By M. Y. Han
Offers the basic points of relativistic quantum box thought with minimum use of arithmetic. It covers the advance of quantum box thought from the unique quantization of electromagnetic box to the gauge box thought of interactions between quarks and leptons.
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Extra info for A story of light: a short introduction to quantum field theory of quarks and leptons
The plane-wave solutions can be written in the form: d3 k(a(k)fk (x) + a∗ (k)fk∗ (x)) φ(x) = where fk (x) = 1 (2π)3 2ω e−ikx k and fk∗ (x) = 1 (2π)3 2ω e+ikx . k The integral is over d3 k only and a(k) and a∗ (k) are the respective Fourier transforms for “positive frequency” and “negative frequency” parts. Two remarks about the standard practice of notations are called for here: The star superscript (*) stands for complex conjugate in classical ﬁelds, but when they are quantized and become non-commuting operators, the notation will stand for Hermitian adjoint.
One can go so far as to claim that the Dirac equation and relativistic quantum mechanics are virtually synonymous. What originally prompted Dirac to search for and discover the Dirac equation is simple and straightforward enough. The Klein– Gordon equation is a second-order diﬀerential equation — second derivatives with respect to both space and time — and as a relativistic equation for single particle, it encounters some diﬃculties; the nature of second-order diﬀerential equations and the probability interpretation of quantum mechanics clash.
The theory of free ﬁelds provides the foundation upon which one can build the framework for introducing real physics, namely, the interaction among particles. We must now ﬁnd ways to introduce interactions into the procedure of canonical quantization based on the Lagrangian and Hamiltonian formalism. The question then is what is the clue and prescription by which we can introduce interactions into the Lagrangian densities. There are very few clues. In fact, there is only one known prescription to introduce electromagnetic interactions and it comes from the Hamiltonian formalism of classical physics, as discussed in Chapter 2.