Space-time Description Research Articles

Flavor oscillations from a spatially localized source: A simple general treatment

A unique description avoiding confusion is presented for all flavor oscillation experiments in which particles of a definite flavor are emitted from a localized source. The probability for finding a particle with the wrong flavor must vanish at the position of the source for all times. This condition requires flavor-time and flavor-energy factorizations which determine uniquely the flavor mixture observed at a detector in the oscillation region, i.e., where the overlaps between the wave packets for different mass eigenstates are almost complete. Oscillation periods calculated for ``gedanken'' time-measurement experiments are shown to give the correct measured oscillation wavelength in space when multiplied by the group velocity. Examples of neutrino propagation in a weak field and in a gravitational field are given. In these cases the relative phase is modified differently for measurements in space and time. Energy-momentum (frequency-wave number) and space-time descriptions are complementary, equally valid, and give the same results. The two identical phase shifts obtained describe the same physics; adding them together to get a factor of 2 is double counting.

Five-dimensional rindler spacetime

We obtain solutions to the field equations for the massless scalar, massless spinor, and electromagnetic fields in a Rindler coordinate system consisting of four space dimensions and one time dimension. The solutions are shown to allow energy > momentum and so may represent massive particles even though the corresponding field equations contain no mass term. The solutions are confined to a narrow interval in the Rindler coordinate and thus, to an observer who sees only these fields, appear to exist in a three-dimensional space. We propose this description of spacetime and fields as model of the universe in which we live.

Quantum fields in disequilibrium: Squeezed states

A spacetime description of squeezed states in quantum fields is presented, revealing the connection between squeezing and nonequilibrium dynamics. Squeezings in configuration space, occupation number space, and phase space are distinguished; generating transformations and criteria for their physical realization are discussed. The results have an immediate applicability to atoms and ions in traps, as well as to quantum optics in relativistic and nonequilibrium systems. Squeezing, sub-Poissonian statistics, and antibunching are all shown to be a direct consequence of spacetime inhomogeneities in the quantum field. The finite speed of communication between separate regions of the field (finite speed of light) places a lower limit on the attainable spectral width of squeezed states. The squeezing parameter for field quadratures has the appearance of a chemical potential in an inhomogeneous field, and through a renormalization may be generated by a Chern-Simons-like term. {copyright} {ital 1997} {ital The American Physical Society}

Causal anomalies and the completeness of quantum theory

Hans Reichenbach’s Philosophic Foundations of Quantum Mechanics (1944) has attracted the attention of philosophers because of its proposal for the interpretation of the theory in terms of a non-standard, threevalued logic.1 Such an interpretation is, as Reichenbach calls it, a ‘restrictive’ one; that is, it leaves certain propositions formulable in the language of the theory without standard truth conditions.2 These propositions can be neither verified nor falsified, and the facts they express thus neither predicted nor explained by the theory. A typical such proposition assigns a determinate position and momentum to a particle at some instant. Clearly, embracing such an interpretation involves renouncing a spacetime description of the world, and is thus not to be entered into lightly.

Deep-inelastic final states in a space-time description of shower development and hadronization.

We extend a quantum kinetic approach to the description of hadronic showers in space, time, and momentum space to deep-inelastic $\mathrm{ep}$ collisions, with particular reference to experiments at DESY HERA. We follow the history of hard scattering events back to the initial hadronic state and forward to the formation of color-singlet prehadronic clusters and their decays into hadrons. The time evolution of the spacelike initial-state shower and the timelike secondary partons are treated similarly, and cluster formation is treated using a spatial criterion motivated by confinement and a nonperturbative model for hadronization. We calculate the time evolution of particle distributions in rapidity, transverse, and longitudinal space. We also compare the transverse hadronic energy flow and the distribution of observed hadronic masses with experimental data from HERA, finding encouraging results, and discuss the background to large-rapidity-gap events. The techniques developed in this paper may be applied in the future to more complicated processes such as $\mathrm{eA}$, $\mathrm{pp}$, $\mathrm{pA}$, and $\mathrm{AA}$ collisions.

