Table of contents

Although the subject of relativistic dynamics has been explored from both classical and quantum mechanical points of view since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anamolous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical realtivistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There moreover remains the important question of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge's book, The Relativistic Gas, and in Balescu's book on relativistic statistical mechanics. In recent years, the study of high energy plasmas and heavy ion collisions has emphasized the importance of developing the techniques of relativistic mechanics.

The results of Linder et al (Phys. Rev. Lett.95 0040401 (2005)) as well as the more recent work of Palacios et al (Phys. Rev. Lett.103 253001 (2009)) and others, have shown that there must be a quantum theory with coherence in time. Such a theory, manifestly covariant under the transformations of special relativity with an invariant evolution parameter, such as that of Stueckelberg (Helv. Phys. Acta14 322, 588 (1941); 15 23 (1942); see also R P FeynmanPhys. Rev.80 4401 and J S Schwinger Phys. Rev.82 664 (1951)) could provide a suitable basis for the study of such questions, as well as many others for which the application of the standard methods of quantum field theory are difficult to manage, involving, in particular, local properties of spacetime structure.

The scope of this series of conferences is, however, much wider. There have been recent develpments in the understanding of the quantum properties of spacetime, the application of quantum field theory and statistical quantum field theory to problems in relativistic dynamics, as well as new techniques in general relativity; some of these topics have been discussed in the IARD 2010 conference, and which will be reported in these Proceedings.

It was for this purpose, to bring together researchers from a wide variety of fields, such as particle physics, astrophysics, cosmology, heavy ion collisions, plasma research, and mathematical physics, with a common interest in relativistic dynamics, that this Association was founded.

The International Association for Relativistic Dynamics was organized at its first meeting as an informal session of seminars among researchers with common interest in February 1998 in Houston, Texas, with John R Fanchi as president.

The second meeting took place, in 2000, at Bar Ilan University in Ramat Gan, Israel, the third, in 2002, at Howard University in Washington, DC, and the fourth, on 12–19 June 2004, in Saas Fee, Switzerland. In 2006, the meeting took place at the University of Connecticut campus in Storrs, Connecticut, and the sixth meeting, in Thessaloniki, Greece. The seventh meeting, took place at the National Dong Hwa University in Hulien, Taiwan from 30 May to 1 June 2010.

This meeting forms the basis for the Proceedings that are recorded in this volume of Journal of Physics: Conference Series. Along with the work of some of the founding members of the Association, we were fortunate to have lecturers from application areas that provided strong challenges for further developments in quantum field theory, statistical quantum field theory and its potential applications to relativistic quantum information theory, cosmological problems, and in the dynamics of systems described in the framework of general relativity.

The opening session of IARD 2010 was held jointly with the closing seesion of the RQI-N workshop on relativistic quantum information that took place from 28–30 May. This joint meeting emphasized the importance of including dynamical models in relativistic quantum information theory, and of utilizing the perspective of quantum information in extracting results with strong implications for application in relativistic dynamics.

Topics discussed at the conference and reported in this volume included investigations into problems in general relativity, relations between quantum field theory, cosmology and, in its statistical aspects, to the extraction of classical attributes of macroscopic quantum systems. There was also a very fundamental study by David R Finkelstein, of the stucture of spacetime itself, posing the possibility that the spacetime manifold emerges from an underlying quantum complex, composed of simplices with spin 1/2 and Fermi statistics, resulting in the regularization of the Standard Model and perhaps a regularized structure for quantum gravity.

H T Cho and B L Hu study the vacuum expectation value of the stress energy tensor of a minimally coupled massless scalar field and its role as a source in the Einstein–Langevin equations of quantum gravity, governing the induced metric of fluctuations above the mean field dynamics of the semiclassical theory. C H Chou, B L Hu and Y Subasi study macroscopic quantum phenomena from the point of view of correlations, coupling and criticality, and explain how a macroscopic quantum system may, in this way, acquire classical attributes but still retain some quantum features. S Y Lin discusses a connection with quantum information science as one of the consequences of his work on local projective measurements on relativistic fields.

