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# Quantum electrodynamics

Belongs to subject Quantum Electrodynamics

Relativistic field theory of electromagnetism In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. The probability is the square of the absolute value of total probability amplitude,

probability

=

|

If a process involves a number of independent sub-processes, then its probability amplitude is the product of the component probability amplitudes.

This gives a simple estimated overall probability amplitude, which is squared to give an estimated probability.

Each diagram involves some calculation involving definite rules to find the associated probability amplitude. Probabilities are still represented by the usual real numbers we use for probabilities in our everyday world, but probabilities are computed as the square of probability amplitudes, which are complex numbers. +=

|

v

That change, from probabilities to probability amplitudes, complicates the mathematics without changing the basic approach. γ

μ

D

μ

− m ) ψ −

1 F

μ μ ν

,

{\displaystyle {μ

{\displaystyle \gamma ^{\mu }}

are Dirac matrices;

ψ

{\displaystyle \psi }

ψ

e

A

μ

+ i e

B

μ

{\displaystyle D_{\mu }\equiv \partial μ

{\displaystyle B_{\mu }}

is the external field imposed by external source;

F

μ ν

=

μ

A

ν

ν

A

μ

{\displaystyle F{\mu \nu }=\partial {\mu }A_{\nu }ψ ¯

γ

μ

μ

ψ − e

ψ ¯

γ

μ

(

A

μ

+

B

μ

) ψ − ψ ¯

ψ −

1 F

μ μ ν

.

{\displaystyle {\partial _{\mu }\psi \gamma \psi \psi μ

(

L

∂ (

μ

ψ )

)

L

∂ ψ

= 0.

\displaystyle \partial {\partial {\mathcal {L}}}{\partial \psi }}=0.}

μ

(

L

∂ (

μ

ψ )

)

=

μ

(

i

ψ ¯

γ

μ

)

,

{\displaystyle \partial ψ

= − e

ψ ¯

γ

μ

(

A

μ

+

B

μ

) − m

ψ {\partial {\mathcal {L}}}{\partial \psi }}=\gamma μ

ψ ¯

γ

μ

+ e

ψ ¯

γ

μ

(

A

μ

+

B

μ

) + ψ ¯

= 0 ,

{\displaystyle i\partial \gamma +m{\bar {\psi }}=0,}

with Hermitian conjugate

i

γ

μ

μ

ψ − e

γ

μ

(

A

μ

+

B

μ

) ψ −

# ψ

0.

{\displaystyle i\gamma ^{\mu }\partial {\mu }\psi -e\gamma \psi -m\psi =0.}

Bringing the middle term to the right-hand side yields

i

γ

μ

μ

ψ − m

# ψ

e

γ

μ

(

A

μ

+

B

μ

) ψ .

{\displaystyle }\partial {\mu }\psi -m\psi =(

μ

)

)

L

A

μ

= 0 ,

{\displaystyle \partial ∂

L

∂ (

ν

A

μ

)

)

=

ν

(

μ

A

ν

ν

{\displaystyle \partial ),}

L

A

μ

= − e

ψ ¯

γ

μ

ψ .

{\displaystyle {\frac {\partial μ

= e

ψ ¯

γ

μ

ψ .

\displaystyle \partial }=e{\bar {\psi }}\gamma ^{\mu }\psi .}

A

μ

= 0 ,

{\displaystyle \partial ◻

A

μ

= e

ψ ¯

γ

μ

ψ ,

{\displaystyle \Box A^{\mu }α

α

{\displaystyle \Box =\partial _|

{\displaystyle \langle i

# =

x

ψ ¯

γ

μ

ψ

A

μ

,

{\displaystyle V=e\int = From them, computations of probability amplitudes are straightforwardly given. i

= e

+ e

{\displaystyle M_{fi}=(ie)^{2}{\overline