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Proceedings of a Seminar Series Held at DAPHE, Observatoire de Meudon, and LPTHE, Université Pierre et Marie Curie, Paris, Between October 1984 and October 1985
Certain mathematical aspects of Kaluza-Klein theories are discussed, concerned with the ability to truncate the four-dimensional spectrum of states to a finite subsector, including the graviton and Yang-Mills gauge bosons. This yields a criterion by means of which certain exceptional theories are singled out from the generic case.
We review recent results in non-inertial quantum field theory. By formulating Q.F.T. in a large class of accelerated frames, the classical and the quantum aspects of the theory are unified. We describe the thermal effects, their asymptotic character and the role of the P.C.T. symmetry. A discussion of quantum covariance and detection processes is also given.
The dynamics of a large-scale quasi-homogeneous scalar field producing the de Sitter (inflationary) stage in the early universe is strongly affected by small-scale quantum fluctuations of the same scalar field and, in this way, becomes stochastic. The evolution of the corresponding large-scale space-time metric follows that of the scalar field and is stochastic also. The Fokker-Planck equation for...
Liouville equation is put on the lattice in a completely integrable way. The classical version is investigated in details and a lattice deformation of the Virasoro algebra is obtained. The quantum version still lacks a satisfactory definition of the Hamiltonian.
General form of the integrable equations in 1+1 and 2+1 dimensions and their group - theoretical and Hamiltonian properties are considered. General theory of recursion operators is discussed.
The infinite families of Poisson brackets $$\{ S_{i_1 k_1 } (\lambda _1 ),S_{i_2 k_2 } (\lambda _2 )\} _\pi$$ (n = 0,1,2,...) between the elements of scattering matrices are calculated for the linear NxN matrix spectral problem and differential spectral problem of an arbitrary order.
An equation originally derived from non-relativistic ideal gasdynamics turns out to be reducible to a Lorentz invariant nonlinear version of the Klein-Gordon equation. We present its interacting soliton solutions, which are here constructed by means of a Bäcklund transformation, starting from the “vacuum”.
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