Space-time description of the splitting and coalescence of wave fronts in film flows

Abstract Simultaneous space-time measurements of two-dimensional waves on the surface of a flowing film are recorded using a fluorescence imaging method and analyzed by means of both Fourier and biorthogonal decomposition techniques. The analysis, performed at various Reynolds numbers and perturbation frequencies, reveals that the splitting and coalescence of wavefronts is due to purely spatial modulations of the original uniformly traveling wave. The modulations cannot be described by a single modulating function. A phase space description of this change in the dynamics is given, and the effect of the modulations on the global entropy function is discussed. At higher Reynolds number, the modulations are both spatial and temporal.

Comments on three-branes

The Born-Infeld-like effective world-volume theory of a single 3-brane is deduced from a manifestly space-time supersymmetric description of the corresponding D-brane. This is shown to be invariant under SL(2, R) transformations that act on the abelian gauge field as well as the bulk fields. The effective theory of two nearby parallel three-branes involves massive world-volume supermultiplets which transform under SL(2, Z) into the dyonic solitons of four-dimensional N = 4 spontaneously broken SU(2) Yang-Mills theory.

Superspace effective actions for 4D compactifications of heterotic and Type II superstrings

Two-dimensional sigma models are defined for the new manifestly spacetime supersymmetric description of four-dimensional compactified superstrings. The resulting target-superspace effective action is constrained by the way the spacetime dilaton couples to the worldsheet curvature: For the heterotic superstring, the worldsheet curvature couples to the real part of a chiral multiplet, and for Type II it couples to the real part of the sum of a vector multiplet and a tensor hypermultiplet. For the Type II supestring, this contradicts the standard folklore that only a hypermultiplet counts string loops, explains the peculiar dilaton coupling of Ramond-Ramond fields, and allows the effective action to be easily written in N = 2 4D superspace. It also implies that vector multiplet interactions get no quantum corrections, while hypermultiplet interactions can only get corrections if mirror symmetry is non-perturbatively broken.

BOSE-EINSTEIN CORRELATIONS AND THE FRAGMENTATION RADIUS

In nuclear reactions the radii of the fragmentation volume obtained with Bose-Einstein correlations reflect the effective radius of the projectile. However, according to the phenomenological parametrizations of the effect, the Compton wavelength scale of the meson is actually extracted. We propose a solution to this puzzle and conclude that in heavy-ion collisions Bose-Einstein interference does allow the spacetime description of the fragmentation region.

Spatio-temporal complexities and chaos in a two-phase flashing flow

In order to study the two-phase natural circulation phenomena in a hot-leg-U-bend, an important aspect of a small-break loss-of-coolant accident in a light-water reactor, a Freon-113 flow visualization loop for simulating the natural circulation flow and various effects that occur in the process has been constructed based on the predetermined scaling criteria. Since the void fraction distribution represents the major factor in determination of flow rate, interruption and re-establishment of the two-phase natural circulation, we present a space-time description of regular and complex phenomena based on the bi-orthogonal decomposition of a spatio-temporal void fraction distribution into orthogonal temporal modes (chronos) and orthogonal spatial modes (topos) (Aubry, 1991). Such a description allowed for the computation of global (spatial and temporal) quantities such as the energy of the void fraction configuration, global entropy and characteristic dimension (the effective number of degrees of freedom of the signal). The global energy function is used to identify the space-time structures independently participating in the (kinetic) energy of the flow. The global entropy characterizes the full space and time structure of the signal and we use this quantity to obtain an objective indicator of different flow regimes appearing in two-phase natural circulation flow.

