arXiv subjects

C. N. Kozameh

Publications and source records attributed to C. N. Kozameh.

6 recordsLinked to original sources

arXiv2026

Perturbative Reconstruction of Self-Adjoint Generators from Bosonic Canonical Commutation Relations: Application to the Null-Surface Formulation

We study the inverse adjoint problem for a perturbative bosonic outgoing map. Within the polynomial bosonic canonical-commutation-relation (CCR) algebra, we prove a constructive integrability theorem: order-by-order preservation of the CCRs is sufficient to reconstruct recursively a formal self-adjoint generator whose exponential implements the outgoing map by adjoint conjugation. At each order, the Baker--Campbell--Hausdorff contribution determined by previously reconstructed generators is subtracted from the outgoing coefficient, and the remaining homogeneous CCR conditions determine the next generator explicitly. We apply the construction to graviton scattering in the null-surface formulation (NSF), specialized to the flat solution-space sector with Minkowski metric, null generators, affine parameter, and cone measure. The NSF outgoing map preserves the Ashtekar radiative CCRs through (δa_3), corresponding to order (\varepsilon^2). At this order, the scalar CCR sector uniquely selects the symmetric ordering (c=1) for the nontrivial interacting kernel. The associated linear contraction, generated by the same cubic kernel, cancels the double-contraction contribution from ([δa_2,δa_2^\dagger]). The theorem then reconstructs the self-adjoint generators (δT_1) and (δT_2), providing a formal perturbative unitary implementation. The resulting canonical organization also separates the direct (2\to2) contribution into irreducible-loop, one-particle-reducible, and factorized sectors.

hep-th↗

arXiv2026

Quantum graviton scattering with definite helicities in the null surface formulation. III: Fourth-order recursion and ultraviolet finiteness

We extend the perturbative null-surface formulation (NSF) scattering map to fourth order and derive an all-order recursion for the quantum cut. After the antipodal matching, both cone sources are evaluated on the same retarded solution determined by the free incoming radiative data. The perturbative NSF equations therefore determine every coefficient $Z_n$ from that data, without introducing new independent asymptotic information. The partial cut $Z_{[N]}=\sum_{j=1}^{N}\ep^j Z_j$ defines the cumulative operator $U_{ω,[N]}=\exp[-\iiωZ_{[N]}]$. An exact factor recursion for this operator gives a generating formula for $δa_{n,λ}^{\mathrm{out}}$ in terms of the order-$n$ cone source and lower-order operators. The scalar flux term $Σ$, which begins quadratically, is included on the cut side of the matching equation; its free quadratic part cancels between future and past infinity and it never introduces a new order-$n$ radiative operator. For smooth smeared radiative data, every finite-order cut is well defined and self-adjoint, so $U_{ω,[N]}$ and its recursive factors are unitary and bounded. The frequency powers in the perturbative coefficients are thus part of the expansion of a bounded unitary operator, rather than separate ultraviolet enhancements. At fourth order we formally determine $δa_{4,λ}^{\mathrm{out}}$ and identify the mixed one-loop sector $\mathcal M_{24}=\mathcal M^{(24)}+\mathcal M^{(42)}$. A general radial power-counting proposition proves ultraviolet finiteness at arbitrary perturbative order for the flat-cone two-vertex sectors. In particular, $\mathcal M_{24}$ and the previously obtained $\mathcal M_{33}$ both scale as $\int^\infty \dd K/K^4$ in the uniform radial ultraviolet region.

hep-th↗

arXiv2019

A relativistic center of mass in general relativity

The center of mass and spin for isolated sources of gravitational radiation that move at relativistic speeds are defined. As a first step, we also present these definitions in flat space. This contradicts some general wisdom given in textbooks claiming that such definitions are not covariant and thus, have no physical meaning. We then generalize the definitions to asymptotically flat spacetimes giving their equations of motion when gravitational radiation is emitted by the isolated sources. The resulting construction has some similarities with the Mathisson-Papapetrou equations which describes the motion of the particle in an external field. We analyze the relationship between the center of mass velocity and the Bondi linear momentum and show they are not proportional to each other. A similar situation happens between the total and intrinsic angular momentum when the Bondi momentum vanishes. We claim that extra terms should be added in other approaches to adequately describe the time evolution of isolated sources of gravitational radiation.

gr-qc↗

arXiv2012

Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation

Shear-free or asymptotically shear-free null geodesic congruences possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant affects. It is the purpose of this paper to develop these issues and find applications in GR. The applications center around the problem of extracting interior physical properties of an asymptotically flat space-time directly from the asymptotic gravitational (and Maxwell) field itself in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity. More specifically we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center of mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular momentum conservation law with well-defined flux terms. When a Maxwell field is present the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world-line and intrinsic magnetic dipole moment.

gr-qc↗

arXiv2004

Lorentz Invariance and the semiclassical approximation of loop quantum gravity

It is shown that the field equations derived from an effective interaction hamiltonian for Maxwell and gravitational fields in the semiclassical approximation of loop quantum gravity using rotational invariant states (such as weave states) are Lorentz invariant. To derive this result, which is in agreement with the observational evidence, we use the geometrical properties of the electromagnetic field.

gr-qc↗

arXiv1996

Fuzzy spacetime from a null-surface version of GR

The null-surface formulation of general relativity -- recently introduced -- provides novel tools for describing the gravitational field, as well as a fresh physical way of viewing it. The new formulation provides ``local'' observables corresponding to the coordinates of points --- which constitute the spacetime manifold --- in a {\em geometrically defined chart\/}, as well as non-local observables corresponding to lightcone cuts and lightcones. In the quantum theory, the spacetime point observables become operators and the spacetime manifold itself becomes ``quantized'', or ``fuzzy''. This novel view may shed light on some of the interpretational problems of a quantum theory of gravity. Indeed, as we discuss briefly, the null-surface formulation of general relativity provides (local) geometrical quantities --- the spacetime point observables --- which are candidates for the long-sought physical operators of the quantum theory.

gr-qc↗