Related papers: Polar decomposition and Brion's theorem
The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…
We introduce Tadao Oda's famous question on lattice polytopes which was originally posed at Oberwolfach in 1997 and, although simple to state, has remained unanswered. The question is motivated by a discussion of the two-dimensional case -…
The h^*-polynomial of a lattice polytope is the numerator of the generating function of the Ehrhart polynomial. Let P be a lattice polytope with h^*-polynomial of degree d and with linear coefficient h^*_1. We show that P has to be a…
We derive the particle asymmetry due to inflationary baryogenesis involving a complex inflaton, obtaining a different result to that in the literature. While asymmetries are found to be significantly smaller than previously calculated, in…
According to the Weinstein splitting theorem, any Poisson manifold is locally, near any given point, a product of a symplectic manifold with another Poisson manifold whose Poisson structure vanishes at the point. Similar splitting results…
This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions…
We generate anti-self-polar polytopes via a numerical implementation of the gradient flow induced by the diameter functional on the space of all finite subsets of the sphere, and prove related results on the critical points of the diameter…
We show that a large class of Euclidean extended supersymmetric lattice gauge theories constructed in [hep-lat/0302017 - hep-lat/0503039] can be regarded as compact formulations by using the polar decomposition of the complex link fields.…
Rectangulations are decompositions of a square into finitely many axis-aligned rectangles. We describe realizations of $(n-1)$-dimensional polytopes associated with two combinatorial families of rectangulations composed of $n$ rectangles.…
After a brief discussion of baryon and lepton number nonconservation, we review the status of thermal leptogenesis with GUT scale neutrino masses, as well as low scale alternatives with keV neutrinos as dark matter and heavy neutrino masses…
We consider two-body and quasi-two-body decays of the type $f_1 \to f_2 B$, where $f_1$ and $f_2$ are spin-1/2 fermions and $B$ a spin-0 or spin-1 boson. After recalling the non-covariant formalism for decay amplitudes, we derive the…
We apply a simple decomposition to the energy of a moving particle. Based on this decomposition, we identify the potential and kinetic energies, then use them to give general definitions of momentum and the various kinds of forces exerted…
Baryogenesis by heavy-neutrino decay and sphaleron reprocessing of both baryon and lepton number is reconsidered, paying special attention to the flavour structure of the general evolution equations and developing an approximate but…
A novel basis of discrete analytic polynomials on a rhombic lattice is introduced and the associated convolution product is studied. A class of discrete analytic functions that are rational with respect to this product is also described.
The formula for dipole radiation reaction torque acting on a system of charges, and the Larmor-like formula for the angular momentum loss by this system, differ in the time derivative term which is the analogue of the Schott term in the…
We explicate the combinatorial/geometric ingredients of Arthur's proof of the convergence and polynomiality, in a truncation parameter, of his non-invariant trace formula. Starting with a fan in a real, finite dimensional, vector space and…
We discuss baryogenesis using the flipped $SU(5)$ model for lepton mass matrices. We show that the generalized see-saw mechanism in this model can not only provide MSW neutrino mixing suitable for solving the solar neutrino problem, and…
Polarons can naturally form in materials from the interaction of extra charge carriers with the atomic lattice. Ubiquitous, they are central to various topics and phenomena such as high-T$_c$ superconductivity, electrochromism,…
The polarized lepton pair forward-backward asymmetries in (B -> rho l^+ l^-) decay using a general, model independent form of the effective Hamiltonian is studied. The general expression for nine double-polarization forward-backward…
We discuss the production of hadrons in polarized lepton nucleon interactions and in the current jet fragmentation region; using the QCD hard scattering formalism we compute the helicity density matrix of the hadron and show how its…