In the field of cosmology, F H Ho and J M Nester study Poincaré gauge theory with a metric compatible connection to an independent dynamics associated with torsion and curvature. They find a propagating 0⁺ mode that could account for accelerated expansion. They discuss, in particular, a model in the Bianchi class A, and present a Lagrangian and a typical dynamical evolution. J T Hsiang, C H Wu, L H Ford and K W Ng review investigations of the effects of a quantum stress tensor of a conformal field on inflationary cosmology. They find that the quantum stress tensor fluctuations lead to effects that can depend upon the total expansion factor during inflation, which may contribute to a non-scale invariant and non-Gaussian component to the primordial spectrum of perturbations,and may be observable.

In the framework of quantum field theory, A N Kvinikhidze and B Blankleider show that a relativistic quantum mechanics emerges from light frame quantum field theory, and that in the case of baryon-like conservation, these theories are equivalent. With T Skawronski, they show in a second paper the power of gauging for several body problems, and demonstrate how this idea can be applied to the study of parton distributions, two nucleon currents in cutoff quantum field theory, and in a potential model for πN scattering. C M Chen and J R Sun study a holographic dual of the Reissner–Nordström black hole in a quantum gravity description from the perspective of the AdS/CFT correspondence.

On a fundamental level, somewhat related to the ideas of Finkelstein, A Gersten and A Moalem discuss the factorization of the d'Alembertian in a 4×4 representation of 'relativistic quaternions' to find an interpretation of Maxwell's equations; with an 8×8 factorization, they obtain spin two fields as in gravitation. They discuss a general method for obtaining field equations for zero mass particles and arbitrary spin.

M Pavsic has developed a generalization of the theory of Stueckelberg, mentioned above, applicable to general relativity. He finds a source of the world time τ in M_2,4, achieving a 5D metric tensor and a resolution of the 'problem of time' in this framework. In a basic investigation of the structure of the theory of special relativity, closely related to the original work of Minkowski and previous work of M Pavsic, Z Oziewicz has proposed a groupoid (non-group) covariance, defining the electric and magnetic fields as tensor on the 4D spacetime. P O'Hara, using a linearized metric of general relativity had previoulsy found that on the geodesics, one finds the Dirac equation. In the paper in this volume he studies the result on arbitrary curves, and proposes equations of motion.

In the application of Stueckelberg's theory to the covariant harmonic oscillator problem (such as the model studied by Feynman, Kislinger and Ravndal (R P Feynman, M Kislinger and F Ravndal Phys. Rev. D 3 2706 (1971)), it has long been known (R Arshansky and L P Horwitz J. Math. Phys.30 66, 213 (1989)) that there are exact solutions providing the non-relativistic spectrum up to relativistic corrections, with no 'ghosts', in terms of variables separated in terms of the (relative) spacelike invariant radial coordinate, angular and hyperbolic angular coordinates. However, no ladder representation for annihilation-creation operators was obtained. M Land has made considerable progress in this direction in his paper on harmonic oscillator states by studying the problem in two and three dimensions, with symmetries O(1), O(3) and O(2,1). He finds that for all s≠ 0 solutions, the SU(n) symmetry of the general oscillator Hamiltonian discussed by Bars (I Bars Phys. Rev. D 79 045009 (2009)) is spontaneously broken by the ground state, and he demonstrates the connection of this symmetry breaking to non-separability into one dimensional Cartesian solutions. In a second paper, Land discusses the 5D (based on the gauge fields that leave the Stueckelberg–Schrödinger equation locally gauge invariant) Abraham–Lorentz–Dirac equations of self-interaction of a relativistic charged particle; he shows that a statistical interpretation of the contributions of the event current to the measured currents can lead to an effective regularization of the theory, in which pre-acceleration of the event by future values of the fields is not present.

