An alternative interpretation of the Weinberg-Salam model
A problem of mass generation in the Unified EM+W theory is discussed. Two hypothetical possibilities for the nature of Higgs field are proposed.
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arXiv subjects
L. Faddeev
Publications and source records attributed to L. Faddeev.
Partial duality in SU(N) Yang-Mills theory
Recently we have proposed a set of variables for describing the infrared limit of four dimensional SU(2) Yang-Mills theory. here we extend these variables to the general case of four dimensional SU(N) Yang-Mills theory. We find that the SU(N) connection A decomposes according to irreducible representations of SO(N-1) and the curvature two-form F is related to the symplectic Kirillov two forms that characterize irreducible representations of SU(N). We propose a general class of nonlinear chiral models that may describe stable, soliton-like configurations with nontrivial topological numbers.
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Toroidal Confugurations As Stable Solitons
Previously we have proposed that in certain relativistic quantum field theories knotlike configurations may appear as stable solitons. Here we present a detailed investigation of the simplest knotted soliton, the torus-shaped unknot.
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Knots and Particles
Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly simulated the unknot and trefoil configurations, and our results suggest that all torus knots appear as solitons. Our observations open new theoretical possibilities in scenarios where stringlike structures appear, including physics of fundamental interactions and early universe cosmology. In nematic liquid crystals and 3He superfluids such knotted solitons might actually be observed.
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Shift Operator for Nonabelian Lattice Current Algebra
The shift operator for a quantum lattice current algebra associated with sl(2) is produced in the form of product of local factors. This gives a natural deformation of the Sugawara construction for discrete space-time.
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Discrete Heisenberg-Weyl Group and Modular Group
It is shown that the generators of two discrete Heisenberg-Weyl groups with irrational rotation numbers $θ$ and $-1/ θ$ generate the whole algebra $\cal B$ of bounded operators on $L_2(\bf R)$. The natural action of the modular group in $\cal B$ is implied. Applications to dynamical algebras appearing in lattice regularization and some duality principles are discussed.
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Hirota equation as an example of integrable symplectic map
The hamiltonian formalism is developed for the sine-Gordon model on the space-time light-like lattice, first introduced by Hirota. The evolution operator is explicitely constructed in the quantum variant of the model, the integrability of the corresponding classical finite-dimensional system is established.
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Abelian Current Algebra and the Virasoro Algebra on the Lattice
We describe how a natural lattice analogue of the abelian current algebra combined with free discrete time dynamics gives rise to the lattice Virasoro algebra and corresponding hierarchy of conservation laws.
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