Feynman propagator

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Feynman propagator

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Feynman propagator

Definition/Summary

The Feynman propagator

is the propagator (the probability amplitude) for a scalar particle of non-zero mass,

, to travel over a space-time interval

.

It is obtained by integrating, over all possible 3-momentums

of a particle of mass

, the function

is "forward in time" or the function

is "backward in time".

This is the same as integrating, over all possible 4-momentums

(of any mass, and including those with negative energy), the function

The propagator for a non-scalar particle is

where P is a polynomial dependent on the spin of the particle.

Equations

DEFINITIONS:

Step function:

Feynman propagator:

Propagator for spin-1/2 particle:

Scientists

Recent forum threads on Feynman propagator

Breakdown

Physics
> Quantum
>> Relativistic Waves & Fields

See Also

Images

Extended explanation

Re-calculation of ∆₊(-x):

So, replacing

and

Calculation of the Feynman propagator:

where a new "energy" variable

has been substituted for

in the left part, and for

in the right part

which, writing

as the 4-vector

, is:

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