Classical space–times from the S-matrix

We show that classical space–times can be derived directly from the S-matrix for a theory of massive particles coupled to a massless spin two particle. As an explicit example we derive the Schwarzchild space–time as a series in _GN$G_N$. At no point of the derivation is any use made of the Einstein–Hilbert action or the Einstein equations. The intermediate steps involve only on-shell S-matrix elements which are generated via BCFW recursion relations and unitarity sewing techniques. The notion of a space–time metric is only introduced at the end of the calculation where it is extracted by matching the potential determined by the S-matrix to the geodesic motion of a test particle. Other static space–times such as Kerr follow in a similar manner. Furthermore, given that the procedure is action independent and depends only upon the choice of the representation of the little group, solutions to Yang–Mills (YM) theory can be generated in the same fashion. Moreover, the squaring relation between the YM and gravity three point functions shows that the seeds that generate solutions in the two theories are algebraically related. From a technical standpoint our methodology can also be utilized to calculate quantities relevant for the binary inspiral problem more efficiently then the more traditional Feynman diagram approach.     

Stability of circular orbits of spinning particles in Schwarzschild-like space–times

Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space–times the equations of motion admit solutions representing circular orbits with particles spins being constant and normal to the plane of orbits. For the de Sitter background the orbits are always stable with particle velocity and momentum being co-linear along them. The world-line deviation equations for particles of the same spin-to-mass ratios are solved and the resulting deviation vectors are used to study the stability of orbits. It is shown that the orbits are stable against radial perturbations. The general criterion for stability against normal perturbations is obtained. Explicit calculations are performed in the case of the Schwarzschild space–time leading to the conclusion that the orbits are stable.     

Gödel axiom mappings in special relativity and quantum-electromagnetic theory

Exponential mappings into an imaginary space or number field for the axioms of a theory, which are in the form of propositional constants and variables, make possible: (a) an understanding of the meaning and differences between the Lorentz transformation constants, such that their product is still equal to one, but the axioms at each end of the transformations are logically inverse and separately consistent; (b) an interpretation of the psi function phase factor which is part of the axiomE=hf; (c) the unification of the quantum-mechanical psi function and the electromagnetic wave function. Thus, those statements whose mechanisms are unknown (the axioms of the theory) are to be assigned the axiom propositional number symbol and are to be associated with the complex probability eⁱ, which is a uniform factor of the energy equations expressing the physical state. Such probabilistic axiom functions can be associated with both the special theory of relativity and the quantum-electromagnetic theory.     

Quantum motion of a point particle in the presence of the Aharonov–Bohm potential in curved space

The nonrelativistic quantum dynamics of a spinless charged particle in the presence of the Aharonov–Bohm potential in curved space is considered. We chose the surface as being a cone defined by a line element in polar coordinates. The geometry of this line element establishes that the motion of the particle can occur on the surface of a cone or an anti-cone. As a consequence of the nontrivial topology of the cone and also because of two-dimensional confinement, the geometric potential should be taken into account. At first, we establish the conditions for the particle describing a circular path in such a context. Because of the presence of the geometric potential, which contains a singular term, we use the self-adjoint extension method in order to describe the dynamics in all space including the singularity. Expressions are obtained for the bound state energies and wave functions.     

The renormalized stress-energy tensor and its associated operators for photons in curved four-dimensional space–time

We establish expressions for the renormalized stress-energy (or energy-momentum) tensor and its associated operators relative to photons as a Klein–Gordon field of non-zero rest-mass particles (with gravitational interaction) in curved four-dimensional space–time.     

The special theory of relativity as applied to the Born–Oppenheimer–Huang approach

In two recent publications (Int. J. Quant. Chem. 114, 1645 (2014) and Mole. Phys. 114, 227 (2016)) it was shown that the Born–Hwang (BH) treatment of a molecular system perturbed by an external field yields a set of decoupled vectorial wave equations, just like in electro-magnetism. This finding led us to declare on the existence of a new type of Fields, which were termed Molecular Fields. The fact that such fields exist implies that at the vicinity of conical intersections exist a mechanism that transforms a passing-by electric beam into a field which differs from the original electric field. This situation is reminiscent of what is encountered in astronomy where Black Holes formed by massive stars may affect the nature of a near-by beam of light. Thus, if the non-adiabatic-coupling-terms (NACT) with their singular points may affect the nature of such a beam (see the above two publications), then it would be interesting to know to what extend NACTs (and consequently also the BH equation) will be affected by the special theory of relativity as introduced by Dirac. Indeed, while applying the Dirac approach we derived the relativistic affected NACTs as well as the corresponding BH equation.     

Is quantum theory compatible with special relativity?

How a proposed quantum nonlocal phenomenon could be incompatible with the requirements of special relativity is studied. To show this, the least set of assumptions about the formalism and the interpretation of non-relativistic quantum theory is considered. Then, without any reference to the collapse assumption or any other stochastic processes, an experiment is proposed, involving two quantum systems, that interacted at an arbitrary time, with results which seem to be in conflict with requirements of special relativity.     

Singular lensing from the scattering on special space–time defects

It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space–times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space–times is described by amplitudes that exhibit resonant behaviour when thescattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent (“singular lensing”). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of the Minkowski space–time, and thus the disappearance of the lensing phenomenon, in the no-defect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals.     