On a phenomenological level, the work of S Bai, Z Cao, W B Han, C Y Lin, H J Yo and J P Yu studies a simulation of the two and three black hole configurations, developing new and powerful methods for these important problems. N Ben-Amotz studies the possibiliy of describing gravitation phenomenologically in terms of an exponential model. In a second paper, he studies the measured radial expansion rate of the Universe using the Einstein addition formula for velocity. He finds a modified Hubble law which explains the Olber's paradox (as the linear Hubble law does also), and for which the existence of dark energy becomes unnecessary for explaining existing data on dependence of luminosity as a function of redshift for type Ia supernovas.

We thank the Scientific Advisory Committee for their invaluable guidance and advice:

Stephen Adler (Institute for Advanced Study) Itzhak Bars (University of Southern California) Gordon Baym (University of Illinois) Jacob Bekenstein (Hebrew University) Fred Cooper (Los Alamos National Laboratory) Bei-Lok Hu (University of Maryland) Werner Israel (University of Victoria) E V Shuryak (Brookhaven National Laboratory) L S Shulman (Clarkson University) William Unruh (University of British Columbia)

The organizers express their gratitude to the academic sponsors for their support and hospitality:

National Science Council (Taiwan) National Center for Theoretical Sciences (Taiwan) National Dong Hwa University (Taiwan) Institute of Physics, Academia Sinica (Taiwan)

Finally, we thank the participants who contributed through their lectures, personal discussions, and these papers, to the advancement of the subject and our understanding.

For the Editors and Organizing Committee,

L P Horwitz (Tel-Aviv University, Bar Ilan University), Editor-in-Chief Martin C Land (Hadassah College), IARD President Da-Shin Lee (National Dong Hwa University), Chairman of the Local Organizing Committee Bei-Lok Hu (University of Maryland) Tepper Gill (Howard University)

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

Present-day quantum field theory can be regularized by a decomposition into quantum simplices. This replaces the infinite-dimensional Hilbert space by a high-dimensional spinor space and singular canonical Lie groups by regular spin groups. It radically changes the uncertainty principle for small distances. Gaugeons, including the gravitational, are represented as bound fermion-pairs, and space-time curvature as a singular organized limit of quantum non-commutativity.

We calculate the vacuum expectation values of the stress-energy bitensor of a minimally coupled massless scalar field in anti-de Sitter (AdS) spaces. These correlators, also known as the noise kernel, act as sources in the Einstein-Langevin equations of stochastic gravity [1, 2] which govern the induced metric fluctuations beyond the mean-field dynamics described by the semiclassical Einstein equations of semiclassical gravity. Because the AdS spaces are maximally symmetric the eigenmodes have analytic expressions which facilitate the computation of the zeta-function [3, 4]. Upon taking the second functional variation of the generalized zeta function introduced in [5] we obtain the correlators of the stress tensor. Both the short and the long geodesic distance limits of the correlators are presented.

In this sequel paper we explore how macroscopic quantum phenomena can be measured or understood from the behavior of quantum correlations which exist in a quantum system of many particles or components and how the interaction strengths change with energy or scale, under ordinary situations and when the system is near its critical point. We use the nPI (master) effective action related to the Boltzmann-BBGKY / Schwinger-Dyson hierarchy of equations as a tool for systemizing the contributions of higher order correlation functions to the dynamics of lower order correlation functions. Together with the large N expansion discussed in our first paper [1] we explore 1) the conditions whereby an H-theorem is obtained, which can be viewed as a signifier of the emergence of macroscopic behavior in the system. We give two more examples from past work: 2) the nonequilibrium dynamics of N atoms in an optical lattice under the large (field components), 2PI and second order perturbative expansions, illustrating how N and enter in these three aspects of quantum correlations, coherence and coupling strength. 3) the behavior of an interacting quantum system near its critical point, the effects of quantum and thermal fluctuations and the conditions under which the system manifests infrared dimensional reduction. We also discuss how the effective field theory concept bears on macroscopic quantum phenomena: the running of the coupling parameters with energy or scale imparts a dynamical-dependent and an interaction-sensitive definition of 'macroscopia'.

