Absence Of Matter Research Articles

ARE THERE TOPOLOGICALLY CHARGED STATES ASSOCIATED WITH QUANTUM ELECTRODYNAMICS?

We present a generalization of quantum electrodynamics (QED) in terms of an antisymmetric tensor gauge field. In this formulation the topological current of this field appears as a source for the electromagnetic field and the topological charge therefore acts physically as an electric charge. The charged states of QED lie in the sector where the topological charge is identical to the matter charge. The antisymmetric field theory, however, admits new sectors where the topological charge is more general. These nontrivial, electrically charged sectors contain massless states orthogonal to the vacuum which are created by a gauge-invariant operator and can be interpreted as coherent states of photons. We evaluate the correlation functions of these states in the absence of matter. The new states have a positive definite norm and do interact with the charged states of QED in the usual way. It is argued that if these new sectors are in fact realized in nature, then a very intense background electromagnetic field is necessary for their experimental observation. The order of magnitude of the intensity threshold is estimated. The value of the quantum of charge is also obtained.

One-photon operators and the role of vacuum fluctuations in the Casimir force.

It is proposed that the contribution of vacuum fluctuations to spontaneous emission and the Casimir force can be attributed to the creation of single photons at the positions of charged particles as in relativistic quantum field theory. Thus the change from normal to symmetric order in the particle-field interaction Hamiltonian and the preservation of the equal-time commutation relations need not imply vacuum fluctuations in the absence of matter.

Jordan-Brans-Dicke quantum wormholes and Coleman's mechanism

We consider the quantum gravity and cosmology of a Jordan-Brans-Dicke theory, predicted by string effective actions. We study its canonical formalism and find that the constraint algebra is that of general relativity, as a consequence of the general covariance of scalar-tensor theories. We also analyze the problem of boundary conditions and propose that they must be imposed in the Jordan frame, in which particles satisfy the strong equivalence principle. Specifically, we discuss both Hartle-Hawking and wormhole boundary conditions in the context of quantum cosmology. We find quantum wormhole solutions for Jordan-Brans-Dicke gravity even in the absence of matter. Wormholes may affect the constants of nature and, in particular, the Brans-Dicke parameter. Following Coleman's mechanism, we find a probability distribution which is strongly peaked at zero cosmological constant and infinite Brans-Dicke parameter. That is, we recover general relativity as the effective low energy theory of gravity.

A New Conservation Law for Classical Electrodynamics

In a vacuum the scalar field 4 and vector field A of electromagnetic radiation satisfy wave equations. Certain mathematically natural measures of energy density and power flux arise for any solutions of any wave equation, and, as components of a conservation law, these measures are utilized like Lyapunov functions in an associated PDE stability theory [Hahn, Stability of Motion, Springer-Verlag, New York, 1967, pp. 216’217], [Walker, Dynamical Systems and Evolution Equations, Plenum, New York, 1990, p. 106], [Zachmanoglov and Thoe, Introduction to Partial Differential Equations with Applications, Dover, New York, 1986, p. 283]. But energy conservation in electrodynamics is conventionally accounted for with the Poynting equation, another mathematical conservation law. The purpose of this paper is to compare the contending measures and conservation laws. A consequence of the new measures is that power flux vanishes if the scalar and vector potentials are constant with respect to time, in contrast to the Poynting system. The new measures also provide an alternative to the classical Larmor formula for radiation from an accelerating charged particle. Concerning antennas, it can be shown that the alternative measure of power radiated from an idealized dipole antenna is about twice that predicted by the Poynting vector. It should be possible to measure carefully antenna power input and perhaps heating to test this prediction. Certain idealized capacitors might also be experimentally approximated to test mathematical predictions of power consumption. The new energy density and power flux can be couched in tensor theory, and this leads to an energy tensor with nonzero trace in the presence of radiation and absence of matter. (The analogous tensor built from the Poynting measure discriminates between those forms of energy, a fact that once led Einstein to propose changing the Einstein field equation.) Thus the range of physical implications of the new conservation law is considerable.

