Relativistic quantum mechanics

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Relativistic quantum mechanics


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Special relativity
Space time point
not invariant under translations
Space-time vector
Invariant under translations but not invariant
under rotations or boosts
Einstein postulate the real invariant distance
is
Physics invariant under all transformations that
leave all such distances invariant
Translations and Lorentz transformations
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Lorentz transformations
(Summation assumed)
Solutions
3 boosts B
3 rotations R
Space reflection parity P
Time reflection, time reversal T
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4 vector notation
contravariant
covariant
4 vectors
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The Klein Gordon equation (1926)
Scalar field (J0)
Energy eigenvalues
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Physical interpretation of Quantum Mechanics
Schrödinger equation (S.E.)
probability current
probability density
Klein Gordon equation
Normalised free particle solutions
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Physical interpretation of Quantum Mechanics
Schrödinger equation (S.E.)
probability current
probability density
Klein Gordon equation
Negative probability?
Normalised free particle solutions
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Relativistic QM - The Klein Gordon equation (1926)
Scalar particle (field) (J0)
Energy eigenvalues
1927 Dirac tried to eliminate negative solutions
by writing a relativistic equation linear in E
(a theory of fermions)
1934 Pauli and Weisskopf revived KG equation with
Elt0 solutions as Egt0 solutions for particles of
opposite charge (antiparticles). Unlike Diracs
hole theory this interpretation is applicable
to bosons (integer spin) as well as to fermions
(half integer spin).
As we shall see the antiparticle states make the
field theory causal
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But energy eigenvalues
Feynman Stuckelberg interpretation
Two different time orderings giving same
observable event
time
space