# A. Shadi Tahvildar-Zadeh

## Rutgers, The State University of New Jersey

H-index: 17

North America-United States

## About A. Shadi Tahvildar-Zadeh

A. Shadi Tahvildar-Zadeh, With an exceptional h-index of 17 and a recent h-index of 13 (since 2020), a distinguished researcher at Rutgers, The State University of New Jersey, specializes in the field of General Relativity, Mathematical Physics.

His recent articles reflect a diverse array of research interests and contributions to the field:

Detection Time of Dirac Particles in One Space Dimension

On the discrete Dirac spectrum of general-relativistic hydrogenic ions with anomalous magnetic moment

Joint evolution of a Lorentz-covariant massless scalar field and its point-charge source in one space dimension

Essential self-adjointness of Dirac operators under the influence of general-relativistic gravity

The point spectrum of the Dirac Hamiltonian on the zero-gravity Kerr-Newman spacetime

On the relativistic quantum mechanics of a photon between two electrons in 1+ 1 dimensions

One-dimensional hydrogenic ions with screened nuclear Coulomb field

The Einstein-Infeld-Hoffmann legacy in mathematical relativity I: The classical motion of charged point particles

### A. Shadi Tahvildar-Zadeh Information

University | Rutgers, The State University of New Jersey |
---|---|

Position | (New Brunswick) |

Citations(all) | 1720 |

Citations(since 2020) | 508 |

Cited By | 1475 |

hIndex(all) | 17 |

hIndex(since 2020) | 13 |

i10Index(all) | 20 |

i10Index(since 2020) | 14 |

University Profile Page | Rutgers, The State University of New Jersey |

#### A. Shadi Tahvildar-Zadeh Skills & Research Interests

General Relativity

Mathematical Physics

## Top articles of A. Shadi Tahvildar-Zadeh

### Detection Time of Dirac Particles in One Space Dimension

Authors

A Shadi Tahvildar-Zadeh,Stephanie Zhou

Published Date

2024/2/4

We consider particles emanating from a source point inside an interval in one-dimensional space and passing through detectors situated at the endpoints of the interval that register their arrival time. Unambiguous measurements of arrival or detection time are problematic in the orthodox narratives of quantum mechanics, since time is not a self-adjoint operator. By contrast, the arrival time at the boundary of a particle whose motion is being guided by a wave function through the deBroglie-Bohm guiding law is well-defined and unambiguous, and can be computationally feasible provided the presence of detectors can be modeled in an effective way that does not depend on the details of their makeup. We use an absorbing boundary condition for Dirac’s equation (ABCD) proposed by Tumulka, which is meant to simulate the interaction of a particle initially inside a domain with the detectors situated on the boundary of …

### On the discrete Dirac spectrum of general-relativistic hydrogenic ions with anomalous magnetic moment

Authors

Elie Kapengut,Michael K-H Kiessling,Eric Ling,A Shadi Tahvildar-Zadeh

Journal

arXiv preprint arXiv:2401.15802

Published Date

2024/1/28

The Reissner-Weyl-Nordstr\"om (RWN) spacetime of a point nucleus features a naked singularity for the empirically known nuclear charges and masses , where is the proton mass and the atomic mass number, with the number of protons and the number of neutrons in the nucleus. The Dirac hamiltonian for a test electron with mass , charge , and anomalous magnetic moment in the electrostatic RWN spacetime of such a 'naked point nucleus' is known to be essentially self-adjoint, with a spectrum that consists of the union of the essential spectrum and a discrete spectrum of infinitely many eigenvalues in the gap , having as accumulation point. In this paper the discrete spectrum is characterized in detail for the first time, for all and that cover all known isotopes. The eigenvalues are mapped one-to-one to those of the traditional Dirac Hydrogen spectrum. Numerical evaluations that go beyond into the realm of not-yet-produced hydrogenic ions are presented, too. A list of challenging open problems concludes this publication.