An embarrassing question about reproduction

Abstract Standard objections to dualism focus on problems of individuation: what, in the absence of matter, serves to diversify immaterial items? and interaction: how can material and immaterial elements causally affect one another? Given certain ways of conceiving mental phenomena and causation, it is not obvious that one cannot reply to these objections. However, a different kind of difficulty comes into view when one considers the question of the origin of the mental. Here attention is directed upon the case of intentionality. It might seem that the transition between non‐intentional and intentional phenomena could be dealt with by adopting a version of Dennett's discharging strategy, but this is argued against. Several responses to the origination problem are identified, including a creationist one.

O(5)�U(1) electroweak gauge theory and the neutrino oscillations in matter

A study is made of the groupO(5)×U(1). The group is economical in the number of gauge bosons, which we associate with each of its generators, and is anomaly-free. The left-handed leptonsL ≡(v e ,e,μ,v μ ) L are assigned to the four-dimensional spinorial representations ofO(5). The right-handed particles are taken to be the singlets of the group. The theory has three sets of gauge bosons: (1) analogues of the GWS model, (2) additional charged gauge bosons, and (3) a set of three additional neutral gauge bosons as compared to the GWS model. We introduce neutrino mixing by mixing the additional charged gauge bosons. We develope a theory of neutrino oscillations in matter in such a way that in the absence of matter the scattering length reduces to the usual scattering length in vacuum. Even if the neutrino masses are equal or the neutrinos are massless, we still have neutrino oscillations in matter, a result already noted by Wolfenstein.

Dynamics of anisotropic cosmological model with ultrarelativistic matter, magnetic field, and fluxes of free isotropic particles

Within the framework of general relativity a dynamics of homogeneous anistropic axially symmetric model of the Bianchi type I is considered for the case when sources of gravitational field are ultrarelativistic matter, homogeneous magnetic field, and fluxes of free particles. Qualitative analysis of the field equations on a phase plane is given. All solutions of a considered type for large values of proper time asymptotically approach the flat Friedmann model while the value of energy density of free particles approaches the double value of magnetic field energy density. Near a singular state the solution exhibits oscillating behavior with successive interchange of Kasner singularities of “pancake”-like and “filament”-like types. It is also shown that in the absence of matter a solution retains its character.

Regge-Palatini calculus

We formulate a Palatini version of the Regge calculus by constructing a discrete torsion field on the simplicial manifold. The action has two components, the original Regge action and an additional action for the torsion field. In the absence of matter the variational equations reduce the torsion field to zero. Matter fields can act as sources of torsion.

Theories of gravitation with nonminimal coupling of matter and the gravitational field

The foundations of a theory of nonminimal coupling of matter and the gravitational field in the framework of Riemannian (or Riemann-Cartan) geometry are presented. In the absence of matter, the Einstein vacuum field equations hold. In order to allow for a Newtonian limit, the theory contains a new parameter l0 of dimension length. For systems with finite total mass, l0 is set equal to the Schwarzschild radius.

Note on gravitational energy

We compute the limiting behaviour of an energy integral proposed by Hawking. In the presence of matter, we find that the leading-order contribution to this integral is just the energy density of the matter. In the absence of matter, the leading-order contribution is the (time component of the) Bel-Robinson tensor.

Riemann-Cartan type gravitational theories satisfying Birkhoff's theorem

In the class of nine-parameter Riemann-Cartan type gravitational theories we find two theories that are unitary and satisfy a generalized Birkhoff's theorem: In the absence of matter, Schwarzschild metric with vanishing torsion is the unique spherically symmetric solution to the field equations.

Multidimensional Unified Theories

AbstractAn extended spacetime, M4+N, is a Riemannian (4 + N)‐dimensional manifold which admits an N‐parameter group G of (spacelike) isometries and is such that ordinary spacetime M4 is the space M4+N/G of the equivalence classes under G‐transformations of M4+N. A multidimensional unified theory (MUT) is a dynamical theory of the metric tensor on M4+N, the metric being determined from the Einstein‐Hilbert action principle: in absence of matter, the Lagrangian is (essentially) the total curvature scalar of M4+N. A MUT is an extension of the Cho‐Freund generalization of Jordan's five‐dimensional theory. A MUT can be faithfully translated in four‐dimensional language: as a theory on M4, a MUT is a gauge field theory with gauge group G. A unifying aspect of MUT's is that all fields occur as elements of the metric tensor on M4+N. When the isometry generators are subjected to strongest constraints, a MUT becomes the De Witt‐Trautman generalization of Kaluza's five‐dimensional theory; in four‐dimensional language, this is the theory of Yang‐Mills gauge fields coupled to gravity. With weaker constraints, a MUT appears to be more natural than a Yang‐Mills theory as a physical realization of the gauge principle for an exact symmetry of gauged confined color. Such weakly‐constrained MUT leads to bag‐type models without the need for ad hoc surgery on the basic. Lagrangian. The present paper provides a detailed introduction to the formalism of multidimensional unified gauge field theory.

