By M. Y. Han

ISBN-10: 9812560343

ISBN-13: 9789812560346

This publication provides the basic facets of relativistic quantum box conception, with minimum use of arithmetic. It covers the advance of quantum box idea from the unique quantization of electromagnetic box to the gauge box conception of interactions between quarks and leptons.Aimed at either scientists and non-specialists, it calls for just some rudimentary wisdom of the Lagrangian and Hamiltonian formula of Newtonian mechanics and a simple realizing of the designated thought of relativity and quantum mechanics.

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**Additional resources for A Story of Light. A Short Introduction to Quantum Field Theory of Quarks and Leptons**

**Example text**

In the case of electronic orbits of an atom, for example, the solutions φ(xi ) successfully specify the radii of the orbits (the principal quantum number), the angular momentum of an electron in an orbit (the total angular momentum quantum number), and the tilts of the planes of an orbit (the magnetic quantum number). The complete knowledge of the structure and physical properties of atoms, however, requires speciﬁcation of the electron spin and Pauli’s exclusion principle, without which the physics of atoms, and by extension, all 28 A Story of Light known matter in the universe, would not have been what it is.

This is the third and, so far the ﬁnal, evolution in our concept of a particle. The quantization of an electromagnetic ﬁeld is virtually identical to that discussed above for the Klein–Gordon ﬁeld, except that due to the polarization degrees of freedom (the spin of photons), the ﬁeld Aµ (x) requires a little more care. The polarization of the electromagnetic ﬁeld has only two degrees of freedom, the right-handed and left-handed circular polarizations, but the ﬁeld Aµ (x) has four indices (µ = 0, 1, 2, 3).

The electric and magnetic ﬁelds, E and B, correspond to components of the antisymmetric electromagnetic ﬁeld tensor F µν deﬁned as 0 −Ex −Ey −Ez Ex 0 −Bz By . F µν ≡ ∂ µ Aν − ∂ ν Aµ = Ey Bz 0 −Bx Ez −By Bx 0 The electromagnetic ﬁeld tensor is thus a four-dimensional “curl” of the four-vector potential. In terms of the electromagnetic ﬁeld tensor, the inhomogeneous Maxwell’s equations become ∂µ F µν = J ν . We can now draw two very important conclusions about Maxwell’s equations. First, the four-potential Aµ = (φ, A) is not unique in the sense that the same electromagnetic ﬁeld tensor F µν is obtained from the potential Aµ + ∂ µ Λ = φ+ ∂Λ , A − ∇Λ , ∂t where Λ(x) is an arbitrary function and its contribution to F µν is identically zero (it is the four-dimensional analogue of the curl of gradient being identically zero).

### A Story of Light. A Short Introduction to Quantum Field Theory of Quarks and Leptons by M. Y. Han

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