In an explicitly covariant system with point-like detectors coupled to a relativistic quantum field, the Gaussian states of the combined system and the reduced states of the detectors derived from them are consistent, but not have to be covariant, in different frames of different observers. Even in the presence of spatially local projective measurements, which result instantaneous wave functional collapses on different time-slices in different reference frames, the consistency still holds.

The Poincaré gauge theory of gravity has a metric compatible connection with independent dynamics that is reflected in the torsion and curvature. The theory allows two good propagating spin-0 modes. Dynamical investigations using a simple expanding cosmological model found that the oscillation of the 0⁺ mode could account for an accelerating expansion similar to that presently observed. The model has been extended to include a 0⁻ mode and more recently cross parity couplings. We investigate the dynamics of this model in a situation which is simple, non-trivial, and yet may give physically interesting results that might be observable. We consider homogeneous cosmologies, more specifically, isotropic Bianchi class A models. We find an effective Lagrangian for our dynamical system, a system of first order equations, and present some typical dynamical evolution.

We review several related investigations of the effects of the quantum stress tensor of a conformal field in inflationary cosmology. Particular attention will be paid to the effects of quantum stress tensor fluctuations as a source of density and tensor perturbations in inflationary models. These effects can possibly depend upon the total expansion factor during inflation, and hence be much larger than one might otherwise expect. They have the potential to contribute a non-scale invariant and non-Gaussian component to the primordial spectrum of perturbations, and might be observable.

A relativistic quantum mechanics (RQM) on the light-front (LF) is derived from quantum field theory (QFT) through the use of a unitary transformation. Cluster separability of the derived RQM is proved by solving the so-called decoupling equation for the disconnected parts of the unitary transformation relating the Poincaré generators of RQM to the ones of QFT. For processes involving baryon-like number conservation (NN → NN, Nd → Nd, etc.), we show that the two theories, RQM and QFT, are equivalent.

The gauging of equations method was developed some years ago in order to extract gauge invariant electromagnetic currents from strongly interacting few-body systems described by integral equations. Although the method is by now well-established for this purpose, it is not so well known that the same approach can be used to solve a wide variety of problems. The purpose of this paper is to demonstrate the true power of this method by using it to solve key problems in three very different areas of study; in particular, we show (i) how generalized parton distributions (GPDs) can be determined in the case where hadrons are described in terms of their partonic degrees of freedom through solutions of dynamical equations, (ii) how to construct gauge invariant two-nucleon currents in cutoff effective field theory (EFT), even though the cutoff usually violates the gauge invariance of the underlying Lagrangian, and (iii) how to construct a potential model of πN scattering that is crossing symmetric and approximately unitary.

It is noteworthy that in each case, the gauging of equations method produces results that are consistent with the relevant requirements of quantum field theory. For example, in extracting GPDs from the model of strong interactions defined by dynamical equations, all possible mechanisms contributing to the GPDs are taken into account, so that all GPD sum rules are satisfied automatically. Similarly, in the construction of electromagnetic currents in cutoff EFT, gauge invariance is a consequence of the fact that an external photon is effectively coupled to every part of every strong interaction diagram in the model.

In this article we give a brief, nevertheless, comprehensive review on recent studies in the quantum gravity description of the Reissner-Nordstrom (RN) black hole from the perspective of the AdS/CFT correspondence. We survey the known evidence supporting a two-dimensional conformal field theory (CFT) description holographically dual to the RN black hole.

