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It is shown that every higher Korteveg‐de Vries equation can be included in a one‐parameter family of integrable equations.
We show that in the Minkowski space, a self‐dual gauge field can be linearly superposed with either another self‐dual gauge field or a non‐self‐dual gauge field to give a new solution of the Yang–Mills equation. From these new solutions, Euclidean solutions are constructed. Some of...
Stochastic mechanics is an explanation of nonrelativistic quantum phenomena in terms of stochastic differential equations. In this note a simple example of a measurement is constructed and the behavior of the sample paths of the corresponding stochastic differential equation is examined. The...
We continue our study of complex aesthetic field theory using a set of group theoretical data introduced previously. Our more detailed study shows significant differences with the corresponding real theory. We find that our theory allows for a four‐dimensional particle system, where the...
A framework is proposed in which supersymmetries can be defined in the language of axiomatic quantum field theory. This framework contains a nuclear ∗‐algebra into which the Borchers’ algebra of a general supermultiplet is embedded through a map which, in some sense, generalizes the concept...
We derive necessary and sufficient tensor conditions for the existence of a four‐parameter isometry group G 4 which acts multiply transitively on a Riemannian V 3 . We then apply these results to determine which spatially homogeneous cosmological models have induced 3‐metrics which are...
We calculate numerically a few terms of the corrections to the large‐order behavior of the ground state energy of the O ( N ) anharmonic oscillator by analyzing the perturbation series. We then generate 94 terms of the perturbative expansion of the difference between the energies of the two low...
If gradient terms in the linear Bose chain Hamiltonian couple nearest neighbors only, then in the spin 1/2 approximation they reduce to the spin 1/2 x ‐ y ‐ z Hamiltonian. Hence, spin 1/2 approximation reveals the Thirring model as the one, whose spectrum is completely included in the...
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