Vibrational Spectroscopy of Phenols and Phenolic Polymers. Theory,Experiment, and Applications

In the first part of this review, the authors give a survey on the literature of vibrational spectroscopy of phenol, phenol derivatives, and other phenolic componds from the last decade of the last century through today. The classical and modern methods of vibrational spectroscopy are also introduced and a glossary is included to aid comprehension. The second part deals with the literature regarding the importance of vibrational spectroscopy in the investigation and identification of phenolic compounds in natural substances, the application of vibrational spectroscopy in composite and synthetic polymer chemistry, and following of chemical processes and investigating their resulting products. Vibrational spectroscopy is a very good tool for determination of molecular structures and is important in chemical analysis and in the chemical industry.     

Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion

The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system ?^{( n )} of observables “up to n loops”, where ?⁽⁰⁾ is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of Green's functions. Received: 9 February 2000 / Accepted: 21 March 2000     

Peirce, Clifford, and Quantum Theory

Beginning in 1870 Charles Sanders Peirce published a series of papers on a logic of relations, which corresponded to a linear associative algebra. This algebra is related by a linear transformation to quaternions and thus to the C(3, 0) algebra of William Kingdon Clifford. This Clifford algebra contains the Pauli matrices and so constitutes an operator basis for the nonrelativistic quantum theory of spin one-half particles. A further unification is achieved by taking the wave functions themselves to be 2 × 2 matrices which are Peirce logical operators and also elements of the Clifford algebra. Thus we have discovered a direct path from the Peirce logic to quantum theory. A diagrammatic method follows from the Peirce/Clifford algebraic approach and is suitable for describing particle interactions.     

Quantum Field Theory and the Standard Model,by Matthew D. Schwartz

Molecular Optical Activity and the Chiral Discriminations. By S. F. Mason. (Cambridge University Press, 1982.) [Pp. viii + 273.] £20·00. Scope: Treatise/Textbook; Level: Specialist post-graduate.

Elements of Quantum Chemistry. By R. Zahradnik and R. Polak. (Plenum Press; SNTL, Prague, 1981.) [Pp. 462.] $39.50. Scope: Textbook.

Quantum Field Theory and Parastatistics. By Y. Ohnuki and S. Kamefuchi. (University of Tokyo Press/Springer-Verlag, 1982.) [Pp. xiv +489.] DM 154; $c.64.30. Scope:Treatise/Textbook; Level: For specialists only.

Quantum Fields. By N. N. Bogoliubov and D. V. Shirkov, translated by D. B. Pontecorvo.(Addison-WesleyiBenjamin Cummings, 1982.) [Pp. vii + 863.] £19.46. Scope:Treatise/Textbook; Level: Specialist post-graduate.

Handbuch der Physik Encyclopaedia of Physics. In English. Volume 31. Corpuscles and Radiation in Matter, 1. By T. Von Aberg, G. Howat, H. Siegbahn, L. Karlsson, J. A. R. Samson and A. F. Starace. Edited by W. Melhorn. (Springer-Verlag, 1982.) [Pp. xii + 630.] DM 328; $131.20. Scope: Library (reference); Level: For specialists and specialist post-graduate.

Group Theoretical Methods in Physics. Edited by M. Serdaroglu and E. Inono. (Springer-Verlag, 1983.) [Pp. xi + 569.1 DM 70; $30.20. Scope: Conference proceedings; Level: For specialists only.

Electron Correlation in Solids, Molecules and Atoms. Edited by J. T. Devreese and F. Brosens.(Plenum Press, 1983.) [Pp. xi + 435.] $55.00. Scope: Conference proceedings; Level: For specialists only, Specialist post-graduate.     

Index Theory, Gerbes, and Hamiltonian Quantization

We give an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and prove that this leads in a simple manner to the known Schwinger terms (Faddeev-Mickelsson cocycle) for the gauge group action. We relate the APS construction to the bundle gerbe approach discussed recently by Carey and Murray, including an explicit computation of the Dixmier-Douady class. An advantage of our method is that it can be applied whenever one has a form of the APS theorem at hand, as in the case of fermions in an external gravitational field. Received: