Fu Chun Yu Lab Notebooks

Part II

Electromagnetic field with given sources

Charge density Current density satisfy the

eqn of continuity:

Put

Then

Introduce the skew symmetric tensor The Maxwell's equations: μνλ all different (I)

Then f_μν can be expressed in terms of a 4-potential

(II) zero net mass

A generalized equation with rest mass given by μ

[Schweizer?]-Tomonago covariant

In the scalar theory there is no difference whether μ=0 or ≠0. However with vector theory, [?] is quite different for the following reason.

Ψ_μ are not all independent fields. This equation helps to eliminate one of Ψ_μ. If μ=0, under the gauge transf^[n?]

gauge-invariant quantities

The scalar & vector potentials are not physically observed qualities. Only the field strengths are observed, significant because the force is determined by them. (For μ≠0, the gauge invariante does not hold.) It is customary way to choose the right gauge at which . (which is not in general true). Gauge transfⁿ [?] can be made.

Suppose μ=0

In the gauge

July 12, 1949

Saturation formulas for absorption & dispersion in the stationary state

We start with the absorption for I=1/2. The situation to be described is that of a competition between the applied signal & the local field spectrum, the former tending to make the surplus number zero, the latter to keep it at the value of temperature equilm.

The surplus number n can formally be thought of as being distributed over a frequency range according to a fn φ(ν)

The frequency of the applied signal {tex: $H_1 = \int H(\nu)d\nu :tex}} is so well defined, that φ(ν) can be considered as constant over the region where H₁ is different from zero. In the radio frequency range such a pure sine wave for H₁ is practically realizable. According to This signal causes a surplus number of transitions per second

Assume

Half width =

The local field will vary from nuclues to nucleus, slightly changing the Larmor frequencies of each.

[Diagram of 6 dots arrranged in a circle with one dot in the center labeled ith. An arrow is drawn from the central dot to the dot to its upper left.] Distances between the nuclei fixed. Geometrical configuration fixed * spin configuration may be different at different time.

At the i^th nucleus, let us suppose for simplicity that the neighboring nuclei have spin I = 1/2. Each of them can be parallel or antiparallel to H₀. For each spin configuration we have a definite value of the z-component of the local field. Let us first consider only the nearest neighbors. Instead of one value H₀, we have e.g. ten possible values around H₀, depending which neighbors are parallel & which antiparallel to H₀. Now all the configurations of the next nearest neighbors will split each of the ten values into many more, and so on for the third nearest, etc. The result will be a continuum of values of the z-component of the local field & therefore a distribution over a range of Larmor frequencies.

Prob. of transition = W

Distribution of energy of resonance transition between the two levels is

Due to scalar perturbation

Case II.

[therefore]

Rest mass of particle m = ħμ. = energy of particle.

no zero pt. momentum.

We must assume the source for ρ has the same periodicity as the field.

describing the emission & absorption processes.

The Schrödinger equation

All the other representations can be obtained from the one already obtained by unitary ħ and fⁿ:

If

If t=t, both can be obtained from by the same unitary ħ and [formation?], ∴ If t ≠ t', we cannot do this.