By M. Y. Han

Provides the basic features of relativistic quantum box idea with minimum use of arithmetic. It covers the improvement of quantum box idea from the unique quantization of electromagnetic box to the gauge box thought of interactions between quarks and leptons.

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**Additional info for A story of light: a short introduction to quantum field theory of quarks and leptons**

**Example text**

The equation for the electromagnetic ﬁeld predates the advent of both relativity and quantum mechanics. One might go so far as to say that the equation for wave, the electromagnetic wave, has been “waiting” all this while for the equations for particles to “catch up” with it! We will now turn to this classical wave equation for the electromagnetic ﬁeld in the next chapter. September 23, 2004 10:11 WSPC/SPI-B241: A Story of Light chap06 6 Electromagnetic Field The classical theory of electromagnetism, as mentioned in Chapter 1, developed along an entirely diﬀerent path from that of Newton’s classical mechanics.

The works of Coulomb, Gauss, Biot–Savart, Amp`ere, and Faraday led Maxwell to the great uniﬁcation of electricity and magnetism into a single theory of an electromagnetic ﬁeld. Together with Einstein’s theory of gravitational ﬁeld, Maxwell’s theory of electromagnetic ﬁeld is one of the most elegant of classical ﬁeld theories. Maxwell’s equations are given, in the natural unit system, as ∇ · E = ρ, ∇ · B = 0, ∂E = J, (inhomogeneous) ∂t ∂B ∇×E+ = 0. (homogeneous) ∂t ∇×B− where E and B are the electric and magnetic ﬁelds and ρ and J are the electric charge and current densities.

This relationship between the classical electromagnetic ﬁeld and photons, the discreet energy quanta of the radiation ﬁeld that correspond to particles of light with no mass, provided an entirely new insight into the interpretation of particles. The concept of particles would then go through another fundamental evolution, from that of quantum-mechanical wave–particle duality to that of the quanta of a quantized ﬁeld. For particles to be described by relativistic quantum ﬁelds, however, there were no corresponding classical ﬁelds.