space

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time
space
where
are positive and negative energy solutions to
free KG equation
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Transition operator
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Physical interpretation of Quantum Mechanics
Klein Gordon equation
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Transition operator
Feynman rule associated with Feynman diagram
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Compton scattering of a p meson
Klein Gordon
Feynman rules
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The Dirac equation
RELATIVISTIC QUANTUM MECHANICS
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The Lorentz group

Generate the group SO(3,1)
To construct representations a more convenient
(non-Hermitian) basis is

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The Lorentz group

Generate the group SO(3,1)
To construct representations a more convenient
(non-Hermitian) basis is
Representations
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Weyl spinors
2-component spinors of SU(2)
Rotations and Boosts
Dirac spinor
Can combine
to form a 4-component Dirac spinor
Lorentz transformations
where
Weyl basis
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Weyl spinors
2-component spinors of SU(2)
Rotations and Boosts
Dirac spinor
Can combine
to form a 4-component Dirac spinor
Lorentz transformations
where
(Dirac gamma matrices, new 4-vector )
Note
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The Dirac equation
Fermions described by 4-cpt Dirac spinors
New 4-vector
In momentum space