Nonlinear Dirac Equation, Magnetic Monopoles and Double Space-Time
Nonlinear Dirac Equation, Magnetic Monopoles and Double Space-Time
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ISBN: 9788130922942
Bind: Hardbound
Year: 2013
Pages: 176
Size: 6.25 x 9 Inch
Publisher: Cambridge International Science Publishing
Published in India by: Viva Books
Exclusive Distributors: Viva Books
Sales Territory: India, Nepal, Pakistan, Bangladesh, Sri Lanka
Description:
Beginnings of quantum mechanics are revised and the author starts from the point where relativity and quantum mechanics were compatible. A modified wave equation for the electron is used. The relativistic invariance is then enlarged to a greater invariance group and the first consequences are studied. This invariance applies to the whole electromagnetism, including magnetic monopoles. Another space-time variety is seen which is very different from the usual relativistic space-time.
In this book:
• Clifford algebra
• Dirac equation
• The homogeneous nonlinear Dirac equation
• Invariance of electromagnetic laws
• Consequences
• Magnetic monopoles
• A new world
Contents:
Clifford algebras
What is a Clifford algebra? • Clifford algebra of an Euclidean plan : Cl2 • Clifford algebra of the physical space : Cl3 • Cross-product, orientation • Pauli algebra • Three conjugations will be useful : • Gradient, divergence and curl : • Space-time with space algebra : • Relativistic invariance : • Restricted Lorentz group : • Clifford algebra of the space-time : Cl1,3 • Dirac matrices
Dirac equation
With the Dirac matrices • Second order equation • Conservative current • Tensors • Gauge invariances • Relativistic invariance • The wave with the Pauli algebra • Relativistic invariance • More tensors • Plane waves • The Dirac equation in space-time algebra
The homogeneous nonlinear Dirac equation
Plane waves • Charge conjugation • Relativistic invariance • Wave normalization
The hydrogen atom
Separating variables • Cinetic momentum operators • Resolution of the linear radial system • Calculation of the Yvon-Takabayasi angle • Case of the radial polynomials with degree 0 • Nonlinear radial system • Case of radial polynomials with degree 1
Invariance of electromagnetic laws
Maxwell-de Broglie electromagnetism • Invariance under Cl*3 • Electromagnetism with monopoles • Back to space-time • From Cl3 to Cl1,3 • Electromagnetism
Consequences
Anisotropy • Torsion • Case of a plane wave • Fermions and bosons • Quarks and color
Magnetic monopoles
Russian experimental works • Works at E.C.N. • Results about powders and gas • Traces
A new world
Mathematics versus physics • Prospects and questions •
A Calculations inPauli algebra
Calculation of tensors • Calculation of Ω1 and Ω2 • Calculation of Dνμ • Calculation of Sk • Various calculations • Proving
Ñ=M- Ñ¢M • Proving Rνμ gn = eNgmN • Calculation of –Rνμ • Proving det(Rνμ ) = r4 • Relations between tensors
Impulse-energy tensor
Noether’s theorem • Case M = 1 • Case M = g12 • Case M = γ0123 = i • T´etrode’s tensor • Trace of T • Second-order equation • Dynamics of the T tensor • Cinetic momentum operators
Affine connection
Calculating S(k) and A(k) • Calculating Gμμν • Calculating G0jν and Gj0ν , j = 1, 2, 3 • Calculating G01ν • Calculating G02ν • Calculating G03ν • Calculating Gklν • Calculating G12ν • Calculating G23ν • Calculating G31ν