Cosmological black holes are coloured too

A new solution of the Einstein-Yang-Mills system with axial symmetry and cosmological constant is given here. This new metric, which in the absence of matter becomes the de Sitter universe, is the natural generalization of both a recent result of Perry for stellar (asymptotically flat) black holes and a well-knwn family of solutions of the Einstein-Maxwell system with nonvanishing cosmological constant given some time ago by Carter. Calculations have been carried out making extensive use of the coordinates found by Plebanski.

THE GRAVIMETRIC DENSITY FORMULA FOR A SPHERICAL SHELL

The formula for the gravimetric density (ρ) of material, between two stations a vertical distance ΔZ apart in a borehole, is (Hammer, 1950): [Formula: see text]where k is the gravitational constant, F the free air gradient (the derivative of gravity with respect to depth in the absence of matter), and Δg the change in gravity. This formula is generally derived by integrating the vertical component of gravity caused, at a measuring point, by an infinite horizontal plate of thickness t, and then doubling it to account for one measuring point above and below the plate. This results in (Heiskanen and Vening‐Meinesz, 1958), [Formula: see text]In fact, however, the earth is not made up of infinite horizontal plates; it can perhaps more reasonably be regarded as a series of spherical shells. It is therefore instructive to derive the expression for the change in gravity associated with passing through one of these spherical shells.

Gravitational energy from a quadratic Lagrangian with torsion

Gravitation is considered as a gauge field within the formalism of Utiyama and Kibble. In empty space-time a Lagrangian density, quadratic in Riemann's curvature tensor and in Cartan's torsion tensor, is introduced. The equations of motion are coupled differential equations for the curvature and torsion tensors. The spin of the torsion field behaves as a curvature source and the energy of both fields acts as a torsion source. Each field has an energy tensor, similar to the Maxwell tensor of electrodynamics, vanishing in a torsionless space. It thus appears that the torsion of space-time is a geometric property that makes possible the propagation of gravitational energy in the absence of matter.

A background-dependent approach to the theory of gravitation II. Relativistic gravitational equations

On the basis of the results of Paper I and guided by a Machian view of nature, we find new gravitational equations which are background dependent. Such equations describe a purely geometrical theory of gravitation, and their dependence on the background structure is through the total energy-momentum tensor on the past sheet of the light cone of each space-time pointx [θμνx, say], i.e., through the integral on the past sheet of the light cone ofx of the parallel transport of the energy-momentum tensor from the space-time point in which it is defined tox along the geodesic connecting the two space-time points. Following Gursey, we assume that the source of the De Sitter metric is not the cosmological term, but, rather, the energy-momentum tensor of a “uniform distribution of mass scintillations” [Tμνx, say].Tμνx, indeed, turns out to be equal to the metric tensor times a constant factor. As a consequence, in any local inhomogeneity A of a space-time whose background structure is determined by the Perfect Cosmological Principle,θμν turns out to be approximately equal to the metric tensor times a constant factor, providedT=gαβTαβ is sufficiently small and the structure of the past sheet of the light cones of the space-time points belonging to Λ is not too much perturbed by the local gravitational field. As a consequence, in Λ the new equations approximately reduce to Einstein's equations. If one considers a “superuniverse model” in which our universe is considered as a local inhomogeneity in a De Sitter background, then from the above result there follows a fortiori the agreement of the new gravitational equations with the classical tests of gravitation. Furthermore, the dependence on the background structure is such that the new equations (i) incorporate the idea that the frame has to be fixeddirectly in connection with cosmological observations, and (ii) are singular in the absence of matter in the whole space-time. Moreover, (iii) the coupling constant turns out to be dimensionless in natural units (c=1=ħ), and (iv) a local inertial frame in a De Sitter background is determined by the condition that with respect to it the background structure is homogeneous in space and in time and is Lorentz invariant.

