Search results for "Homogeneous space"
showing 10 items of 142 documents
The Geometry of Space-Time and Its Deformations from a Physical Perspective
2007
We start with an epistemological introduction on the evolution of the concepts of space and time and more generally of physical concepts in the context of the relation between mathematics and physics from the point of view of deformation theory. The concepts of relativity, including anti de Sitter space-time, and of quantization, are important paradigms; we briefly present these and some consequences. The importance of symmetries and of space-time in fundamental physical theories is stressed. The last section deals with “composite elementary particles” in anti de Sitter space-time and ends with speculative ideas around possible quantized anti de Sitter structures in some parts of the univer…
Spontaneous symmetry breaking as a resource for noncritically squeezed light
2010
[EN] In the last years we have proposed the use of the mechanism of spontaneous symmetry breaking with the purpose of generating perfect quadrature squeezing. Here we review previous work dealing with spatial (translational and rotational) symmetries, both on optical parametric oscillators and four-wave mixing cavities, as well as present new results. We then extend the phenomenon to the polarization state of the signal field, hence introducing spontaneous polarization symmetry breaking. Finally we propose a Jaynes-Cummings model in which the phenomenon can be investigated at the singlephoton-pair level in a non-dissipative case, with the purpose of understanding it from a most fundamental …
Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
2016
We elaborate a simple classification scheme of all rank-5 SU(2)-spin rotational symmetric tensors according to i) the on-site physical spin-$S$, (ii) the local Hilbert space $V^{\otimes 4}$ of the four virtual (composite) spins attached to each site and (iii) the irreducible representations of the $C_{4v}$ point group of the square lattice. We apply our scheme to draw a complete list of all SU(2)-symmetric translationally and rotationally-invariant Projected Entangled Pair States (PEPS) with bond dimension $D\leqslant 6$. All known SU(2)-symmetric PEPS on the square lattice are recovered and simple generalizations are provided in some cases. More generally, to each of our symmetry class can…
Heavy Quark Symmetries: Molecular partners of theX(3872) andZb(10610)/Zb′(10650)
2014
In this work, we have made use of the identification of the X (3872) and Z b (10610)/Z b ′(10650) as heavy meson-heavy antimeson molecules to establish some consequences derived from the symmetries that these heavy meson-heavy antimeson systems must have. We show the most general effective lagrangian that respects these symmetries only depends on four undetermined low energy constants (LECs), which will be fitted to reproduce the experimental data about the resonances we are identifying as molecular states. Then, we obtain a whole new set of states in the spectrum that could also be thought as heavy meson-heavy antimeson molecules. Finally, using another different symmetry: Heavy Antiquark-…
Asymmetric tri-bi-maximal mixing and residual symmetries
2019
Asymmetric tri-bi-maximal mixing is a recently proposed, grand unified theory (GUT) based, flavor mixing scheme. In it, the charged lepton mixing is fixed by the GUT connection to down-type quarks and a $\mathcal{T}_{13}$ flavor symmetry, while neutrino mixing is assumed to be tri-bi-maximal (TBM) with one additional free phase. Here we show that this additional free phase can be fixed by the residual flavor and CP symmetries of the effective neutrino mass matrix. We discuss how those residual symmetries can be unified with $\mathcal{T}_{13}$ and identify the smallest possible unified flavor symmetries, namely $(\mathbb{Z}_{13}\times\mathbb{Z}_{13})\rtimes \mathrm{D}_{12}$ and $(\mathbb{Z}_…
Dimensional Regularization. Ultraviolet and Infrared Divergences
2015
The cornerstone of Quantum Field Theory is renormalization. We shall speak more about in the next chapters. Before, it is necessary to discuss the method. The best and most simple is, of course, dimensional regularization (doesn’t break the symmetries, doesn’t violate the Ward Identities, preserves Lorentz invariance, etc.). When explained consistently, it becomes very simple and clear. Here, we shortly discuss ultraviolet (UV) and infrared (IR) divergences with a few examples. However, in Chap. 8, we shall extensively treat one-loop two and three-point functions and analyse many more examples of IR and UV divergences.
Polarization observables for elastic electron scattering off a moving nucleon
2019
General expressions for all parity-conserving polarization observables of elastic electron-nucleon scattering in the one-photon exchange approximation are derived for a general frame of reference, i.e.\ not assumming scattering off a nucleon at rest and not specializing to a specific system of coordinates. Essentially, the given expressions are also valid for the inverse process, i.e.\ nucleon scattering off electrons.
Type D vacuum solutions: a new intrinsic approach
2013
We present a new approach to the intrinsic properties of the type D vacuum solutions based on the invariant symmetries that these spacetimes admit. By using tensorial formalism and without explicitly integrating the field equations, we offer a new proof that the upper bound of covariant derivatives of the Riemann tensor required for a Cartan-Karlhede classification is two. Moreover we show that, except for the Ehlers-Kundt's C-metrics, the Riemann derivatives depend on the first order ones, and for the C-metrics they depend on the first order derivatives and on a second order constant invariant. In our analysis the existence of an invariant complex Killing vector plays a central role. It al…
Note on the pragmatic mode-sum regularization method: Translational-splitting in a cosmological background
2021
The point-splitting renormalization method offers a prescription to calculate finite expectation values of quadratic operators constructed from quantum fields in a general curved spacetime. It has been recently shown by Levi and Ori that when the background metric possesses an isometry, like stationary or spherically symmetric black holes, the method can be upgraded into a pragmatic procedure of renormalization that produces efficient numerical calculations. In this note we show that when the background enjoys three-dimensional spatial symmetries, like homogeneous expanding universes, the above pragmatic regularization technique reduces to the well established adiabatic regularization metho…
Route towards Dirac and Weyl antiferromagnetic spintronics
2017
Topological quantum matter and spintronics research have been developed to a large extent independently. In this Review we discuss a new role that the antiferromagnetic order has taken in combining topological matter and spintronics. This occurs due to the complex microscopic symmetries present in antiferromagnets that allow, e.g., for topological relativistic quasiparticles and the newly discovered N\'{e}el spin-orbit torques to coexist. We first introduce the concepts of topological semimetals and spin-orbitronics. Secondly, we explain the antiferromagnetic symmetries on a minimal Dirac semimetal model and the guiding role of $\textit{ab initio}$ calculations in predictions of examples of…