Relativistic quantum theory

Berestetski V. B., Lifshitz E. M., Pitaevski L. P. Relativistic Quantum Theory (Nauka, Moscow) (1968). 

Grant, I.P. (2007) Relativistic Quantum Theory of Atoms and Molecules. Theory and Computation, Springer, New York. 

The position, momentum, and energy are all dynamical quantities and consequently possess quantum-mechanical operators from which expectation values at any given time may be determined. Time, on the other hand, has a unique role in non-relativistic quantum theory as an independent variable dynamical quantities are functions of time. Thus, the uncertainty in time cannot be related to a range of expectation values. 

Prior to Dirac s relativistic quantum theory, W. Pauli (1927) showed how spin could be incorporated into non-relativistic quantum mechanics. Since the subject of relativistic quantum mechanics is beyond the scope of this book, we present in this chapter Pauli s modification of the wave-function description so... 

The relationship between spin and the symmetry character of the wave function can be established in relativistic quantum theory. In non-relativistic quantum mechanics, however, this relationship must be regarded as a postulate. 

Most particles of interest to physicists and chemists are found to be antisymmetric under permutation. They include electrons, protons and neutrons, as well as positrons and other antiparticles These particles, which are known as Fermions, all have spins of one-half. The relation between the permutation symmetry and the value of the spin has been established by experiment and, in the case of the electron, by application of relativistic quantum theory. 

V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Relativistic Quantum Theory, Addison-Wesley, Reading, MA, 1971. 

Berestetskii, V.B.. Lifshitz, E.M. and Pitaevskii, L.P. Relativistic Quantum Theory, Vol. 4 of Course of Theoretical Physics, Part 1, 73 Pergamon Press, Oxford, 1971. 

Advances in relativistic quantum theory and computational methods made it possible to predict properties of the heaviest element compounds by performing accurate calculations of their electronic structures. Relativistic atomic and molecular calculations in combination with various models were useful in helping to design sophisticated and expensive chemical experiments. Experimental results, in turn, were helpful in defining the scope of the theoretical problems and provided an important input. The synergism between the theoretical and experimental research in the last decade led to better understanding the chemistry of these exotic species. 

Quantum chemistry. 2. Relativistic quantum theory. 3. Heavy elements. I. Hess, Bemd. II Series. 

Thus, the most common assumption was that a material s properties are governed by quantum theory and that relativistic effects are mostly minor and of only secondary importance. Quantum electrodynamics and string theory offer some possible ways of combining quantum theory and the theory of relativity, but these theories have only very marginally found their way into applied quantum theory, where one seeks, from first principles, to calculate directly the properties of specific systems, i.e. atoms, molecules, solids, etc. The only place where Dirac s relativistic quantum theory is used in such calculations is the description of the existence of the spin quantum number. This quantum number is often assumed to be without a classical analogue (see, however, Dahl 1977), and its only practical consequence is that it allows us to have two electrons in each orbital. 

Non-relativistic quantum theory for three-body systems. 

This short historical introduction to relativistic electronic structure, and even more so the chapters that follow, illustrates a very alive and active field of research whose vigom is illustrated by the increasing number of publications in this field. Indeed, if in 1986 a single volume published by Pyykkp [2] was sufficient to list all the related publications on relativistic quantum theory (about 3 100) over a period of 70 years, the next 15 years required two more volumes to hold the list of almost 8 000 new articles or reviews devoted to this subject. Although inflation in publishing is a common feature of all fields of research, these figures clearly show the importance to take relativistic and QED contributions into account. The need to include relativistic effects in quantum chemical calculations has stimulated both conceptual and numerical developments to finally fulfil the wish of Dirac for "approximate practical methods"... 

H. Halvorson, R. Clifton, No place for particles in relativistic quantum theories Preprint quant-ph/0l03041. 

The breakdown of the Bom-Oppenheimer approjcimation in molecules is already difficult in non-relativistic quantum theory, and the problem is far worse in the relativistic case. Since we shall usually deal with situations in which the nuclear motion is essentially nonrelativistic we can usually apply non-relativistic corrections for nuclear motion without major error. 

A key quantity in relativistic quantum theory is the charge-current density... 

Non-relativistic quantum theory of atoms and molecules is built upon wave-functions constructed from antisymmetrized products of single particle wave-functions. The same scheme has been adopted for relativistic theories, the main difference now being that the single particle functions are 4-component spinors (bispinors). The finite matrix method approximates such 4-spinors by writing... 

S. S. Schweber, Introduction to Relativistic Quantum Theory, Harper and Row, New York, 1964. 

In the introduction of his probably most-quoted paper Dirac [1] claims that relativistic effects are unimportant for chemistry and most of physics. It is hard to understand [2] that the father of relativistic quantum theory underestimated so much the importance of his own fundamental work [3]. Nevertheless Dirac s claim keeps some meaning if we attenuate it to ... 

We start this chapter with a discussion of the non-relativistic limit (nrl) of relativistic quantum theory (section 2). The Levy-Leblond equation will play a central role. We also discuss the nrl of electrodynamics and study how properties differ at their nrl from the respective results of standard non-relativistic quantum theory. We then present (section 3) the Foldy-Wouthuysen (FW) transformation, which still deserves some interest, although it is obsolete as a starting point for a perturbation theory of relativistic corrections. In this context we discuss the operator X, which relates the lower to the upper component of a Dirac bispinor, and give its perturbation expansion. The presentation of direct perturbation theory (DPT) is the central part of this chapter (section 4). We discuss the... 

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