By M. Y. Han
This ebook offers the basic points of relativistic quantum box conception, with minimum use of arithmetic. It covers the improvement of quantum box thought from the unique quantization of electromagnetic box to the gauge box thought 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 uncomplicated figuring out of the detailed conception of relativity and quantum mechanics.
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Extra resources for A Story Of Light: A Short Introduction To Quantum Field Theory Of Quarks And Leptons
The positive 47 September 23, 2004 48 10:10 WSPC/SPI-B241: A Story of Light chap09 A Story of Light frequency part corresponds to raising the energy of an electromagnetic system by one unit of quantum and this corresponds to the creation operator of a photon. Likewise, the negative energy frequency part corresponds to lowering the energy of an electromagnetic system by one unit of quantum and this is the annihilation operator of a photon. The successful incorporation of photons, the zero-mass particles of light, into the fold of quantized electromagnetic fourpotential was in fact the catalyst, as discussed in previous chapters, for the reinterpretation of relativistic wave equations of particles as “imitation” matter ﬁelds which started the whole ball rolling toward today’s quantum ﬁeld theory of particles.
The choice, however, is not unique since the Euler–Lagrange equations involve only the derivatives of the Lagrangian densities. A Lagrangian density is chosen to be the simplest choice possible that meets the requirement of reproducing the ﬁeld equations when substituted into the Euler–Lagrange September 23, 2004 10:12 WSPC/SPI-B241: A Story of Light Road Map for Field Quantization chap08 45 equations. The Lagrangian densities are: 1 L = (∂µ φ ∂ µ φ − m2 φ2 ) for the Klein–Gordon ﬁeld, 2 1 L = − Fµν F µν for the electromagnetic ﬁeld, and 4 ¯ µ ∂µ − m)ψ for the Dirac-ﬁeld L = ψ(iγ where ψ is the four-component Dirac ﬁeld (column) and ψ¯ is deﬁned as ψ¯ = ψ ∗ γ 0 , an adjoint (row) multiplied by γ 0 , referred to as the Dirac adjoint, which is simply a matter of notational convenience that became a standard notation.
The case of Klein–Gordon ﬁeld is speciﬁed by, as discussed in Chapter 8: Field: Field equation: φ(x) (∂ µ ∂µ + m2 )φ(x) = 0 1 Lagrangian density: L = (∂µ φ∂ µ φ − m2 φ2 ) 2 ∂L ∂φ Momenta ﬁeld: π(x, t) ≡ = . ∂(∂φ/∂t) ∂t The ﬁeld equation, that is, the Klein–Gordon equation, allows planewave solutions for the ﬁeld φ(x) and it can be written as φ(x) = 1 (2π)3/2 b(k)eikx dk where kx = k 0 x0 − kr, dk = dk 0 dk and b(k) is the Fourier transform that speciﬁes particular weight distribution of plane-waves with different k’s.