Compensation of medium-induced fluctuations for synthetic aperture sonar

There are two primary obstacles to achieving aperture coherence in synthetic aperture sonar (SAS); motion compensation (MOCOMP) accuracy, and medium fluctuations along the acoustic propagation paths. The feasibility of MOCOMP for high-resolution SAS using a combination of commercial MOCOMP sensor components with existing autofocus processing algorithms has been previously assessed. This paper discusses the experimental measurement of acoustic fluctuations induced by inhomogeneities in sea water, their impact on SAS imagery, and whether autofocusing algorithms can compensate for medium-induced fluctuations. Spatial as well as temporal fluctuations over propagation path lengths of 1000 ft and frequencies of 100 kHz are relevant to high resolution SAS. A historical survey discovered no data in this parameter regime. Therefore, a joint IR&D effort, the Acoustic Medium Stability Experiment (AMSE), was conducted to collect appropriate data. AMSE’s unique data set provides space-time statistical descriptions of the medium-induced phase fluctuations. Using the AMSE data and an end-to-end SAS simulation capability, it was found that medium-induced fluctuations do degrade SAS imagery significantly. However, available autofocusing algorithms are capable of estimating and compensating the medium-induced phase errors (in addition to MOCOMP errors), allowing fully focused imagery to be obtained.

Une approche stochastique pour la modélisation du bruit des écoulements turbulents

A new approach to noise modeling for free turbulent flows is presented. A set of equations is derived from the acoustic variables. In the left-hand side of this system, one finds the linearized Euler equations, whereas the right-hand side exibits source terms. These source terms are modeled in using a stochastic space-time description of the three-dimensionnal turbulent motion. The linearized Euler equations including a stochastic description of noise sources are solved numerically. The Stochastic and Noise Generation (SNGR) model is applied to a subsonic free jet. The weak interaction between the stationnary mean flow and the acoustic field is taken account. The limitations of the SNGR model lie in the statistical properties of the synthetic turbulent field and in the use of an axisymmetric modeling of the acoustic propagation

QCD based space-time description of high energy nuclear collisions

The current understanding of the early stage of heavy ion collisions at collider energies on the basis of the improved parton model and kinetic theory is presented. The space-time evolution of these reactions is investigated in terms of t the dissipative dynamics of (semi)hard quark and gluon interactions within perturbative QCD. The partons' phase-space distributions are evolved in real time according to a transport equation through multiple collisions, emission and absorption processes. The resulting parton cascade picture is applied to study the issues of thermalization, chemical equilibration, and particle production in AA collisions at RHIC and LHC.

Strangeness, charm, and bottom production from dense parton matter in high energy nuclear collisions.

The production properties of strange, charm, and bottom quarks in ultrarelativistic A+A collisions at heavy ion colliders are investigated for systems from p+p to Au+Au in the energy range \ensuremath{\surd}s /A=200--6300 GeV, using the parton cascade model. Within this kinetic space-time description of the parton dynamics, based on the current understanding of semihard and hard QCD interactions, it is found that a substantial enhancement of s, c, and b production can be expected in AA collisions with plasma formation of the deconfined parton matter relative to the case of a purely hadronic scenario without plasma formation. Because of the large number of initially produced energetic gluons the main contribution comes from decays of virtually excited gluons and gluon fusion. The associated resonance production of \ensuremath{\varphi}, J/\ensuremath{\psi}, and \ensuremath{\Upsilon} is estimated and it is shown that the resulting abundances of these vector mesons can be used as a sensitive thermometer of the hot and dense QCD matter formed in the central region durng the very early stage of the collisions. Therefore the future heavy ion collider experiments would have an attractive opportunity to probe the evolution of partons through preequilibrium toward plasma formation by measuring the multiplicities and momentum spectra of heavy mesons.