### Joint evolution of a Lorentz-covariant massless scalar field and its point-charge source in one space dimension

Authors

Lawrence Frolov,Samuel Leigh,A Shadi Tahvildar-Zadeh

Journal

arXiv preprint arXiv:2307.03149

Published Date

2023/7/6

In this paper we prove that the static solution of the Cauchy problem for a massless real scalar field that is sourced by a point charge in dimensions is asymptotically stable under perturbation by compactly-supported incoming radiation. This behavior is due to the process of back-reaction. Taking the approach of Kiessling, we rigorously derive the expression for the force on the particle from the principle of total energy-momentum conservation. We provide a simple, closed form for the self-force resulting from back-reaction, and show that it is restorative, i.e. proportional to negative velocity, and causes the charge to return to rest after the radiation passes through. We establish these results by studying the joint evolution problem for the particle-scalar field system, and proving its global well-posedness and the claimed asymptotic behavior.

### Essential self-adjointness of Dirac operators under the influence of general-relativistic gravity

Authors

Michael K-H Kiessling,A Shadi Tahvildar-Zadeh,Ebru Toprak

Published Date

2023

Physical reasoning gives expressions for the hamiltonian of a system of quantummechanical particles. These hamiltonians are often differential operators that are symmetric in a densely-defined domain. However, to study the dynamics of the unitary group corresponding to a hamiltonian, it is required that the hamiltonian be self-adjoint or essentially self-adjoint. This study analyzes the effect of the static non-linear electromagnetic-vacuum spacetime of a point nucleus on the self-adjointness and the spectrum of the general–relativistic Dirac hamiltonian for a test electron.

### The point spectrum of the Dirac Hamiltonian on the zero-gravity Kerr-Newman spacetime

Authors

M Kiessling,Eric Ling,A Shadi Tahvildar-Zadeh

Published Date

2023

In this short paper, we review the Dirac equation on the zero-gravity Kerr-Newman spacetime. Our main objective is to provide a correspondence between the classification of the bound states for the zGKN spectrum and the usual hydrogenic states , etc. of the Hydrogen atom.

### On the relativistic quantum mechanics of a photon between two electrons in 1+ 1 dimensions

Authors

Lawrence Frolov,Samuel E Leigh,A Shadi Tahvildar-Zadeh

Journal

arXiv preprint arXiv:2312.06019

Published Date

2023/12/10

A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two electrons (or alternatively, two positrons). Manifest covariance is achieved using Dirac's formalism of multi-time wave functions, i.e, wave functions where are generic spacetime events of the photon and two electrons respectively. Their interaction is implemented via a Lorentz-invariant no-crossing-of-paths boundary condition at the coincidence submanifolds and compatible with conservation of probability current. The corresponding initial-boundary value problem is shown to be well-posed under the additional assumption of anti-symmetry given by the Pauli exclusion principle, and a closed-form solution to the ensuing coupled system of Klein-Gordon and transport equations is given.

### One-dimensional hydrogenic ions with screened nuclear Coulomb field

Authors

Suchindram Dasgupta,Chirag Khurana,A Shadi Tahvildar-Zadeh

Journal

arXiv preprint arXiv:2312.04033

Published Date

2023/12/7

We study the spectrum of the Dirac Hamiltonian in one space dimension for a single electron in the electrostatic potential of a point nucleus, in the Born-Oppenheimer approximation where the nucleus is assumed fixed at the origin. The potential is screened at large distances so that it goes to zero exponentially at spatial infinity. We show that the Hamiltonian is essentially self-adjoint, the essential spectrum has the usual gap in it, and that there are only finitely many eigenvalues in that gap, corresponding to ground and excited states for the system. We find a one-to-one correspondence between the eigenfunctions of this Hamiltonian and the heteroclinic saddle-saddle connectors of a certain dynamical system on a finite cylinder. We use this correspondence to study how the number of bound states changes with the nuclear charge.

