signature (+2).
,
Some Further Topics on the Dirac Equation in Special Relativity -- D.1 Chiral Representation Set -- D.2 Calculating the Polarizations for u(p) -- D.3 Normalization of ψ -- Examples of Using Cartan in General Relativity -- E.1 Using Cartan in the F-I Approach -- E.2 Using Cartan in the N-P Approach -- Solutions to the Exercises -- References -- Index.
