Consider Hankel operators Hf on the weighted Bergman space L 2 a(B, dvα). In this paper we characterize the membership of (H∗ fHf ) s/2 = |Hf | in the norm ideal CΦ, where 0 < s ≤ 1 and the symmetric gauge function Φ is allowed to be arbitrary.

We construct an example of a finite dimensional L∞ algebra which is generated by a Lie algebra together with a non-Lie action on another vector space. We then show how this example fits into the gauge transformation theory of Berends, Burgers and Van Dam.

Let P be the orthogonal projection from L(B, dv) onto the Bergman space La(B, dv) of the unit ball in C . In this paper we characterize the membership of commutators of the form [Mf , P ] in the norm ideal CΦ, where the symmetric gauge function Φ is allowed to be arbitrary.

“Pictorial space” is the mental structure that appears to be the scaffold for the visual awareness when looking “into” (as opposed to “at”) a picture. Its structure differs from the “visual space” that is the scaffold for the visual awareness when looking into the scene in front of the observer. The structure of pictorial space has been probed empirically and explored theoretically. Here we pro...

We perform a covariant (Lagrangian) quantization of perturbative gravity in the background Schwarzschild black hole. The key tool is decomposition field into spherical harmonics. fix Regge-Wheeler gauge for modes with angular momentum quantum number $l \geq 2$, while low multipole $l$ $=$ $0$ or $1$ -- which inapplicable we propose set fixing conditions are 2D and perturbatively well-defined. f...

It is shown that the nonhomogeneous Dirichlet and Neuman problems for the 2nd-order Seiberg-Witten equation on a compact 4-manifold X admit a regular solution once the nonhomogeneous Palais-Smale condition is satisfied. The approach consists in applying the elliptic techniques to the variational setting of the Seiberg-Witten equation. The gauge invariance of the functional allows to restrict th...

By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the biadjoint representation, we derive in linearized approximation, the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance, and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global su...

In loop quantum gravity in the connection representation, the quantum configuration space A/G, which is a compact space, is much larger than the classical configuration space A/G of connections modulo gauge transformations. One finds that A/G is homeomorphic to the space Hom(L∗, G))/Ad. We give a new, natural proof of this result, suggesting the extension of the hoop group L∗ to a larger, compa...

we study different completeness definitions for two categories of lattice-valued cauchy spaces and the relations between these definitions. we also show the equivalence of a so-called completion axiom and the existence of a completion.

We consider 2-dimensional QCD on a cylinder, where space is a circle. We find the ground state of the system in case of massless quarks in a 1/N expansion. We find that coupling to fermions nontrivially modifies the large N saddle point of the gauge theory due to the phenomenon of ‘decompactification’ of eigenvalues of the gauge field. We calculate the vacuum energy and the vacuum expectation v...