Relativistic generalizations of the

As is well known (Chirikov, 1979 Izrailev, 1990), the phase-space evolution of the norelativistic classical kicked rotor is described by nonrelativistic standard map. The analysis of this map shows that the motion of the nonrelativistic kicked rotor is accompanied by unlimited diffusion in the energy and momentum. However, this diffusion is suppressed in the quantum case (Casati et.al., 1979 Izrailev, 1990). Such a suppression of diffusive growth of the energy can be observed when one considers the (classical) relativistic extention of the classical standard map (Nomura et.al., 1992) which was obtained recently by considering the motion of the relativistic electron in the field of an electrostatic wave packet. The relativistic generalization of the standard map is obtained recently (Nomura et.al., 1992)... 

In any relativistic generalization of the formalism used so far, the 2-component spin-orbitals,... 

P. R. Holland, A. Kyprianidis, Z. Marie, and J. P. Vigier, Relativistic generalization of the Wigner function and its interpretation in the causal stochastic formulation of quantum mechanics, Phys. Rev. A (Special Issue General Physics) 33(6), 4380—4383 (1986). 

Numerical self-consistent fields have been established (see, for example [9,30,31]) and we shall record below a few of the consequences of the calculations, in particular for the chemical potential p, when we have considered the relativistic generalization of the TF theory (Sect. 6.4 below). 

Having derived the relativistic order parameter in Equation (5.17), the relativistic generalization of the BdG equations (5.8) and (5.9) is straightforward (Capelle and Gross 1995, 1999a). We obtain... 

More correction terms arise if, additionally, the relativistic generalizations of the nonrelativistic triplet order parameters in Equation (5.14) are considered. Some of these terms are highly unusual, containing, for example, products of the pair potential with the vector potential (Capelle et al. 2001 Marques et al. 1999). 

An overview of relativistic density functional theory (RDFT) is presented with special emphasis on its field theoretical foundations and the construction of relativistic density functionals. A summary of quantum electrodynamics (QED) for bound states provides the background for the discussion of the relativistic generalization of the Hohenberg-Kohn theorem and the effective single-particle equations of RDFT. In particular, the renormalization procedure of bound state QED is reviewed in some detail. Knowledge of this renormalization scheme is pertinent for a careful derivation of the RDFT concept which necessarily has to reflect all the features of QED, such as transverse and vacuum corrections. This aspect not only shows up in the existence proof of RDFT, but also leads to an extended form of the single-particle equations which includes radiative corrections. The need for renormalization is also evident in the construction of explicit functionals. 

In order to prepare the discussion of the relativistic generalization of the HK-theorem in Section 3 we finally consider the renormalization procedure for inhomogeneous systems. As the underlying renormalization program of vacuum QED is formulated within a perturbative framework (see Appendix B) we assume the perturbing potential to be sufficiently weak to allow a power series expansion of all relevant quantities with respect to V. In particular, this allows an explicit derivation of the counterterms required for the field theoretical version of the KS equations, i.e. for the four current and kinetic energy of noninteracting particles. 

The relativistic generalization of the above expression, which has been considered in Refs. [20-23] is difficult in as much as there is no proper relativistic two-body Hamiltonian. One starting point for the discussion of the relativistic electron-nuclear two-body problem is the effective Hamiltonisin... 

Marconi and March [45], in early work, studied relativistic generalizations of the l/Z expansion (1) by invoking the Vallarta-Rosen [46] generalization of the original Thomas-Fermi method [4] [5]. This generalization replaces the constant chemical potential unr of non-relativistic density-functional... 

For a relativistic generalization of the time-dependent coupled Hartree-Fock equations see J. Ladik, J. Ci2ek, and P. K. Mukherjee, in Relativistic Effects in Atomsy Molecules and Solids (G. L. Malli, ed.), p. 305, Plenum Press, New York-London (1983). 

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