Symmetries of the Kac-Peterson modular matrices of affine algebras.
Symmetries, variational principles, and quantum dynamics.
Symmetry breaking for molecular open systems
Symmetry breaking via internal geometry.
Symmetry operators of a Hartree-type equation with quadratic potential.
Symmetry transformation in extended phase space: the harmonic oscillator in the Husimi representation.
Symplectic solution supermanifolds in field theory
Summary: For a large class of classical field models used for realistic quantum field theoretic models, an infinite-dimensional supermanifold of classical solutions in Minkowski space can be constructed. This solution supermanifold carries a natural symplectic structure; the resulting Poisson brackets between the field strengths are the classical prototypes of the canonical (anti-) commutation relations. Moreover, we discuss symmetries and the Noether theorem in this context.
Symplectic twistor operator and its solution space on
We introduce the symplectic twistor operator in symplectic spin geometry of real dimension two, as a symplectic analogue of the Dolbeault operator in complex spin geometry of complex dimension 1. Based on the techniques of the metaplectic Howe duality and algebraic Weyl algebra, we compute the space of its solutions on .
Système à corps dans un champ magnétique
Système de Yang-Mills-Vlasov en jauge temporelle
Systems of orthogonal polynomials defined by hypergeometric type equations.
Temperature states on gauge groups
Tensor and spinor equivalence on generalized metric tangent bundles.
Tensor product construction of 2-freeness
From a sequence of m-fold tensor product constructions that give a hierarchy of freeness indexed by natural numbers m we examine in detail the first non-trivial case corresponding to m=2 which we call 2-freeness. We show that in this case the constructed tensor product of states agrees with the conditionally free product for correlations of order ≤ 4. We also show how to associate with 2-freeness a cocommutative *-bialgebra.
Tensor products of sequential effect algebras
Ternary symmetries and the Lorentz group
We show that the Lorentz and the SU(3) groups can be derived from the covariance principle conserving a Z₃-graded three-form on a Z₃-graded cubic algebra representing quarks endowed with non-standard commutation laws. The ternary commutation relations on an algebra generated by two elements lead to cubic combinations of three quarks or antiquarks that transform as Lorentz spinors, and binary quark-anti-quark combinations that transform as Lorentz vectors.
TFT Construction of RCFT correlators. V: Proof of modular invariance and factorisation.
The 2D Schrödinger equation for a neutral pair in a constant magnetic field
The ℤ₂-graded sticky shuffle product Hopf algebra
By abstracting the multiplication rule for ℤ₂-graded quantum stochastic integrals, we construct a ℤ₂-graded version of the Itô Hopf algebra, based on the space of tensors over a ℤ₂-graded associative algebra. Grouplike elements of the corresponding algebra of formal power series are characterised.
The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl (2, C).