### The Einstein-Infeld-Hoffmann legacy in mathematical relativity I: The classical motion of charged point particles

Authors

Michael K-H Kiessling,AS Tahvildar-Zadeh

Published Date

2019/6/10

Einstein, Infeld, and Hoffmann (EIH) claimed that the field equations of general relativity theory alone imply the equations of motion of neutral matter particles, viewed as point singularities in space-like slices of spacetime; they also claimed that they had generalized their results to charged point singularities. While their analysis falls apart upon closer scrutiny, the key idea merits our attention. This rapport identifies necessary conditions for a well-defined general-relativistic joint initial value problem of N classical point charges and their electromagnetic and gravitational fields. Among them, in particular, is the requirement that the electromagnetic vacuum law guarantees a finite field energy-momentum of a point charge. This disqualifies the Maxwell (–Lorentz) law used by EIH. On the positive side, if the electromagnetic vacuum law of Bopp, Landé–Thomas, and Podolsky (BLTP) is used, and the singularities equipped with a non-zero bare rest mass, then a joint initial value problem can be formulated in the spirit of the EIH proposal, and shown to be locally well-posed—in the special-relativistic zero-G limit. With gravitational coupling (ie G> 0), though, changing Maxwell’s into the BLTP law and assigning a bare rest mass to the singularities is by itself not sufficient to obtain even a merely well-defined joint initial value problem: the gravitational coupling also needs to be changed, conceivably in the manner of Jordan and Brans–Dicke. c (2019) The authors. Reproduction of this preprint, in its entirety, is permitted for non-commercial purposes only.

### On the Joint Evolution Problem for a Scalar Field and its Singularity

Authors

Aditya Agashe,Ethan Lee,A Shadi Tahvildar-Zadeh

Journal

arXiv preprint arXiv:2211.00452

Published Date

2022/11/1

In the classical electrodynamics of point charges in vacuum, the electromagnetic field, and therefore the Lorentz force, is ill-defined at the locations of the charges. Kiessling resolved this problem by using the momentum balance between the field and the particles, extracting an equation for the force that is well-defined where the charges are located, so long as the field momentum density is locally integrable in a neighborhood of the charges. In this paper, we examine the effects of such a force by analyzing a simplified model in one space dimension. We study the joint evolution of a massless scalar field together with its singularity, which we identify with the trajectory of a particle. The static solution arises in the presence of no incoming radiation, in which case the particle remains at rest forever. We will prove the stability of the static solution for particles with positive bare mass by showing that a pulse of incoming radiation that is compactly supported away from the point charge will result in the particle eventually coming back to rest. We will also prove the nonlinear instability of the static solution for particles with negative bare mass by showing that an incoming radiation with arbitrarily small amplitude will cause the particle to reach the speed of light in finite time. We conclude by discussing modifications to this simple model that could make it more realistic.

### On the discrete Dirac spectrum of a point electron in the zero-gravity Kerr–Newman spacetime

Authors

Michael K-H Kiessling,Eric Ling,A Shadi Tahvildar-Zadeh

Journal

Journal of Mathematical Physics

Published Date

2022/11/1

The discrete spectrum of the Dirac operator for a point electron in the maximal analytically extended Kerr–Newman spacetime is determined in the zero-G limit (zGKN), under some restrictions on the electrical coupling constant and on the radius of the ring-singularity of the zGKN spacetime. The spectrum is characterized by a triplet of integers, associated with winding numbers of orbits of dynamical systems on cylinders. A dictionary is established that relates the spectrum with the known hydrogenic Dirac spectrum. Numerical illustrations are presented. Open problems are listed.