Quantum wave equations for massless particles and arbitrary spin are derived by factorizing the d'Alembertian operator. The procedure is extensively applied to the spin one photon equation which is related to Maxwell's equations via the proportionality of the photon wavefunction Ψ to the sum E + iB of the electric and magnetic fields. Thus Maxwell's equations can be considered as the first quantized one-photon equation. The photon wave equation is written in two forms, one with additional explicit subsidiary conditions and second with the subsidiary conditions implicitly included in the main equation. The second equation was obtained by factorizing the d'Alembertian with 4×4 matrix representation of "relativistic quaternions". Furthermore, scalar Lagrangian formalism, consistent with quantization requirements is developed using derived conserved current of probability and normalization condition for the wavefunction. Lessons learned from the derivation of the photon equation are used in the derivation of the spin two quantum equation, which we call the quantum graviton. Quantum wave equation with implicit subsidiary conditions, which factorizes the d'Alembertian with 8×8 matrix representation of relativistic quaternions, is derived. Scalar Lagrangian is formulated and conserved probability current and wavefunction normalization are found, both consistent with the definitions of quantum operators and their expectation values. We are showing that the derived equations are the first quantized equations of the photon and the graviton.

We first consider the Klein-Gordon equation in the 6-dimensional space M_2,4 with signature +−−−−+ and show how it reduces to the Stueckelberg equation in the 4-dimensional spacetime M_1,3. A field that satisfies the Stueckelberg equation depends not only on the four spacetime coordinates x^μ, but also on an extra parameter τ, the so called evolution time. In our setup, τ comes from the extra two dimensions. We point out that the space M^2,4 can be identified with a subspace of the 16-dimensional Clifford space, a manifold whose tangent space at any point is the Clifford algebra Cl(1,3). Clifford space is the space of oriented r- volumes, r = 0,1,2,3, associated with the extended objects living in M_1,3. We consider the Einstein equations that describe a generic curved space M_2,4. The metric tensor depends on six coordinates. In the presence of an isometry given by a suitable Killing vector field, the metric tensor depends on five coordinates only, which include τ. Following the formalism of the canonical classical and quantum gravity, we perform the 4 + 1 decomposition of the 5-dimensional general relativity and arrive, after the quantization, at a generalized Wheeler-DeWitt equation for a wave functional that depends on the 4-metric of spacetime, the matter coordinates, and τ. Such generalized theory resolves some well known problems of quantum gravity, including "the problem of time".

Electric and magnetic fields are relative. They depend not only on a choice of electromagnetic sources via Maxwell equations, but also on a choice of observer, a choice of material reference-system. In 1908 Minkowski defined electric and magnetic fields on a four-dimensional spacetime, as tensorial concomitants of observer. Minkowski defined Lorentz-group-covariance of concomitant tensor field as group-action that commute with contractions. Present-day textbooks interpret Lorentz-group-covariance of concomitant tensor differently than Minkowski in 1908. In 2003-2005 Tomislav Ivezíc re-invented Minkowski's group-covariance. Different interpretations of group-covariance, lead to different relativity transformations of electric and magnetic fields.

An objective of present article is to explore third possibility, implicit in [Minkowski 1908, §11.6], where a set of all relativity transformations of all material observers forms a groupoid category, which is not a group.

In a previous article a relationship was established between the linearized metrics of General Relativity associated with geodesics and the Dirac Equation of quantum mechanics. In this paper the extension of that result to arbitrary curves is investigated. A generalized Dirac equation is derived and shown to be related to the Lie derivative of the momentum along the curve. In addition,the equations of motion are derived from the Hamilton-Jacobi equation associated with the metric and the wave equation associated with the Hamiltonian is then shown not to commute with the Dirac operator. Finally, the Maxwell-Boltzmann distribution is shown to be a consequence of geodesic motion.

