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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 O1 and O2 • Calculation of D?µ • Calculation of Sk • Various calculations • Proving ?=M- ?`M • Proving R?µ ?? = eN?µN • Calculation of –R?µ • Proving det(R?µ ) = r4 • Relations between tensors
Impulse-energy tensor: Noether’s theorem • Case M = 1 • Case M = ?12 • Case M = ?0123 = 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 Gµµ? • Calculating G0j? and Gj0? , j = 1, 2, 3 • Calculating G01? • Calculating G02? • Calculating G03? • Calculating Gkl? • Calculating G12? • Calculating G23? • Calculating G31? ISBN - 9788130922942
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Pages : 176
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