### Arrival/Detection Time of Dirac Particles in One Space Dimension

Authors

A Shadi Tahvildar-Zadeh,Stephanie Zhou

Journal

arXiv preprint arXiv:2112.07366

Published Date

2021/12/13

In this paper we study the arrival/detection time of Dirac particles in one space dimension. We consider particles emanating from a source point inside an interval in space and passing through detectors situated at the endpoints of the interval that register their arrival time. Unambiguous measurements of "arrival time" or "detection time" are problematic in the orthodox narratives of quantum mechanics, since time is not a self-adjoint operator. We instead use an absorbing boundary condition proposed by Tumulka for Dirac's equation for the particle, which is meant to simulate the interaction of the particle with the detectors. By finding an explicit solution, we prove that the initial-boundary value problem for Dirac's equation satisfied by the wave function is globally well-posed, the solution is smooth, and depends smoothly on the initial data. We verify that the absorbing boundary condition gives rise to a non-negative probability density function for arrival/detection time computed from the flux of the conserved Dirac current. By contrast, the free evolution of the wave function (i.e., if no boundary condition is assumed) will not in general give rise to a nonnegative density, while Wigner's proposal for arrival time distribution fails to give a normalized density when no boundary condition is assumed. As a consistency check, we verify numerically that the arrival time statistics of Bohmian trajectories match the probability distribution for particle detection time derived from the absorbing boundary condition.

### Covariant guiding laws for fields

Authors

Maaneli Derakhshani,Michael K-H Kiessling,A Shadi Tahvildar-Zadeh

Journal

arXiv preprint arXiv:2110.09683

Published Date

2021/10/19

After reviewing what is known about the passage from the classical Hamilton--Jacobi formulation of non-relativistic point-particle dynamics to the non-relativistic quantum dynamics of point particles whose motion is guided by a wave function that satisfies Schr\"odinger's or Pauli's equation, we study the analogous question for the Lorentz-covariant dynamics of fields on spacelike slices of spacetime. We establish a relationship, between the DeDonder--Weyl--Christodoulou formulation of covariant Hamilton--Jacobi equations for the classical field evolution, and the Lorentz-covariant Dirac-type wave equation proposed by Kanatchikov amended by our proposed guiding equation for such fields. We show that Kanatchikov's equation is well-posed and generally solvable, and we establish the correspondence between plane-wave solutions of Kanatchikov's equation and solutions of the covariant Hamilton--Jacobi equations of DeDonder--Weyl--Christodoulou. We propose a covariant guiding law for the temporal evolution of fields defined on constant time slices of spacetime, and show that it yields, at each spacetime point, the existence of a finite measure on the space of field values at that point that is equivariant with respect to the flow induced by the solution of Kanatchikov's equation that is guiding the actual field, so long as it is a plane-wave solution. We show that our guiding law is local in the sense of Einstein's special relativity, and therefore it cannot be used to analyze Bell-type experiments. We conclude by suggesting directions to be explored in future research.

### Weak second Bianchi identity for static, spherically symmetric spacetimes with timelike singularities

Authors

Annegret Burtscher,Michael KH Kiessling,A Shadi Tahvildar-Zadeh

Journal

Classical and Quantum Gravity

Published Date

2021/8/23

The (twice-contracted) second Bianchi identity is a differential curvature identity that holds on any smooth manifold with a metric. In the case when such a metric is Lorentzian and solves Einstein's equations with an (in this case inevitably smooth) energy–momentum–stress tensor of a'matter field'as the source of spacetime curvature, this identity implies the physical laws of energy and momentum conservation for the'matter field'. The present work inquires into whether such a Bianchi identity can still hold in a weak sense for spacetimes with curvature singularities associated with timelike singularities in the'matter field'. Sufficient conditions that establish a distributional version of the twice-contracted second Bianchi identity are found. In our main theorem, a large class of spherically symmetric static Lorentzian metrics with timelike one-dimensional singularities is identified, for which this identity holds. As an important …

