In interaction the between the leads to a quantum liquids particles variety of and unusual states of condensed matter interesting systems, super e.g. and the fractional in electron Hall effect conductivity quantum (FQHE) sys tems. In this book for we investigate quantum field theoretical approaches fermion the is interacting systems. Originally, quantum fieldtheory designed describe as a to perturbation theory weakly interacting many particle sys tems. For treatment of interaction and correlation effects a proper beyond the the series of must beresummed perturbation theory, Feynmandiagrams...

has been in the of a Symmetry major ingredient development quantum perturba tion and it is a basic of the of theory, ingredient theory integrable (Hamiltonian and of the the use in context of non Hamiltonian) systems; yet, symmetry gen eral is rather recent. From the of view of nonlinear perturbation theory point the use of has become dynamics, widespread only through equivariant symmetry bifurcation in this attention has been confined to linear even theory; case, mostly symmetries. in recent the and of methods for dif Also, theory practice symmetry years ferential has become and has been to...

All kind ofinformationfrom distant celestialbodies comestous intheform of radiation. Inmost the of electromagnetic cases thisradiation propagation be can as a reasonable in described, terms of This is approximation, rays. truenot inthe but also inthe radio only ofthe electro opticalrange range Forthis the of reason laws areoffundamental magneticspectrum. optics ray for importance and astronomy, astrophysics, cosmology. to According arethe of general relativity, light light likegeodesics a rays Lorentzianmetric whichthe is described. how by spacetimegeometry This, is true as as the under the...

There countlessnumberof of few area examples quantum mechanical constituent in subnuclear few nucleon quarks bodysystems: physics, or few cluster in nuclear smallatomsandmolecules physics, systems inatomic few electron dots insolidstate or physics quantum physics, Theintricatefeatureofthe isthat etc. few bodysystems theydevelop individual characters thenumber ofconstituent on depending parti cles.Themesonsand the andthe'Li alpha particle baryons, nucleus, theHeatomandtheBeatom have different or very physicalproper ties.Themost ofthesedifferences thecorrelated importantcauses are motion and...

Self-duality greatly reduces the mathematical difficulties of a theory but it is also a notion of considerable physical significance. The new class of self-dual Chern-Simons theories discussed in detail in this book arise in the context of anyonic quantum field theory and have applications to models such as the quantum Hall effect, anyonic superconductivity, and Aharonov-Bohm scattering. There are also interesting connections with the theory of integrable models. The author presents the abelian and non-abelian models for relativistic and non-relativistic realizations of the self-dual...

Thework described in this has somewhat erratically, over monograph grown, of than a more interest inthe was firstaroused period thirty My subject years. thebeautiful and inBroucke.'sthesis also by see computations drawings (1963; Broucke where familiesof orbits in the restricted three 1968), periodic body for the Earth Moon ratio = were mass problem investigated (/.I 0.012155). These that natural for the existence ofthe a explanation drawingssuggested observed familiesand for the found the of orbits could be shapes perhaps by to the limit + 0. a recourse y As first it a to as as step,...

hereafter calledvolume the of In a volume study previous (H6non 1997, I), the restricted initiated. families in problem (We generating three body was recallthat families defined asthe limits offamilies of are periodic generating determinationof orbitsfor Themain wasfoundto lieinthe 4 problem p 0.) bifurcation wheretwo the betweenthebranches ata ormore orbit, junctions A solutionto this was familiesof orbits intersect. partial problem generating and sidesof theuseofinvariants: Manysimple symmetries passage. givenby In the evolution of the bifurcations can be solved in this way. particular,...

This is a textbook on stochastic quantization which was originally proposed by G. Parisi and Y. S. Wu in 1981 and then developed by many workers. I assume that the reader has finished a standard course in quantum field theory. The Parisi-Wu stochastic quantization method gives quantum mechanics as the thermal-equilibrium limit of a hypothetical stochastic process with respect to some fictitious time other than ordinary time. We can consider this to be a third method of quantization; remarkably different from the conventional theories, i. e, the canonical and path-integral ones. Over the past...

These lectures were given to third-year mathematics undergraduates at Oxford in the late 1970s and early 1980s. The notes were produced originally in mimeographed form by the Mathematical Institute at Oxford in 1977, and in a revised edition in 1980. I have made further minor changes and corrections in this edition, and added some examples and exercises from problem sheets given out in lectures by Roger Penrose and Paul Tod. Special relativity provides one of the more interesting pedagogical challenges. This particular course was given to students with a strong mathematical background who...

Molecularly small confined phases play an important role in many scientific and engineering disciplines. For instance, the confining membrane of a living cell is known to affect the structure and transport of cellular water, which mediates the cell's metabolism and other biochemical processes. Transport of hazardous waste through the soil is strongly influenced by the adsorption of bulk phase molecules on the confining mineral _surfaces. Finally, molecularly thin confined fluid films play a prominent part in lubrication. These examples illustrate the broad range of natural and commercial...