Search results for "Differential geometry"
showing 10 items of 462 documents
Supersymmetry from boundary conditions
2004
We study breaking and restoration of supersymmetry in five-dimensional theories by determining the mass spectrum of fermions from their equations of motion. Boundary conditions can be obtained from either the action principle by extremizing an appropriate boundary action (interval approach) or by assigning parities to the fields (orbifold approach). In the former, fields extend continuously from the bulk to the boundaries, while in the latter the presence of brane mass-terms cause fields to jump when one moves across the branes. We compare the two approaches and in particular we carefully compute the non-trivial jump profiles of the wavefunctions in the orbifold picture for very general bra…
On selfdual spin-connections and asymptotic safety
2016
We explore Euclidean quantum gravity using the tetrad field together with a selfdual or anti-selfdual spin-connection as the basic field variables. Setting up a functional renormalization group (RG) equation of a new type which is particularly suitable for the corresponding theory space we determine the non-perturbative RG flow within a two-parameter truncation suggested by the Holst action. We find that the (anti-)selfdual theory is likely to be asymptotically safe. The existing evidence for its non-perturbative renormalizability is comparable to that of Einstein-Cartan gravity without the selfduality condition.
Observations on the Darboux coordinates for rigid special geometry
2006
We exploit some relations which exist when (rigid) special geometry is formulated in real symplectic special coordinates $P^I=(p^\Lambda,q_\Lambda), I=1,...,2n$. The central role of the real $2n\times 2n$ matrix $M(\Re \mathcal{F},\Im \mathcal{F})$, where $\mathcal{F} = \partial_\Lambda\partial_\Sigma F$ and $F$ is the holomorphic prepotential, is elucidated in the real formalism. The property $M\Omega M=\Omega$ with $\Omega$ being the invariant symplectic form is used to prove several identities in the Darboux formulation. In this setting the matrix $M$ coincides with the (negative of the) Hessian matrix $H(S)=\frac{\partial^2 S}{\partial P^I\partial P^J}$ of a certain hamiltonian real fun…
Acceleration radiation and the Planck scale
2008
A uniformly accelerating observer perceives the Minkowski vacuum state as a thermal bath of radiation. We point out that this field-theory effect can be derived, for any dimension higher than two, without actually invoking very high energy physics. This supports the view that this phenomenon is robust against Planck-scale physics and, therefore, should be compatible with any underlying microscopic theory.
Twistor transform inddimensions and a unifying role for twistors
2005
Twistors in four dimensions d=4 have provided a convenient description of massless particles with any spin, and this led to remarkable computational techniques in Yang-Mills field theory. Recently it was shown that the same d=4 twistor provides also a unified description of an assortment of other particle dynamical systems, including special examples of massless or massive particles, relativistic or non-relativistic, interacting or non-interacting, in flat space or curved spaces. In this paper, using 2T-physics as the primary theory, we derive the general twistor transform in d-dimensions that applies to all cases, and show that these more general twistor transforms provide d dimensional ho…
Continuous-variable entanglement sharing in noninertial frames
2007
We study the distribution of entanglement between modes of a free scalar field from the perspective of observers in uniform acceleration. We consider a two-mode squeezed state of the field from an inertial perspective, and analytically study the degradation of entanglement due to the Unruh effect, in the cases of either one or both observers undergoing uniform acceleration. We find that for two observers undergoing finite acceleration, the entanglement vanishes between the lowest frequency modes. The loss of entanglement is precisely explained as a redistribution of the inertial entanglement into multipartite quantum correlations among accessible and unaccessible modes from a non-inertial p…
The QCD analytic effective charge and its dependence on the pion mass
2004
A new model for the QCD analytic running coupling, which incorporates the effects due to the $\pi$ meson mass, is proposed. The properties of this invariant charge in spacelike and timelike regions are examined. Its main distinctive features are a finite infrared limiting value, which depends on the pion mass, and the "plateau-like" behavior in the deep infrared domain of the timelike region.
Development and Study of a Micromegas Pad-Detector for High Rate Applications
2015
In this paper, the design and the performance of two prototype detectors based on Micromegas technology with a pad readout geometry is discussed. In addition, two alternative implementations of a spark-resistent protection layer on top of the readout pads have been tested to optimize the charge-up behavior of the detector under high rates. The prototype detectors consist of 500 pads with a size of 5x4 mm, each connected to one independent readout channel, and cover an active area of 10x10 cm. The design of these prototypes and its associated readout infrastructure was developed in such a way that it can be easily adapted for large-size detector concepts.
Václav Hlavatý on intuition in Riemannian space
2019
Abstract We present a historical commentary together with an English translation of a mathematical-philosophical paper by the Czech differential geometer and later proponent of a geometrized unified field theory Vaclav Hlavatý (1894–1969). The paper was published in 1924 at the height of interpretational debates about recent advancements in differential geometry triggered by the advent of Einstein's general theory of relativity. In the paper he argued against a naive generalization of analogical reasoning valid for curves and surfaces in three-dimensional Euclidean space to the case of higher-dimensional curved Riemannian spaces. Instead, he claimed, the only secure ground to arrive at resu…
Historical Origins of the nine-point conic -- The Contribution of Eugenio Beltrami
2020
In this paper, we examine the evolution of a specific mathematical problem, i.e. the nine-point conic, a generalisation of the nine-point circle due to Steiner. We will follow this evolution from Steiner to the Neapolitan school (Trudi and Battaglini) and finally to the contribution of Beltrami that closed this journey, at least from a mathematical point of view (scholars of elementary geometry, in fact, will continue to resume the problem from the second half of the 19th to the beginning of the 20th century). We believe that such evolution may indicate the steady development of the mathematical methods from Euclidean metric to projective, and finally, with Beltrami, with the use of quadrat…