An arena for model building in the Cohen—Glashow very special relativity

The Cohen—Glashow Very Special Relativity (VSR) algebra is defined as the part of the Lorentz algebra which upon addition of CP or T invariance enhances to the full Lorentz group, plus the space—time translations. We show that noncommutative space—time, in particular noncommutative Moyal plane, with light- like noncommutativity provides a robust mathematical setting for quantum field theories which are VSR invariant and hence set the stage for building VSR invariant particle physics models. In our setting the VSR invariant theories are specified with a single deformation parameter, the noncommutativity scale ╕_NC. Preliminary analysis with the available data leads to ╕_NC ≳ 1–10 TeV.     

Quantum fluctuations in planar domain wall space–times: A possible origin of primordial preferred direction

We study the gravitational effects of a planar domain wall on quantum fluctuations of a massless scalar field during inflation. By obtaining an exact solution of the scalar field equation in de-Sitter space, we show that the gravitational effects of the domain wall break the rotational invariance of the primordial power spectrum without affecting the translational invariance. The strength of rotational violation is determined by one dimensionless parameter β, which is a function of two physical parameters, the domain wall surface tension σ and cosmological constant Λ. In the limit of small β, the leading effect of rotational violation of the primordial power spectrum is scale-invariant.     

The space–time CESE method for solving special relativistic hydrodynamic equations

The special relativistic hydrodynamic equations are more complicated than the classical ones due to the nonlinear and implicit relations that exist between conservative and primitive variables. In this article, a space–time conservation element and solution element (CESE) method is proposed for solving these equations in one and two space dimensions. The CESE method has capability to capture sharp propagating wavefront of the relativistic fluids without excessive numerical diffusion or spurious oscillations. In contrast to the existing upwind finite volume schemes, the Riemann solver and reconstruction procedure are not the building blocks of the suggested method. The method differs from previous techniques because of global and local flux conservation in a space–time domain without resorting to interpolation or extrapolation. The scheme is efficient, robust, and gives results comparable to those obtained with more sophisticated algorithms, even in highly relativistic two-dimensional test problems.     

Local momentum space and two-loop renormalizability of λφ 4 field theory in curved space-time

A generalization is given of some previous work in which a momentum space representation for the Feynman propagator,G(x, y), of a scalar field in an arbitrary curved space-time was obtained. The pointsx andy are allowed to vary in a normal neighborhood of an arbitrary fixed pointz which is taken as an origin of normal coordinates and the representation is obtained by Fourier transformation in the coordinate differencex -y . The generality of this representation enables it to be applied to the evaluation of the divergences in any Feynman graph. As an example, the third-order (two-loop) corrections to the four-point function of ø⁴ field theory are shown to be renormalizable in curved space-time.     

The deformation of Poincar subgroups concerning very special relativity

We investigate here various kinds of semi-product subgroups of Poincar group in the scheme of Cohen-Glashow’s very special relativity along the deformation approach by Gibbons-Gomis-Pope.For each proper Poincar subgroup which is a semi-product of proper lorentz group with the spacetime translation group T(4),we investigate all possible deformations and obtain all the possible natural representations inherited from the 5-d representation of Poincar′e group.We find from the obtained natural representation that rotation operation may have additional accompanied scale transformation when the original Lorentz subgroup is deformed and the boost operation gets the additional accompanied scale transformation in all the deformation cases.The additional accompanied scale transformation has a strong constrain on the possible invariant metric function of the corresponding geometry and the field theories in the spacetime with the corresponding geometry.     

Infinite slabs and other weird plane symmetric space–times with constant positive density

We present the exact solution of Einstein’s equation corresponding to a static and plane symmetric distribution of matter with constant positive density located below z = 0. This solution depends essentially on two constants: the density ρ and a parameter κ. We show that these space–times finish down below at an inner singularity at finite depth. We show that for κ ≥ 0.3513 . . . the dominant energy condition is satisfied all over the space–time. We match this solution to the vacuum one and compute the external gravitational field in terms of slab’s parameters. Depending on the value of κ, these slabs can be attractive, repulsive or neutral. In the first case, the space–time also finishes up above at an empty repelling singular boundary. In the other cases, they turn out to be semi-infinite and asymptotically flat when z → ∞. We also find solutions consisting of joining an attractive slab and a repulsive one, and two neutral ones. We also discuss how to assemble a “gravitational capacitor” by inserting a slice of vacuum between two such slabs.     

Spinning particles in Schwarzschild–de Sitter space–time

After considering the reference case of the motion of spinning test bodies in the equatorial plane of the Schwarzschild space–time, we generalize the results to the case of the motion of a spinning particle in the equatorial plane of the Schwarzschild–de Sitter space–time. Specifically, we obtain the loci of turning points of the particle in this plane. We show that the cosmological constant affect the particle motion when the particle distance from the black hole is of the order of the inverse square root of the cosmological constant.     

Intrinsic spin–orbit interaction in carbon nanotubes and curved nanoribbons

We present a theoretical study of spin–orbit interaction effects on single wall carbon nanotubes and curved graphene nanoribbons by means of a realistic multiorbital tight-binding model, which takes into account the full symmetry of the honeycomb lattice. Several effects relevant to spin–orbit interaction, namely, the importance of chirality, curvature, and a family-dependent anisotropic conduction and valence band splitting are identified. We show that chiral nanotubes and nanoribbons exhibit spin-split states. Curvature-induced orbital hybridization is crucial to understand the experimentally observed anisotropic spin–orbit splittings in carbon nanotubes. In fact, spin–orbit interaction is important in curved graphene nanoribbons, since the induced spin-splitting on the edge states gives rise to spin-filtered states.