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Tensor product construction of 2-freeness

R. Lenczewski (1998)

Banach Center Publications

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.

Ternary symmetries and the Lorentz group

Richard Kerner (2011)

Banach Center Publications

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.

The ℤ₂-graded sticky shuffle product Hopf algebra

Robin L. Hudson (2006)

Banach Center Publications

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 approximate symmetries of the vacuum Einstein equations

Tiller, Petr (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

The author reviews the theory of approximate infinitesimal symmetries of partial differential equations. Based on this and on Ibragimov's result on the general symmetries of the vacuum Einstein equation, he proposes a method to calculate approximate symmetries of the non-vacuum Einstein equation: the energy-momentum tensor is treated like a perturbation.

The boundary value problem for Dirac-harmonic maps

Qun Chen, Jürgen Jost, Guofang Wang, Miaomiao Zhu (2013)

Journal of the European Mathematical Society

Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. We...

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