scholarly journals Divergence-free quantum electrodynamics in locally conformally flat space–time

2021 ◽  
Vol 36 (13) ◽  
pp. 2150083
Author(s):  
John Mashford
Keyword(s):  
Quantum Electrodynamics ◽  
Fock Space ◽  
Grassmann Algebra ◽  
Flat Space ◽  
Space Time ◽  
Conformally Flat ◽  
Direct Sums ◽  
Spectral Regularization ◽  
Locally Conformally Flat ◽  
Divergence Free

This paper describes an approach to quantum electrodynamics (QED) in curved space–time obtained by considering infinite-dimensional algebra bundles associated to a natural principal bundle [Formula: see text] associated with any locally conformally flat space–time, with typical fibers including the Fock space and a space of fermionic multiparticle states which forms a Grassmann algebra. Both these algebras are direct sums of generalized Hilbert spaces. The requirement of [Formula: see text] covariance associated with the geometry of space–time, where [Formula: see text] is the structure group of [Formula: see text], leads to the consideration of [Formula: see text] intertwining operators between various spaces. Scattering processes are associated with such operators and are encoded in an algebra of kernels. Intertwining kernels can be generated using [Formula: see text] covariant matrix-valued measures. Feynman propagators, fermion loops and the electron self-energy can be given well-defined interpretations as such measures. Divergence-free calculations in QED can be carried out by computing the spectra of these measures and kernels (a process called spectral regularization). As an example of the approach the precise Uehling potential function for the [Formula: see text] atom is calculated without requiring renormalization from which the Uehling contribution to the Lamb shift can be calculated exactly.

Pseudo-Z symmetric space-times with divergence-free Weyl tensor and pp-waves

2016 ◽  
Vol 13 (02) ◽  
pp. 1650015 ◽  
Author(s):  
Carlo Alberto Mantica ◽  
Young Jin Suh
Keyword(s):  
Symmetric Space ◽  
Weyl Tensor ◽  
Killing Vector ◽  
Complete Classification ◽  
Space Time ◽  
Conformal Killing ◽  
Conformally Flat ◽  
Conformal Curvature ◽  
Wave Space ◽  
Divergence Free

In this paper we present some new results about [Formula: see text]-dimensional pseudo-Z symmetric space-times. First we show that if the tensor Z satisfies the Codazzi condition then its rank is one, the space-time is a quasi-Einstein manifold, and the associated 1-form results to be null and recurrent. In the case in which such covector can be rescaled to a covariantly constant we obtain a Brinkmann-wave. Anyway the metric results to be a subclass of the Kundt metric. Next we investigate pseudo-Z symmetric space-times with harmonic conformal curvature tensor: a complete classification of such spaces is obtained. They are necessarily quasi-Einstein and represent a perfect fluid space-time in the case of time-like associated covector; in the case of null associated covector they represent a pure radiation field. Further if the associated covector is locally a gradient we get a Brinkmann-wave space-time for [Formula: see text] and a pp-wave space-time in [Formula: see text]. In all cases an algebraic classification for the Weyl tensor is provided for [Formula: see text] and higher dimensions. Then conformally flat pseudo-Z symmetric space-times are investigated. In the case of null associated covector the space-time reduces to a plane wave and results to be generalized quasi-Einstein. In the case of time-like associated covector we show that under the condition of divergence-free Weyl tensor the space-time admits a proper concircular vector that can be rescaled to a time like vector of concurrent form and is a conformal Killing vector. A recent result then shows that the metric is necessarily a generalized Robertson–Walker space-time. In particular we show that a conformally flat [Formula: see text], [Formula: see text], space-time is conformal to the Robertson–Walker space-time.

Perfect fluid in a conformally flat space time

1980 ◽  
Vol 13 (1) ◽  
pp. 191-197 ◽  
Author(s):  
M M Som ◽  
N O Santos
Keyword(s):  
Perfect Fluid ◽  
Flat Space ◽  
Space Time ◽  
Conformally Flat

Fluid with heat flux in a conformally flat space-time

1982 ◽  
Vol 25 (10) ◽  
pp. 2518-2520 ◽  
Author(s):  
S. R. Maiti
Keyword(s):  
Heat Flux ◽  
Flat Space ◽  
Space Time ◽  
Conformally Flat

Some conformally-flat space-times of a divergence-free Riemann tensor

1978 ◽  
Vol 11 (4) ◽  
pp. 709-713
Author(s):  
L J Rose ◽  
A E G Stuart ◽  
G W Barrett
Keyword(s):  
Flat Space ◽  
Riemann Tensor ◽  
Conformally Flat ◽  
Divergence Free

scholarly journals Hypersurfaces in a conformally flat space with curvature collineation

1991 ◽  
Vol 14 (3) ◽  
pp. 595-604
Author(s):  
K. L. Duggal ◽  
R. Sharma
Keyword(s):  
Fundamental Problem ◽  
Energy Condition ◽  
Shape Operator ◽  
Flat Space ◽  
Space Time ◽  
Conformally Flat ◽  
Direct Relation ◽  
Shape Operators

We classify the shape operators of Einstein and pseudo Einstein hypersurfaces in a conformally flat space with a symmetry called curvature collineation. We solve the fundamental problem of finding all possible forms of non-diagonalizable shape operators. A physical example of space-time with matter is presented to show that the energy condition has direct relation with the diagonalizability of shape operator.

scholarly journals Application of the Generalized Bochner Technique to the Study of Conformally Flat Riemannian Manifolds

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 927
Author(s):  
Josef Mikeš ◽  
Vladimir Rovenski ◽  
Sergey Stepanov ◽  
Irina Tsyganok
Keyword(s):  
Riemannian Manifolds ◽  
Ricci Flow ◽  
Flat Space ◽  
Conformally Flat ◽  
Space Forms ◽  
Bochner Technique ◽  
Locally Conformally Flat

In this article, we discuss the global aspects of the geometry of locally conformally flat (complete and compact) Riemannian manifolds. In particular, the article reviews and improves some results (e.g., the conditions of compactness and degeneration into spherical or flat space forms) on the geometry “in the large" of locally conformally flat Riemannian manifolds. The results presented here were obtained using the generalized and classical Bochner technique, as well as the Ricci flow.

Sign in / Sign up

Export Citation Format

Share Document