Chiral symmetry and pion condensation. I. Model-dependent results

The successes of current algebra and partial conservation of axial- vector current can be interpreted as indications that the strong interactions are approximately symmetric under chiral Su(2) times SU(2) transformations. In the absence of matter, the explicit chiral-symmetry breaking defines a unique vacuum state for the theory. The smallness of the chiral-symmetry breaking, however, implies the existence of many other states, approximately degenerate in energy with, but orthogonal to, the true vacuum. In these states, in general does not equal 0; thus they contain a ''pion condensate.'' In a macroscopic system - such as a neutron star - at very high baryon density one of these pion- condensed states might become the true ground state. We study this phenomenon in the linear sigma model. We are able to calculate analytically the ''phase diagram'' describing the ground state of infinite nuclear matter as a function of baryon density. Above a critical baryon density a phase transition to a pion- condensed ground state occurs. We extend the chiral-symmetry approach to include the effects of the N* (1236) and the ill-understood $gamma$-N s waves. In addition to analyzing the ground state, we examine the spectrum of excited states. In themore » condensed phase, the meson excitation spectrum contains a ''Goldstone boson'' associated with the ground state's not being an eigenstate of the conserved operator I$sub 3$. However, when electromagnetic interactions are included, this mode disappears via the Higgs phenomenon indicating that the ground state is a superconductor. The presence of the pion condensate fosters the $beta$ decay of the fermion excitations, and the emitted neutrinos provide the cooling mechanism for neutron stars.« less

A note on the Lorentz-Lorenz formula and the Ewald-Oseen extinction theorem

A new and a relatively simple derivation of two important results of classical electromagnetic theory — the Lorentz-Lorenz formula and the Ewald-Oseen extinction theorem — is presented. The form of the extinction theorem derived here is somewhat different from that usually given. It is shown that, in the absence of matter, the new form of the Ewald-Oseen theorem reduces to the Helmholtz-Kirchoff integral theorem of classical wave theory.

Canonical Variables for the Interacting Gravitational and Dirac Fields

The problem of reducing the Lagrangian for the interacting gravitational and Dirac fields to canonical form is discussed, using the vierbein formalism. The arbitrary gauge variables corresponding to local Lorentz transformations of the vierbein are removed by imposing Schwinger's ``time-guage'' condition, and a further condition that the spatial part of the vierbein be symmetric. It is shown that in this guage the Lagrangian can be expressed in a canonical form involving essentially the same gravitational-field variables as in the absence of matter, and that the generators of spatial translations and rotations have the expected form.

Lorentz Invariance and the Gravitational Field

An argument leading from the Lorentz invariance of the Lagrangian to the introduction of the gravitational field is presented. Utiyama's discussion is extended by considering the 10-parameter group of inhomogeneous Lorentz transformations, involving variation of the coordinates as well as the field variables. It is then unnecessary to introduce a priori curvilinear coordinates or a Riemannian metric, and the new field variables introduced as a consequence of the argument include the vierbein components hkμ as well as the ``local affine connection'' Aijμ. The extended transformations for which the 10 parameters become arbitrary functions of position may be interpreted as general coordinate transformations and rotations of the vierbein system. The free Lagrangian for the new fields is shown to be a function of two covariant quantities analogous to Fμν for the electromagnetic field, and the simplest possible form is just the usual curvature scalar density expressed in terms of hkμ and Aijμ. This Lagrangian is of first order in the derivatives, and is the analog for the vierbein formalism of Palatini's Lagrangian. In the absence of matter, it yields the familiar equations Rμν=0 for empty space, but when matter is present there is a difference from the usual theory (first pointed out by Weyl) which arises from the fact that Aijμ appears in the matter field Lagrangian, so that the equation of motion relating Aijμ to hkμ is changed. In particular, this means that, although the covariant derivative of the metric vanishes, the affine connection Γλμν is nonsymmetric. The theory may be reexpressed in terms of the Christoffel connection, and in that case additional terms quadratic in the ``spin density'' Skij appear in the Lagrangian. These terms are almost certainly too small to make any experimentally detectable difference to the predictions of the usual metric theory.