To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial interpolation 5. Divided differences 6. The uniform convergence of polynomial approximations 7. The theory of minimax approximation 8. The exchange algorithm 9. The convergence of the exchange algorithm 10. Rational approximation by the exchange algorithm 11. Least squares approximation 12. Properties of orthogonal polynomials 13. Approximation of periodic functions 14. The theory of best L1 approximation 15. An example of L1 approximation and the discrete case 16. The order of convergence of polynomial approximations 17. The uniform boundedness theorem 18. Interpolation by piecewise polynomials 19. B-splines 20. Convergence properties of spline approximations 21. Knot positions and the calculation of spline approximations 22. The Peano kernel theorem 23. Natural and perfect splines 24. Optimal interpolation Appendices Index.

Approximation theory and methods, by M. J. D. Powell. Pp 339. £25 (hardcover), £8·50 (paperback). 1981. ISBN 0-521-22472-1/29514-9 (Cambridge University Press)

Francis Halzen and Alan D Martin 1984 Chichester: John Wiley xvi + 396 pp price £23.95 ISBN 0 471 88741 2 It is interesting to conjecture the part that fashion plays in the choice of topics for physics books. Not so long ago special relativity seemed to attract authors and publishers – several books appeared in quick succession.

http://iopscience.iop.org/article/10.1088/0031-9112/36/2/033/pdf

Quarks and Leptons: An Introductory Course in Modern Particle Physics

Current status of Landsat program, science, and applications

Davydov’s Soliton

Classical and quantum approach to Davydov's soliton theory.

We study self-trapping of electrons (excitons) in one-dimensional systems with three realistic types of coupling with phonons, applying a variational procedure valid for the whole range of system parameters. Various types of self-trapped states are identified and mapped in the parameter space. Our results are compared to the results of previous studies. The particular case of biological systems is studied and it is shown that the Davydov-soliton concept can be used for the description of electron transport in biological systems, but not for the energy transfer in terms of amide-I vibrations (CO stretching vibration mode).

Self-trapping in quasi-one-dimensional electron- and exciton-phonon systems.

The dressing effect due to the quantum nature of phonons may cause the creation of bound states of several vibrons in the molecular chain. The possibility of creating soliton states of this type is discussed for the simple Frohlich one-dimensional model. The regions of the system parameter space where different mechanisms dominate the behaviour of such entities are characterized.

http://iopscience.iop.org/article/10.1088/0953-8984/9/2/010/pdf

Effects of quantum lattice fluctuations on multiquanta Davydov-like solitons in a molecular chain

Soliton excitations in the anisotropic Heisenberg chain are studied in the classical limit by means of the Holstein-Primakoff boson representation, taking into account the complete series. The results obtained are equivalent to those obtained by the classical treatment of spins. The connection with different calculations using limited numbers of terms is established, as well as the relation to the generalised coherent-states method.

Darko Kapor

Papers

Classical and quantum approach to Davydov's soliton theory.

Self-trapping in quasi-one-dimensional electron- and exciton-phonon systems.

Effects of quantum lattice fluctuations on multiquanta Davydov-like solitons in a molecular chain

The classical limit for the Holstein-Primakoff representation in the soliton theory of Heisenberg chains

Phase diagram of spin-12 quantum Heisenberg J1–J2 antiferromagnet on the body-centered-cubic lattice in random phase approximation