Search results for "Conformal"
showing 10 items of 234 documents
Radial conformal motions in Minkowski space–time
1999
A study of radial conformal Killing fields (RCKF) in Minkowski space-time is carried out, which leads to their classification into three disjointed classes. Their integral curves are straight or hyperbolic lines admitting orthogonal surfaces of constant curvature, whose sign is related to the causal character of the field. Otherwise, the kinematic properties of the timelike RCKF are given and their applications in kinematic cosmology is discussed.
On the unification of electroweak interactions with gravity
1982
It is shown that the electroweak interactions in the Salam-Weinberg model can be described by a space-time connection form which preserves the space-time metric multiplied by a conformal factor. In addition, one needs an extraSO(2)-connection form. The Dirac field in this formalism is described (after making a certain regularity assumption) by a vierbein field for the space-time metric and a complex scalar field.
New methods for approximating general relativity in numerical simulations of stellar core collapse
2006
We review various approaches to approximating general relativistic effects in hydrodynamic simulations of stellar core collapse and post-bounce evolution. Different formulations of a modified Newtonian gravitational potential are presented. Such an effective relativistic potential can be used in an otherwise standard Newtonian hydrodynamic code. An alternative approximation of general relativity is the assumption of conformal flatness for the three-metric, and its extension by adding second post-Newtonian order terms. Using a code which evolves the coupled system of metric and fluid equations, we apply the various approximation methods to numerically simulate axisymmetric models for the col…
A kinematic method to obtain conformal factors
2000
Radial conformal motions are considered in conformally flat space-times and their properties are used to obtain conformal factors. The geodesic case leads directly to the conformal factor of Robertson-Walker universes. General cases admitting homogeneous expansion or orthogonal hypersurfaces of constant curvature are analyzed separately. When the two conditions above are considered together a subfamily of the Stephani perfect fluid solutions, with acceleration Fermi-Walker propagated along the flow of the fluid, follows. The corresponding conformal factors are calculated and contrasted with those associated with Robertson-Walker space-times.
On the geometry of Killing and conformal tensors
2006
The second order Killing and conformal tensors are analyzed in terms of their spectral decomposition, and some properties of the eigenvalues and the eigenspaces are shown. When the tensor is of type I with only two different eigenvalues, the condition to be a Killing or a conformal tensor is characterized in terms of its underlying almost-product structure. A canonical expression for the metrics admitting these kinds of symmetries is also presented. The space-time cases 1+3 and 2+2 are analyzed in more detail. Starting from this approach to Killing and conformal tensors a geometric interpretation of some results on quadratic first integrals of the geodesic equation in vacuum Petrov-Bel type…
Adiabatic regularization with a Yukawa interaction
2017
We extend the adiabatic regularization method for an expanding universe to include the Yukawa interaction between quantized Dirac fermions and a homogeneous background scalar field. We give explicit expressions for the renormalized expectation values of the stress-energy tensor $\langle T_{\mu\nu} \rangle$ and the bilinear $\langle \bar\psi\psi\rangle$ in a spatially flat FLRW spacetime. These are basic ingredients in the semiclassical field equations of fermionic matter in curved spacetime interacting with a background scalar field. The ultraviolet subtracting terms of the adiabatic regularization can be naturally interpreted as coming from appropriate counterterms of the background fields…
Hawking Radiation by Kerr Black Holes and Conformal Symmetry
2010
The exponential blueshift associated with the event horizon of a black hole makes conformal symmetry play a fundamental role in accounting for its thermal properties. Using a derivation based on two-point functions, we show that the full spectrum of thermal radiation of scalar particles by Kerr black holes can be explicitly derived on the basis of a conformal symmetry arising in the wave equation near the horizon. The simplicity of our approach emphasizes the depth of the connection between conformal symmetry and black hole radiance.
Conformal Symmetry and Feynman Integrals
2018
Singularities hidden in the collinear region around an external massless leg may lead to conformal symmetry breaking in otherwise conformally invariant finite loop momentum integrals. For an $\ell$-loop integral, this mechanism leads to a set of linear $2$nd-order differential equations with a non-homogeneous part. The latter, due to the contact nature of the anomaly in momentum space, is determined by $(\ell-1)$-loop information. Solving such differential equations in general is an open problem. In the case of 5-particle amplitudes up to two loops, the function space is known, and we can thus follow a bootstrap approach to write down the solution. As a first application of this method, we …
The quantum chiral Minkowski and conformal superspaces
2010
We give a quantum deformation of the chiral super Minkowski space in four dimensions as the big cell inside a quantum super Grassmannian. The quantization is performed in such way that the actions of the Poincar\'e and conformal quantum supergroups on the quantum Minkowski and quantum conformal superspaces are presented.
The unitary conformal field theory behind 2D Asymptotic Safety
2015
Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in $d>2$ dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge $c=25$. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety progra…