We consider QED in a constant axial vector background. Lorentz invariance violation(LIV) occurs through radiative corrections. A detailed study of the phenomenology of the model is carried out, clarifying important issues related to the various regularizations employed . In this context, the physical meaning of the cutoffs induced by LIV is emphasized. Finally, finite temperature radiative corr...

In this work, we use Lorentz invariance violation (LIV) introduced as a generic modification to particle dispersion relations to study some consequences of single photon emission, known as vacuum Cherenkov radiation, and photon decay processes in cosmic and gamma rays. These processes are forbidden in a Lorentz invariant theory but allowed under the hypothesis of LIV. We show that the emission ...

Let D be the sheaf of analytic differential operators of n variables x1, . . . , xn. We consider a left ideal I of D generated by {l1, . . . , lm} which are in the Weyl algebra D = C〈x1, . . . , xn, ∂1, . . . , ∂n〉. If no confusion arises, we also denote by I the left ideal D ·{l1, . . . , ln} in D. Assume that D/I is holonomic. It was proved by M.Kashiwara that the germs of the k-th extension ...

Let [Formula: see text] be a compact connected orientable Cauchy–Riemann (CR) manifold with the action of Lie group text]. Under natural pseudoconvexity assumptions we show that CR Guillemin–Sternberg map is an isomorphism at level Sobolev spaces functions, modulo finite-dimensional subspace. As application study this for holomorphic line bundles which are positive near inverse image by momentu...

Given a compact 3-manifold M equipped with the contact form λ we consider smooth maps u : C → R × M solving the Cauchy-Riemann equations Tu ̊ i = J(u) ̊ Tu, for a distinguished class of almost complex structures J on R ×M which are R-invariant and related to λ. If the map is non constant and of finite energy, the projection into M necessarily approaches as |z| → ∞ a periodic solution of the Ree...

domain M parameterization immersed surface Remember that, like the cartographers of yore, our goal is to parameterize a given surface over the plane. In particular, we want to find a map that preserves angles. How can we express this condition more explicitly? Well, we know how to express 90-degree rotations on the surface, using the complex structure J . And we know how to express 90-degree ro...

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...

Let φ : C → C be a bilipschitz map. We prove that if E ⊂ C is compact, and γ(E), α(E) stand for its analytic and continuous analytic capacity respectively, then C−1γ(E) ≤ γ(φ(E)) ≤ Cγ(E) and C−1α(E) ≤ α(φ(E)) ≤ Cα(E), where C depends only on the bilipschitz constant of φ. Further, we show that if μ is a Radon measure on C and the Cauchy transform is bounded on L2(μ), then the Cauchy transform i...

Let φ : C → C be a bilipschitz map. We prove that if E ⊂ C is compact, and γ(E), α(E) stand for its analytic and continuous analytic capacity respectively, then Cγ(E) ≤ γ(φ(E)) ≤ Cγ(E) and Cα(E) ≤ α(φ(E)) ≤ Cα(E), where C depends only on the bilipschitz constant of φ. Further, we show that if μ is a Radon measure on C and the Cauchy transform is bounded on L(μ), then the Cauchy transform is als...