scholarly journals Peeling on Kerr Spacetime: Linear and Semi-linear Scalar Fields

2019 ◽  
Vol 20 (10) ◽  
pp. 3419-3470 ◽  
Author(s):  
Jean-Philippe Nicolas ◽  
Truong Xuan Pham
Keyword(s):  
Scalar Fields ◽  
Kerr Spacetime ◽  
Linear Scalar

scholarly journals 3D simulations of linearized scalar fields in Kerr spacetime

2004 ◽  
Vol 69 (10) ◽  
Author(s):  
Mark A. Scheel ◽  
Adrienne L. Erickcek ◽  
Lior M. Burko ◽  
Lawrence E. Kidder ◽  
Harald P. Pfeiffer ◽  
...  
Keyword(s):  
Scalar Fields ◽  
3D Simulations ◽  
Kerr Spacetime

scholarly journals Continuous Histograms for Anisotropy of 2D Symmetric Piece-Wise Linear Tensor Fields

2021 ◽  
pp. 39-70
Author(s):  
Talha Bin Masood ◽  
Ingrid Hotz
Keyword(s):  
Volume Rendering ◽  
Transfer Functions ◽  
Anisotropy Field ◽  
Scalar Fields ◽  
Linear Interpolation ◽  
Tensor Fields ◽  
Interactive Interfaces ◽  
Scalar Invariants ◽  
Linear Scalar ◽  
Naive Approach

AbstractIn this chapter we present an accurate derivation of the distribution of scalar invariants with quadratic behavior represented as continuous histograms. The anisotropy field, computed from a two-dimensional piece-wise linear tensor field, is used as an example and is discussed in all details. Histograms visualizing an approximation of the distribution of scalar values play an important role in visualization. They are used as an interface for the design of transfer-functions for volume rendering or feature selection in interactive interfaces. While there are standard algorithms to compute continuous histograms for piece-wise linear scalar fields, they are not directly applicable to tensor invariants with non-linear, often even non-convex behavior in cells when applying linear tensor interpolation. Our derivation is based on a sub-division of the mesh in triangles that exhibit a monotonic behavior. We compare the results to a naïve approach based on linear interpolation on the original mesh or the subdivision.

scholarly journals Preferred instantaneous vacuum for linear scalar fields in cosmological space-times

2015 ◽  
Vol 91 (6) ◽  
Author(s):  
Ivan Agullo ◽  
William Nelson ◽  
Abhay Ashtekar
Keyword(s):  
Scalar Fields ◽  
Linear Scalar

scholarly journals Klein–Gordon field from the XXZ Heisenberg model

2019 ◽  
Vol 28 (01) ◽  
pp. 1950020 ◽  
Author(s):  
Jakub Bilski ◽  
Suddhasattwa Brahma ◽  
Antonino Marcianò ◽  
Jakub Mielczarek
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Heisenberg Model ◽  
Anisotropy Parameter ◽  
Scalar Fields ◽  
Scalar Field Theory ◽  
Interaction Terms ◽  
Klein Gordon ◽  
Xxz Heisenberg Model ◽  
Linear Scalar

We examine the recently introduced idea of Spin-Field Correspondence (SFC) focusing on the example of the spin system described by the XXZ Heisenberg model with external magnetic field. The Hamiltonian of the resulting nonlinear scalar field theory is derived for arbitrary value of the anisotropy parameter [Formula: see text]. We show that the linear scalar field theory is reconstructed in the large spin limit. For [Formula: see text], a nonrelativistic scalar field theory satisfying the Born reciprocity principle is recovered. As expected, for the vanishing anisotropy parameter [Formula: see text], the standard relativistic Klein–Gordon field is obtained. Various aspects of the obtained class of the scalar fields are studied, including the fate of the relativistic symmetries and the properties of the emerging interaction terms. We show that, in a certain limit, the so-called polymer quantization of the field variables is recovered. This and other discussed properties suggest a possible relevance of the considered framework in the context of quantum gravity.

scholarly journals Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 115 ◽  
Author(s):  
Jerónimo Cortez ◽  
Guillermo A. Mena Marugán ◽  
José Velhinho
Keyword(s):  
Scalar Fields ◽  
Complex Structures ◽  
De Sitter ◽  
Quantum Theories ◽  
Bianchi I ◽  
Uniqueness Results ◽  
Klein Gordon ◽  
Globally Hyperbolic Spacetimes ◽  
Hyperbolic Spacetimes ◽  
Linear Scalar

In this work, we present an overview of uniqueness results derived in recent years for the quantization of Gowdy cosmological models and for (test) Klein-Gordon fields minimally coupled to Friedmann-Lemaître-Robertson-Walker, de Sitter, and Bianchi I spacetimes. These results are attained by imposing the criteria of symmetry invariance and of unitary implementability of the dynamics. This powerful combination of criteria allows not only to address the ambiguity in the representation of the canonical commutation relations, but also to single out a preferred set of fundamental variables. For the sake of clarity and completeness in the presentation (essentially as a background and complementary material), we first review the classical and quantum theories of a scalar field in globally hyperbolic spacetimes. Special emphasis is made on complex structures and the unitary implementability of symplectic transformations.

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