The Quantum Theory of RadiationThis book is unique in covering phenomena in photon- matter interactions in a unified way over a range of many orders in energy. The quantum field theoretic approach to the fully relativistic theory of quantum electrodynamics (QED) is presented together with the non- relativistic theory in both confined and unconfined geometries. The predictions of QED have been verified to a greater accuracy than any other physical theory. Moreover QED is a paradigm for other gauge theories and is presented in such a way that the generalisation to other gauge theories is natural. Gauge and Poincare symmetry properties and the non-existence of a photon wave function are thoroughly discussed. Starting from the Dirac equation the non-relativistic interaction of the electron with the electromagnetic field is derived as an effective Hamiltonian of multipole expansions. Much of quantum optics is based on the lowest order dipole approximation. From this point on the treatment of fully relativistic QED and quantum optics is done in parallel. Applications of perturbation theory such as Compton and Moller scattering and the theory photdetection are given. After the impressive successes of QED, the limitation of the theory and the necessity of electroweak theory and quantumchromodynamics are discussed. The remaining chapters are devoted to quantum optics inside cavaties. Various approaches to open systems such as master equations are discussed within the context of active systems (e.g. the laser) and passive systems. Semi- classical approximarions are shown to imply a rich non- linear dynamics including chaos for certain parameter regimes. The effect of fluctuations on such non-linear dynamics is also studied. The final chapter is devoted to highly non- classical states of the light field such as photon number, squeezed and two photon entangled states. The latter are studied for the important system of parametric down conversion and the localisation properties of photons are characterised in terms of asympotic tails in photodetection probabilities as a function of time delay. The range of the book has wider benefits. Workers in quantum optics will gain a deeper understanding of the foundations of their subject and field theorists will see concrete examples of open systems, which are beginning to impinge on fundamental theories. |
Contents
9 | |
BecchiRouetStora symmetry | 15 |
Functional integral approach to quantum Maxwell fields | 23 |
Massive relativistic particle | 35 |
Generalized imprimitivity | 41 |
ELECTRONPHOTON AND MATTER | 51 |
Lorentz covariance of the Dirac equation | 57 |
Canonical quantization of the Dirac field | 63 |
QUANTUM ELECTRODYNAMIC PROCESSES | 135 |
EXTENSIONS OF QUANTUM | 177 |
The SalamWeinberg model | 185 |
OPEN SYSTEMS | 199 |
INSTABILITIES AND CHAOS IN QUANTUM | 231 |
Optical bistability | 239 |
Instabilities in the laser | 245 |
the Ikeda map | 251 |
5 | 78 |
9 | 88 |
35 | 94 |
Relativistic perturbations | 98 |
62 | 101 |
Change of gauge | 105 |
Renormalization group | 115 |
Renormalization of a selfinteracting scalar field theory | 121 |
Renormalization in QED | 127 |
Common terms and phrases
algebra approximation attractor bosons calculate cavity Chapter classical commutation Consequently consider d³x define denotes density matrix density operator derivative dipole Dirac equation discussion distribution divergence dynamics eigenstates electromagnetic electron energy exp(i factor Feynman field theory finite Fokker-Planck equation gauge given gives Green functions H₁ Hamiltonian Hence Hilbert space imprimitivity infinitesimal interaction invariant Lagrangian laser Lorentz Lyapunov exponent master equation matrix elements mode momenta momentum non-relativistic obtain optical bistability P₁ parameter particle path integral perturbation theory photon physics Poincaré group positron possible potential quantization quantum electrodynamics quantum fluctuations quantum mechanics quantum optics quark relativistic renormalization representation satisfies scalar scattering semi-classical solution symmetry t₁ t₂ tensor theorem tion transformation transition amplitude two-level atoms variables vector x₁ Y₁ zero μν
References to this book
The Nature of Light: What is a Photon? Chandra Roychoudhuri,A.F. Kracklauer,Kathy Creath Limited preview - 2008 |