Canonical transformation

About: Canonical transformation is a research topic. Over the lifetime, 1854 publications have been published within this topic receiving 38019 citations.

Ground State and Resonances in the Standard Model of Non-relativistic QED

Abstract: We prove existence of a ground state and resonances in the standard model of the non-relativistic quantum electro-dynamics (QED). To this end we introduce a new canonical transformation of QED Hamiltonians and use the spectral renormalization group technique with a new choice of Banach spaces.

Gaussian beam synthetic seismograms in a vertically varying medium

Abstract: Summary We develop the Gaussian beam summation method for a medium in which velocity is only a function of depth. We show that in such a medium the kinematic and dynamic ray tracing equations, i.e. trajectories and amplitudes, may be solved in closed form for any initial wavefield specified at the source. The solution for an individual Gaussian beam is written in terms of the usual functions of ray theory: distance, travel time, intercept time and geometrical spreading. An important result of this analysis, confirmed by numerical experiments, is that one of the base functions selected by Cervený, Popov & Psencik to solve the dynamic ray tracing equations should be modified to avoid causality problems. Finally, by means of a simple canonical transformation we rewrite all the equations in a geographical coordinate system independent of the particular ray trajectories. We then show that Gaussian beam summation is an analytical continuation to complex values of position and slowness of the WKB method proposed by Chapman. A simple computational method is developed in which it is not necessary to determine the coordinates of the observer in ray centred coordinates. This simplifies the computational effort so that Gaussian beam calculation becomes only slightly more expensive than WKB. With respect to the latter method Gaussian beam summation has the advantage that it is possible to control the amplitudes of the cut-off phases due to a finite range of slowness integration.

Exciton dispersion in semiconductors with degenerate bands

Abstract: The problem of energy versus momentum dispersion is considered for excitons in semiconductors of the diamond and zincblende families, which are characterized by a fourfold degeneracy of the upper valence band (in the strong spin-orbit limit). This degeneracy results in the well-known impossibility of a complete decoupling of relative and translational dynamics of the electron-hole pair. It is shown, however, how the canonical transformation to the new coordinates can be optimized to reduce and simplify the coupling terms, and to obtain, on the basis of simple physical arguments, the description of the motion that is most convenient for practical calculations in a particular semiconductor. Results of such calculations are presented for several materials and are favorably compared with experimental information obtained by modulation spectroscopy. The striking deviations from the "hydrogenic" parabolic dispersion law that occur in some materials are briefly discussed.

Uniqueness of the Fock quantization of fields with unitary dynamics in nonstationary spacetimes

Abstract: is introduced as part of a linear, time dependent canonical transformation in phase space. In this context, we prove in full detail a uniqueness result about the Fock quantization requiring that the dynamics be unitary and the spatial symmetries of the field equations have a natural unitary implementation. The main conclusion is that, with those requirements, only one particular canonical transformation is allowed, and thus only one choice of the field-momentum pair (up to irrelevant constant scalings). This complements another previous uniqueness result for scalar fields with a time varying mass on S 3 , which selects a specific equivalence class of Fock representations of the canonical commutation relations under the conditions of a unitary evolution and the invariance of the vacuum under the background symmetries. In total, the combination of these two different statements of uniqueness picks up a unique Fock quantization for the system. We also extend our proof of uniqueness to other compact topologies and spacetime dimensions.