We investigate chiral anomaly for fermions in fundamental representation on noncommutative (fuzzy) 2-sphere. In spite that this system is realized by finite dimensional matrices and no regularization is necessary for either UV or IR, we can reproduce the correct chiral anomaly which is consistent with the calculations done in flat noncommutative space. Like the flat case, there are ambiguities ...

We introduce a new class of nonlinear equations admitting a representation in terms of Darboux-covariant compatibility conditions. Their special cases are, in particular, (i) the “general” von Neumann equation iρ̇ = [H, f(ρ)], with [f(ρ), ρ] = 0, (ii) its generalization involving certain functions f(ρ) which are non-Abelian in the sense that [f(ρ), ρ] 6= 0, and (iii) the Nahm equations.

We present generalized parton distributions for weakly bound systems on the light cone in order to build intuition about the light-front formalism. Physics at the crossover is reviewed in terms of the light-cone Fock space representation. Furthermore, we link light-cone Fock components to the equal (light-cone) time projection of the covariant Bethe-Salpeter amplitude. Continuity of the distrib...

We give an SU(2) covariant representation of the constraints of Euclidean general relativity in the Ashtekar variables. The guiding principle is the use of triads to transform all free spatial indices into SU(2) indices. A central role is played by a special covariant derivative. The Gauss, diffeomorphism and Hamiltonian constraints become purely algebraic restrictions on the curvature and the ...

A mathematically well-defined, manifestly covariant theory of classical and quantum field is given, based on Euclidean Poisson algebras and a generalization of the Ehrenfest equation, which implies the stationary action principle. The theory opens a constructive spectral approach to finding physical states both in relativistic quantum field theories and for flexible phenomenological few-particl...

A generalization of the Yang-Mills covariant derivative, that uses both vector and scalar fields and transforms as a 4-vector contracted with Dirac matrices, is used to simplify and unify the Glashow-Weinberg-Salam model. Since SU (3) assigns the wrong hypercharge to the Higgs boson, it is necessary to use a special representation of U (3) to obtain all the correct quantum numbers. A surplus ga...

Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine structure and a multiresolution associated to a matrix-valued weight. We describe the one-to-one correspondence between the commutant of this structure and the fixed points of the transfer operator. We show how the covariant representation can be realized on Rn if the ...

We re-examine the generalized Pauli–Villars regularization proposed by Frolov and Slavnov, a possible gauge invariant Lagrangian-level regularization for a chiral fermion. When a chiral fermion belongs to a (pseudo-)real representation of the gauge group, the formulation always provides a complete gauge invariant regularization; a chiral fermion in an anomaly free complex representation seems t...

enforces the Landau gauge ∂μA a μ = 0. b a is the Lagrange multiplier and c, c are the ghost and antighost fields. The covariant derivative in the adjoint representation is given by D μ = δ ∂μ − gf Aμ . (4) For d = 3, the coupling g becomes a dimensional quantity itself. As a consequence, the three-dimensional YangMills theory (1) is superrenormalizable. Such theories exhibit serious problems i...

The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as the arising of gauge theory. Furthermore, a manifestly causal and covariant formulation of quantum field theory is presented which surpasses the usual Hamilton...