# The meaning of the "physical" electron charge in Peskin (Chap 7)

• niss
In summary, the textbook states that the "physical" electron charge measured in experiments is $$\sqrt{Z_3} e$$ where Z3 is defined as the residue of the q2 = 0 pole, explicitly as $$Z_3=\frac{1}{1-\Pi(0)}$$ and e is the bare charge.
niss
Homework Statement
Why is the "physical" electron charge e_0 / (1-Pi(0)) and not e_0 / (1-Pi(q^2))
Relevant Equations
(physical charge) = e = sqrt(Z_3) e_0 = sqrt(Z_3) (bare charge)
On p. 246 in the Peskin QFT textbook, below is stated

the "physical" electron charge measured in experiments is $$\sqrt{Z_3} e$$

where Z3 is defined as the residue of the q2 = 0 pole, explicitly as
$$Z_3=\frac{1}{1-\Pi(0)}$$
and e is the bare charge.

In advance, the exact photon two point function is calculated as
$$\frac{-ig_{\mu\nu}}{q^2(1-\Pi(q^2))}$$

Though the photon propagator should be divided by
$$1-\Pi(q^2)$$
, why the defined "physical" charge is divided by
$$1-\Pi(0)$$
?
Why only the low-q2 scattering is being considered here?

niss said:
Homework Statement:: Why is the "physical" electron charge e_0 / (1-Pi(0)) and not e_0 / (1-Pi(q^2))
Relevant Equations:: (physical charge) = e = sqrt(Z_3) e_0 = sqrt(Z_3) (bare charge)

On p. 246 in the Peskin QFT textbook, below is stated
where Z3 is defined as the residue of the q2 = 0 pole, explicitly as
$$Z_3=\frac{1}{1-\Pi(0)}$$
and e is the bare charge.

In advance, the exact photon two point function is calculated as
$$\frac{-ig_{\mu\nu}}{q^2(1-\Pi(q^2))}$$

Though the photon propagator should be divided by
$$1-\Pi(q^2)$$
, why the defined "physical" charge is divided by
$$1-\Pi(0)$$
?
Why only the low-q2 scattering is being considered here?
One could define the electron charge at any momentum transfer. But historically, the value of the electric charge has been measured with precision in the limit ##q^2 \rightarrow 0##. So the value quoted for the electric charge in the particle data booklet is the value measured in that limit.

niss
nrqed said:
One could define the electron charge at any momentum transfer. But historically, the value of the electric charge has been measured with precision in the limit ##q^2 \rightarrow 0##. So the value quoted for the electric charge in the particle data booklet is the value measured in that limit.
Thank you.

nrqed

## 1. What is the physical significance of the electron charge in Peskin (Chap 7)?

The electron charge is a fundamental property of the electron, which determines its interactions with other particles and electromagnetic fields.

## 2. How is the electron charge measured in Peskin (Chap 7)?

In Peskin (Chap 7), the electron charge is measured using the fine structure constant, which is a dimensionless quantity that relates the strength of the electromagnetic force to the speed of light and Planck's constant.

## 3. Why is the electron charge considered to be a fundamental constant in Peskin (Chap 7)?

The electron charge is considered to be a fundamental constant because it is a universal property of the electron that does not change with time or location, and it is a building block for more complex particles and structures in the universe.

## 4. How does the electron charge affect the behavior of electrons in Peskin (Chap 7)?

The electron charge determines the strength of the electromagnetic force that governs the behavior of electrons. It also plays a crucial role in determining the electron's mass and energy.

## 5. Can the electron charge change in Peskin (Chap 7)?

According to current theories, the electron charge is a constant that cannot change. However, some theories propose the existence of particles and interactions that could cause the electron charge to vary slightly. This is an area of ongoing research and debate in the scientific community.

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