We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as basis states for representing their respective symmetry groups — O(2), O(1,1), O(3), and O(2,1). The goal of this study is to establish a correspondence between Hilbert space descriptions found by solving the Schrodinger equation in polar coordinates, and Fock space descriptions constructed by expressing the symmetry operators in terms of creation/annihilation operators. We obtain wavefunctions characterized by a principal quantum number, the group Casimir eigenvalue, and one group generator whose eigenvalue is m + s, for integer m and real constant parameter s. For the three groups that contain O(2), the solutions split into two inequivalent representations, one associated with s = 0, from which we recover the familiar description of the oscillator as a product of one-dimensional solutions, and the other with s > 0 (in three dimensions, solutions are found for s = 0 and s = 1/2) whose solutions are non-separable in Cartesian coordinates, and are hence overlooked by the standard Fock space approach. The O(1,1) solutions are singlet states, restricted to zero eigenvalue of the symmetry operator, which represents the boost, not angular momentum. For O(2), a single set of creation and annihilation operators forms a ladder representation for the allowed oscillator states for any s, and the degeneracy of energy states is always finite. However, in three dimensions, the integer and half-integer eigenstates are qualitatively different: the former can be expressed as finite dimensional irreducible tensors under O(3) or O(2,1) while the latter exhibit infinite degeneracy. Creation operators that produce the allowed integer states by acting on the non-degenerate ground state are constructed as irreducible tensor products of the fundamental vector representation. However, the half-integer eigenstates are infinite-dimensional, as expected for the non-compact O(2,1), and no Fock space description is found for this case. For all s ≠ 0 solutions, the SU(N) symmetry of the harmonic oscillator Hamiltonian recently discovered by Bars is spontaneously broken by the ground state. The connection of this symmetry breaking to the non-separability into one-dimensional Cartesian solutions is demonstrated. We conclude with a discussion of the O(2,1) solutions, and the problem of timelike ghost excitations.

We derive the Abraham-Lorentz-Dirac (ALD) equation in the framework of the electrodynamic theory associated with Stueckelberg manifestly covariant canonical mechanics. In this framework, a particle worldline is traced out through the evolution of an event x^μ (τ). By admitting unconstrained commutation relations between the positions and velocities, the associated electromagnetic gauge fields are in general dependent on the parameter τ, which plays the role of time in Newtonian mechanics. Standard Maxwell theory emerges from this system as a τ-independent equilibrium limit. In this paper, we calculate the τ-dependent field induced by an arbitrarily evolving event, and study the long-range radiation part, which is seen to be an on-shell plane wave of the Maxwell type. Following Dirac's method, we obtain an expression for the finite part of the self-interaction, which leads to the ALD equation that generalizes the Lorentz force. This third-order differential equation is then converted to an integro-differential equation, identical to the standard Maxwell expression, except for the τ-dependence of the field. By studying this τ-dependence in detail, we show that field can be removed from the integration, so that the Lorentz force depends only on the instantaneous external field and an integral over dynamical variables of the event evolution. In this form, pre-acceleration of the event by future values of the field is not present.

Black hole systems are among the most promising sources for a gravitational wave detection project. Now, China is planning to construct a space-based laser interferometric detector as a follow-on mission of LISA in the near future. Aiming to provide some theoretical support to this detection project on the numerical relativity side, we focus on black hole systems simulation in this work. Considering the globular galaxy, multiple black hole systems also likely to exist in our universe and play a role as a source for the gravitational wave detector we are considering. We will give a progress report in this paper on our black hole system simulation. More specifically, we will present triple black hole simulation together with binary black hole simulation. On triple black hole simulations, one novel perturbational method is proposed.

The paper starts with a brief recapitulation of exponential gravitation concepts, and then continue by presenting the following items: a comparison of exponential gravitation with general relativity; gravitational radiation in exponential gravitation theory; supernova formation in the frame of exponential gravitation; a possible exponential gravitation explanation to the origin of jets of Active Galactic Nuclei, quasars and microquasars.

The Hubble law, for which the radial expansion velocity is linear in the distance r, implies a visible Universe limited to a horizon at r = c/H. No information beyond this horizon can reach us.

Here we suggest a modified Hubble law for the measured radial expansion velocity that does not put a limit on the radius of the visible Universe. The modified Hubble law is based on Einstein's well known addition of relativistic velocities, and differs from the (conventional linear) Hubble law in orders of Hr/c that are higher than the first order. The modified Hubble law solves the Olbers's paradox (as the linear Hubble law does), and the existence of dark energy becomes unnecessary for explaining existing astronomical data on dependence of luminosity as a function of redshift for type Ia supernovas.