### On the Dirac operator for a test electron in a Reissner–Weyl–Nordström black hole spacetime

Authors

Michael K-H Kiessling,A Shadi Tahvildar-Zadeh,Ebru Toprak

Journal

General Relativity and Gravitation

Published Date

2021/1

The present paper studies the Dirac Hamiltonian of a test electron with a domain of bi-spinor wave functions supported on the static region inside the Cauchy horizon of the subextremal RWN black hole spacetime, respectively inside the event horizon of the extremal RWN black hole spacetime. It is found that this Dirac Hamiltonian is not essentially self-adjoint, yet has infinitely many self-adjoint extensions. Including a sufficiently large anomalous magnetic moment interaction in the Dirac Hamiltonian restores essential self-adjointness; the empirical value of the electron’s anomalous magnetic moment is large enough. In the subextremal case the spectrum of the self-adjoint Dirac operator with anomalous magnetic moment is purely absolutely continuous and consists of the whole real line; in particular, there are no eigenvalues. The same is true for the spectrum of any self-adjoint extension of the Dirac …

### A Lorentz-covariant interacting electron–photon system in one space dimension

Authors

Michael K-H Kiessling,Matthias Lienert,A Shadi Tahvildar-Zadeh

Journal

Letters in Mathematical Physics

Published Date

2020/12

A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one photon. Manifest Lorentz covariance is achieved using Dirac’s formalism of multi-time wave functions, i.e., wave functions where are the generic spacetime events of the electron and photon, respectively. Their interaction is implemented via a Lorentz-invariant no-crossing-of-paths boundary condition at the coincidence submanifold , compatible with particle current conservation. The corresponding initial-boundary-value problem is proved to be well-posed. Electron and photon trajectories are shown to exist globally in a hypersurface Bohm–Dirac theory, for typical particle initial conditions. Also presented are the results of some numerical experiments which illustrate Compton scattering as well as a new phenomenon …

### On general-relativistic hydrogen and hydrogenic ions

Authors

Michael K-H Kiessling,A Shadi Tahvildar-Zadeh,Ebru Toprak

Journal

Journal of Mathematical Physics

Published Date

2020/9/1

This paper studies how the static non-linear electromagnetic-vacuum spacetime of a point nucleus with a negative bare mass affects the self-adjointness of the general-relativistic Dirac Hamiltonian for a test electron, without and with an anomalous magnetic moment. This study interpolates between the previously studied extreme cases of a test electron in (a) the Reissner–Weyl–Nordström spacetime (Maxwell’s electromagnetic vacuum), which sports a very strong curvature singularity with negative infinite bare mass, and (b) the Hoffmann spacetime (Born or Born–Infeld’s electromagnetic vacuum) with vanishing bare mass, which features the mildest possible curvature singularity. The main conclusion reached is: on electrostatic spacetimes of a point nucleus with a strictly negative bare mass (which may be−∞), essential self-adjointness fails unless the radial electric field diverges sufficiently fast at the nucleus and …

## A. Shadi Tahvildar-Zadeh FAQs

### What is A. Shadi Tahvildar-Zadeh's h-index at Rutgers, The State University of New Jersey?

The h-index of A. Shadi Tahvildar-Zadeh has been 13 since 2020 and 17 in total.

### What are A. Shadi Tahvildar-Zadeh's top articles?

The articles with the titles of

Detection Time of Dirac Particles in One Space Dimension

On the discrete Dirac spectrum of general-relativistic hydrogenic ions with anomalous magnetic moment

Joint evolution of a Lorentz-covariant massless scalar field and its point-charge source in one space dimension

Essential self-adjointness of Dirac operators under the influence of general-relativistic gravity

The point spectrum of the Dirac Hamiltonian on the zero-gravity Kerr-Newman spacetime

On the relativistic quantum mechanics of a photon between two electrons in 1+ 1 dimensions

One-dimensional hydrogenic ions with screened nuclear Coulomb field

The Einstein-Infeld-Hoffmann legacy in mathematical relativity I: The classical motion of charged point particles

...

are the top articles of A. Shadi Tahvildar-Zadeh at Rutgers, The State University of New Jersey.

### What are A. Shadi Tahvildar-Zadeh's research interests?

The research interests of A. Shadi Tahvildar-Zadeh are: General Relativity, Mathematical Physics

### What is A. Shadi Tahvildar-Zadeh's total number of citations?

A. Shadi Tahvildar-Zadeh has 1,720 citations in total.