One of the simplest, and most completely treated, fields of application of quantum mechanics is the theory of atoms with one or two electrons For hydrogen and the analcgous ions He+, Li++, etc, the calculations can be performed exactly, both in Schrodinger’s nonrelativistic wave mechanics and in Dirac’s relativistic theory of the electron More specifically, the calculations are exact for a single electron in a fixed Coulomb potential Hydrogen-like atoms thus furnish an excellent way of testing the validity of quantum mechanics For such atoms the correction terms due to the motion and structure of atomic nuclei and due to quantum electrodynamic effects are small and can be calculated with high accuracy Since the energy levels of hydrogen and similar atoms can be investigated experimentally to an astounding degree of accuracy, some accurate tests of the validity of quantum electrodynamics are also possible Finally, the theory of such atoms in an external electric or magnetic field has also been developed in detail and compared with experiment

Quantum Mechanics of One- and Two-Electron Atoms

The field of laser-matter interaction traditionally deals with the response of atoms, molecules, and plasmas to an external light wave. However, the recent sustained technological progress is opening up the possibility of employing intense laser radiation to trigger or substantially influence physical processes beyond atomic-physics energy scales. Available optical laser intensities exceeding ${10}^{22}\text{ }\text{ }\mathrm{W}/{\mathrm{cm}}^{2}$ can push the fundamental light-electron interaction to the extreme limit where radiation-reaction effects dominate the electron dynamics, can shed light on the structure of the quantum vacuum, and can trigger the creation of particles such as electrons, muons, and pions and their corresponding antiparticles. Also, novel sources of intense coherent high-energy photons and laser-based particle colliders can pave the way to nuclear quantum optics and may even allow for the potential discovery of new particles beyond the standard model. These are the main topics of this article, which is devoted to a review of recent investigations on high-energy processes within the realm of relativistic quantum dynamics, quantum electrodynamics, and nuclear and particle physics, occurring in extremely intense laser fields.

Extremely high-intensity laser interactions with fundamental quantum systems

The infrared divergence phenomena and high-energy processes

For infinitesimal changes of vertex functions under infinitesimal variation of all renormalized parameters, linear combinations are found such that the net infinitesimal changes of all vertex functions are negligible relative to those functions themselves at large momenta in all orders of renormalized perturbation theory. The resulting linear first order partial differential equations for the asymptotic forms of the vertex functions are, in quantum electrodynamics, solved in terms of one universal function of one variable and one function of one variable for each vertex function whereby, in contrast to the renormalization group treatment of this problem, the universal function is obtained from nonasymptotic considerations. A relation to the breaking of scale invariance in renormalizable theories is described.

/pdf/small-distance-behaviour-in-field-theory-and-power-counting-325w8w7rwp.pdf

Small distance behaviour in field theory and power counting

There has recently been growing evidence for the existence of neutron stars possessing magnetic fields with strengths that exceed the quantum critical field strength of 4.4 × 1013 G, at which the cyclotron energy equals the electron rest mass. Such evidence has been provided by new discoveries of radio pulsars having very high spin-down rates and by observations of bursting gamma-ray sources termed magnetars. This paper will discuss the exotic physics of this high-field regime, where a new array of processes becomes possible and even dominant and where familiar processes acquire unusual properties. We review the physical processes that are important in neutron star interiors and magnetospheres, including the behaviour of free particles, atoms, molecules, plasma and condensed matter in strong magnetic fields, photon propagation in magnetized plasmas, free-particle radiative processes, the physics of neutron star interiors and field evolution and decay mechanisms. Application of such processes in astrophysical source models, including rotation-powered pulsars, soft gamma-ray repeaters, anomalous x-ray pulsars and accreting x-ray pulsars will also be discussed. Throughout this review, we will highlight the observational signatures of high magnetic field processes, as well as the theoretical issues that remain to be understood.

Physics of strongly magnetized neutron stars

Theory of Photons and Electrons

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Theory of Photons and Electrons