Download PDF by M. Y. Han: A Story of Light. A Short Introduction to Quantum Field

By M. Y. Han

ISBN-10: 9812560343

ISBN-13: 9789812560346

This ebook provides the fundamental facets 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 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 targeted concept 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

To sum up, when we quantize a field, it turns into a field operator that consists of creation and annihilation operators of the quantum of that field. In the case of an electromagnetic field, the classical field of the four-vector potential turns into creation and annihilation operators for the quantum of that field, the photon. In the case of matter fields, we first reinterpret the one-particle relativistic quantum mechanical wave equations as equations for classical matter fields and then carry out the quantization.

N for a system with n degrees of freedom is taken to the limit n → ∞ and in that limit the values of a field at each point of space are to be considered as independent generalized coordinates. Consider a simple mechanical example of a continuous string: the vertical displacement function, say, ρ(x, t), stands for the amplitude of displacements of the continuous string at position x and at time t and its values at each position can be taken as independent generalized coordinates. The discrete index i of the generalized coordinates for point mechanics is replaced by the continuous coordinate variable x, and the fields themselves — Aµ (x) of the electromagnetic field, φ(x) of 41 42 A Story of Light the Klein–Gordon field, ψα (x) of the Dirac field, and so on — take the place of generalized coordinates.

In the Heisenberg picture, the wavefunction is time-independent and is related to that of the Schr¨ odinger picture by ψH ≡ ψS (0) and the commutators between q and p become, for an arbitrary time t, [qj (t), pk (t)] = iδjk [qj (t), qk (t)] = [pj (t), pk (t)] = 0. In the continuum language of fields and conjugate momenta, they become [φ(x, t), φ(x , t)] = [π(x, t), π(x , t)] = 0 [φ(x, t), π(x , t)] = iδ 3 (x − x ) where the Dirac delta function replaces δjk and is defined by d3 x δ 3 (x − x )f (x ) = f (x).

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


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