Just a core, a fermion → core in oscillation:
impulse, a moment in space ^;
energy, a phase in time ^^.
(Pendulum.)
"All electrical engineers are familiar with the IDEA OF a pulse,
and the δ-function is just a way of EXPRESSING a pulse mathematically."
- Paul Dirac (1963).*
.energy, a phase in space
;impulse, a moment in time
:boson variables, oscillation as core (!) ← Just an oscillation...
| (-1; Ω < 0)
(1) sgn(Ω) = | 0; Ω = 0
| +1; Ω > 0, fermion variables, potentialization ← ^ & ^^.
(2) ∫0Ωcos(ωt)dω
= (1/t)∫0Ωcos(ωt)d(ωt)
= (1/t)sin(ωt)|0Ω
= (1/t)[sin(Ωt) - sin(0t)]
= (1/t)sin(Ωt)
= Ω[1/(Ωt)]sin(Ωt)
= Ωsinc(Ωt).
(3) Power, f(Ω) = [1/(π/Ω)]∫-∞/(π/Ω)+∞/(π/Ω)Ωsinc(Ωt)dt = Ωsgn(Ω) = Ω ≥ 0;
limΩ→∞f(Ω)
→ dΩsgn(Ω)/dΩ ≥ Ω, actualization
→ 0 ≤ Ω ≤ 1, no need of renormalization
→
= [1/(π/1)]∫-∞/(π/1)+∞/(π/1)1sinc(1t)dt = 1, integrity, just an oscillation (! as core).
(4) δ(t) = limΩ→∞Ωsinc(Ωt), Dirac δ-function, boson variables.
Names:
"sgn", sign;
"cos", cosine;
"sin", sine;
"sinc", sine cardinal;
"lim", limit;
"∫", integral;
"d", differential;
"f", function.
"We have boson variables appearing automatically in a THEORY that starts
with only fermion variables, provided the number of fermion VARIABLES is infinite."
- Paul Dirac, "Spinors in Hilbert Space".
(Just an oscillation → "normalization": a time in space & a space in time.)
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* Max Jammer, "The Conceptual Development of Quantum Mechanics":
Slavoj Žižek;
John Nash;
Luitzen Brouwer;
