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By M. Y. Han
This publication provides the basic elements of relativistic quantum box concept, with minimum use of arithmetic. It covers the advance of quantum box conception from the unique quantization of electromagnetic box to the gauge box idea 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 figuring out of the unique thought of relativity and quantum mechanics.
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Additional info for A Story of Light. A Short Introduction to Quantum Field Theory of Quarks and Leptons
Example text
As the quantum of electromagnetic field, the photon is a particle that has zero mass and carries energy and momentum given by E = |p| = ω( = c = 1). 54 A Story of Light The quantization of Dirac field is more involved on several accounts: first, the Dirac field ψ is a four-component object, as discussed in Chapter 5, the Lagrangian density involves not only the field ψ but also its Dirac adjoint ψ¯ = ψ ∗ γ 0 , and the canonical quantization must be carried out in terms of anticommutators rather than the usual commutators, as discussed in Chapter 8.
Such is the humble beginning of the Dirac equation that came to govern the behavior of all particles of halfinteger spin. The five-term expression can be factorized thus pµ pµ − m2 = E 2 − (p2x + p2y + p2z ) − m2 = (γ µ pµ + m)(γ ν pν − m) where the four γ µ matrices are required to satisfy the anticommutation relations γ µ γ ν + γ ν γ µ = 2g µν and by virtue of which γ µ pµ γ ν p ν = p µ p µ . It is the four-dimensional analogue of the three-dimensional relations (σ · p)(σ · p) = p · p. Of the many different matrix representations of four γ matrices, the most-often used is where γ0 = I 0 0 −I , and γ k = 0 −σ k σk 0 and the σ’s are Pauli’s spin matrices and I is the 2 × 2 unit matrix.
The operator Particles and Fields III: Particles as Quanta of Fields 53 a(k) does just the opposite, a(k)Ψ1 = Ψ0 , and the operator a(k) is called the annihilation operator. Repeated application a∗ (k)’s leads to two, three, . . , n-particle state; likewise repeated application of a(k)’s reduces the number of particles from a given state. The quantized Klein–Gordon field operator hence contains two parts, one that creates a particle and the other that annihilates a particle: a field operator acting on the n-particle state gives both (n+1)- and (n−1)-particle states.