From [formula omitted] algebra to κ-Lorentz quasigroup. A deformation of relativistic symmetry

We consider an algebraic ansatz for the class of nonlinear D=4 Poincaré algebras and show that it contains only the quantum κ- Poincar e ́ (real Hopf) algebras, obtained recently by the contraction of U q (O(3,2)). We derive the explicit formulae for the finite κ-Lorentz transformations generated by the realizations of the κ- Poincar e ́ algebra in D=4 momentum space. These finite κ-Lorentz transformations form a quasigroup, with generalized composition law of the boost parameters (rapidities). We consider further the (2 s+1)-component field realizations with arbitrary spin s and their finite κ-Lorentz transformations. For s= 1 2 we obtain the κ-covariant Dirac equation, derived from the finite κ-Lorentz boost formula. After the coupling of the κ-deformed Dirac equation to the electromagnetic potential we show that in the lowest order (linear) in el/ κ the κ-corrections to the hydrogen atom energy levels vanish but the value g=2 of the electron's magnetic moment is modified ( g=2→ g=2[1+( m el / κ)]. Finally the space-time description of κ-relativistic fields is briefly discussed.

(1 + 1)-dimensional field theories and space-times that contain a twist-free null vector field

We present a (1 + 1)-dimensional description of 4-dimensional space-times that contain a twist-free null vector field. It is described by the (1 + 1)-dimensional Yang-Mills action interacting with matter fields, with spatial diffeomorphisms of 2-surface as the gauge symmetry. The constraint appears polynomial in part, whereas the non-polynomial part is a non-linear sigma model type in (1 + 1)-dimensions. The representations of ω ∞-gravity are shown to appear naturally as special cases of this description, and the geometry of ω ∞-gravity is discussed briefly in term of the fibre bundle.

Differential structure of space-time and its prolongations to singular boundaries

After briefly presenting basic ideas of the differential space theory, the global description of space-times in terms of this theory is given. The space-times of a straight cosmic string and that of the closed Friedman world model are our standard examples. A space-time with its singular boundary is no longer a differentiable manifold, but it can be organized into a differential space, and the differential structure of space-time can be prolonged to its singular boundary. In general, the procedure is not unique. A simple classification of differential structure prolongations is also presented.

On Discrete Models of Space-Time

Analyzing the Einstein radiolocation method we come to the conclusion that results of any measurement of space-time coordinates should be expressed in terms of rational numbers. We show that this property is Lorentz invariant and may be used in the construction of discrete models of space-time different from the models of the lattice type constructed in the process of discretization of continuous models. § 1. Discrete models of space-time without elementary length There is a common belief 1 ) that discrete models of space-time must suffer from at least three chronic diseases: i) They introduce the experimentally not found elementary length. ii) They violate experimentally verified relativistic invariance. iii) They legate their mathematics from the continuous models. In the present paper we shall show that this belief is not justified and in order to present our approach we should like to start from the very beginning, i.e., from the analysis of general properties of the experimental methods used to measure space­ time coordinates. The notion of space-time is a physical concept and if we want to be able to understand all its features we should take into account and understand the measure­ ment methods of any quantity used in the mathematical description of space-time. In particular, we must precisely define the method of measuring space-time coordinates the results of which, due to the principle of relativity, have a subjective character for each observer. We consider Einstein radiolocation method 2 ) as a starting point of our discussion. For the completeness of the paper we shall remind here its basic idea in spite of the fact that it is well-known. In this method in any inertial reference frame stiffly connected to a given observer we measure two quantities:

Maximal acceleration of thin shells in Weyl space

It is shown that maximal acceleration, which arises in various theories when aspects of quantum mechanics are taken into account, also arises in a geometric causal approach to quantum mechanics in which a particle is represented by a bubble in Weyl space. This result supports the hypothesis that quantum effects can be given a spacetime description.

Geometric superalgebra and the Dirac equation

A unified mathematical approach to spinors and multivectors or superalgebra is constructed in a form useful to study the mathematical description of matter and its interaction fields. The formalism then encompasses both points of view: multivectors for the description of (space-time) geometry and the description of the integer spin, interaction fields, and spinor representations suitable for the description of half odd integer, matter fields. An application is made to study the change of the Dirac equation under the spinors to multivectors (to scalars) mapping. The physical and geometric content of the multivector solutions of the Dirac–Hestenes equation is clearly shown.