相关论文: The Attenuated Magnetic Ray Transform on Surfaces
We prove the integrability of magnetic geodesic flows of $SO(n)$--invariant Riemannian metrics on the rank two Stefel variety $V_{n,2}$ with respect to the magnetic field $\eta\, d\alpha$, where $\alpha$ is the standard contact form on…
Using Morse-theoretic techniques, we show that the moduli space of U*(2n)-Higgs bundles over a compact Riemann surface is connected.
Starting with the data of a curve of singularity types, we use the Legendre transform to construct weak geodesic rays in the space of locally bounded metrics on an ample line bundle L over a compact manifold. Using this we associate weak…
Certain gauge transformations may act non-trivially on physical states in quantum electrodynamics (QED). This observation has sparked the yet unresolved question of how to characterize allowed boundary conditions for gauge theories. Faddeev…
Magnetic reconnection occurs when two plasmas having co-planar but anti-parallel magnetic fields meet. At the contact point, the field is locally annihilated and the magnetic energy can be released into the surrounding plasma. Theory and…
The hypothesis of an alternative way of obtaining gravitational waves is the physical motivation of this article. Using the linear field approximation and a symmetry transformation of the affine connection, new field equations and new gauge…
We study the effect of a magnetic field on Goos-H\"anchen shifts in gaped graphene subjected to a double triangular barrier. Solving the wave equation separately in each region composing our system and using the required boundary…
A possible extension of the Standard Model of elementary particles is Gauge-Higgs unification, where the Higgs field is identified with (some of) the extra dimensional components of a five-dimensional gauge field. In this scenario there is…
We study the nonlinear $\sigma$-model in an external magnetic field applied on curved surfaces with rotational symmetry. The Euler-Lagrange equations derived from the Hamiltonian yield the double sine-Gordon equation (DSG) provided the…
In the Higgs mechanism, mediators of the weak force acquire masses by interacting with the Higgs condensate, leading to a vector boson mass matrix. On the other hand, a rigid body accelerated through an inviscid, incompressible and…
We study the possible effects of classical gravitational backgrounds on the Higgs field through the modifications induced in the one-loop effective potential and the vacuum expectation value of the energy-momentum tensor. We concentrate our…
This paper concerns the relationship between locally homogeneous geometric structures on topological surfaces and the moduli of polystable Higgs bundles on Riemann surfaces, due to Hitchin and Simpson. In particular we discuss the…
During an operation of surgery on a Riemannian manifold and along a given embedded submanifold, one needs to replace the (old) metric induced by the exponential map on a tubular neighborhood of the submanifold by the Sasakian metric. So a…
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional…
The quantum behavior of electrons in bilayer graphene with applied magnetic fields is addressed. By using second-order supersymmetric quantum mechanics the problem is transformed into two intertwined one dimensional stationary Schr\"odinger…
We solve explicitly the geodesic equation for a wide class of (pseudo)-Riemannian homogeneous manifolds (G/H,m), including those with G compact, as well as non-compact semisimple Lie groups, under a simple algebraic condition for the metric…
The effect of a spatially modulated magnetic field on the weak localization phenomenon in two-dimensional electron gas (2DEG) is studied. Both the dephasing time $\tau_H$ and magnetoresistance are shown to reveal a nontrivial behavior as…
Quantum particles under geometric constraints are sensitive to the geometry and topology of the underlying space. We analytically study the laser-driven nonlinear dynamics of a quantum particle whose motion is constrained to a…
We investigate the metric dependence of the partition function of the self-dual p-form gauge field on an arbitrary Riemannian manifold. Using geometric quantization of the space of middle-dimensional forms, we derive a projectively flat…
Geodesics become an essential element of the geometry of a semi-Riemannian manifold. In fact, their differences and similarities with the (positive definite) Riemannian case, constitute the first step to understand semi-Riemannian Geometry.…