Geometro-stochastic quantization of a theory for extended elementary objects

The geometro-stochastic quantization of a gauge theory based on the (4,1)-de Sitter group is presented. The theory contains an intrinsic elementary length parameter R of geometric origin taken to be of a size typical for hadron physics. Use is made of a soldered Hilbert bundle over curved spacetime carrying a phase space representation of SO(4, 1) with the Lorentz subgroup related to a vierbein formulation of gravitation. The typical fiber of is a resolution kernel Hilbert space constructed in terms of generalized coherent states related to the principal series of unitary irreducible representations of SO(4, 1), namely de Sitter horospherical waves for spinless particles characterized by the parameter . The framework is, finally, extended to a quantum field-theoretical formalism by using bundles with Fock space fibers constructed from .Supported in part by NSERC Research Grant No. A5206.     

Modified Weyl theory and extended elementary objects

To represent extension of objects in particle physics, a modified Weyl theory is used by gauging the curvature radius of the local fibers in a soldered bundle over space-time possessing a homogeneous space G/H of the (4, 1)-de Sitter group G as fiber. Objects with extension determined by a fundamental length parameter R₀ appear as islands D_(i) in space-time characterized by a geometry of the Cartan-Weyl type (i.e., involving torsion and modified Weyl degrees of freedom). Farther away from the domains D_(i), space-time is identified with the pseudo-Riemannian space of general relativity. Extension and symmetry breaking are described by a set of additional fields ( , given as a section on an associated bundle over space-time B with structural group = G D(1), where D(1) is the dilation group. Field equations for the quantities defining the underlying bundle geometry and for the fields are established involving matter source currents derived from a generalized spinor wave function. Einstein's equations for the metric are regarded as the part of the -gauge theory related to the Lorentz subgroup H of G exhibiting thereby the broken nature of the -symmetry for regions outside the domains D_(i).Talk presented at the International Conference on Field Theory and General Relativity held at Utah State University, Logan, Utah, June 26–July 2, 1988.     

Gauge invariance for extended objects

Just as the vector potential (one-form) couples to charged point-particles, antisymmetric tensor fields of higher rank (p-forms) couple to elementary objects of higher dimensionality (strings, membranes, …). It is shown that the only possible gauge invariant interaction of such an extended object with a gauge field in spacetime is based on the abelian group U(1). This is unlike the situation for particles where Yang-Mills actions based on any gauge group may be written down. The properties of the abelian theory are explored. It is pointed out that a compact object is analogous to a particle-antiparticle pair and its quantum rate of production in a constant external field is calculated semiclassically. The analysis is performed keeping generic both the dimension of the object and that of spacetime.     

Ehlers-Harrison-type transformations for Jordan's extended theory of gravitation

It is shown that the hidden symmetry of the stationary Einstein equations under the groupSL(2,R) can be extended to a symmetry under the groupSL(3,R) in the case of Jordan's five-dimensional, unified theory. More generally one obtains an action of the groupSL(n+2,R) on the set of (n+4)-dimensional Einstein spaces admitting a (n+1)-parameter Abelian group of isometries.     

Geometry of gauge fields for extended objects

A geometric interpretation of gauge field for extended objects is given. This interpretation is a generalization of the interpretation of electrodynamics based on connections in principal fibre bundles. Only the geometry of gauge fields is formulated. Field dynamics and interaction of the fields with extended objects will be studied separately.     

Quantized dynamics of a coherent capacitor

A quantum coherent capacitor subject to large amplitude pulse cycles can be made to emit or reabsorb an electron in each half cycle. Quantized currents with pulse cycles in the GHz range have been demonstrated experimentally. We develop a nonlinear dynamical scattering theory for arbitrary pulses to describe the properties of this very fast single electron source. Using our theory we analyze the accuracy of the current quantization and investigate the noise of such a source. Our results are important for future scientific and possible metrological applications of this source.     

Minicompact objects according to the bimetric theory of gravitation

It is shown that, similarly to general relativity, the bimetric theory of gravitation predicts the formation of primordial minicompact objects. Contrary to general relativity, however, it predicts that such objects are stable. Observational consequences are discussed.In partial fulfillment of the requirements for the D.Sc. degree.     

Coherent imaging of extended objects

When used with coherent light, optical imaging systems are inherently unable to reproduce both the amplitude and the phase of a two-dimensional field distribution. This is because their impulse response function varies slowly from point to point, a property known as non-isoplanatism. For sufficiently small objects, this usually results in a phase distortion and has no impact on the measured intensity. Here, we show that the intensity distribution can be dramatically distorted when extended objects are imaged. We illustrate the problem using two simple examples: the pinhole camera and the thin lens. The effects predicted by our theoretical analysis are confirmed by experimental observations.     

Hard-x-ray lensless imaging of extended objects

We demonstrate a hard-x-ray microscope that does not use a lens and is not limited to a small field of view or an object of finite size. The method does not suffer any of the physical constraints, convergence problems, or defocus ambiguities that often arise in conventional phase-retrieval diffractive imaging techniques. Calculation times are about a thousand times shorter than in current iterative algorithms. We need no a priori knowledge about the object, which can be a transmission function with both modulus and phase components. The technique has revolutionary implications for x-ray imaging of all classes of specimen.     

Quantized separations of phase-locked soliton pairs in fiber lasers

We report the discovery of a quantization of the separation between phase-locked soliton pairs that is related to the radiation waves known as Kelly sidebands, in a passively mode-locked fiber ring laser. Our numerical simulations that predict this phenomenon have been confirmed by our experimental results.     

Technique for predicting the number of lightning strokes to extended objects

A technique is developed for predicting the lightning stroke distribution over a territory that is occupied by extended objects protected by lightning arresters (for example, high-voltage substations). It is shown that the techniques used to predict the number of lightning strokes to small objects located in a rated zone protected by lightning arresters are inapplicable to extended objects. The probability distribution is calculated for the number of lightning strokes to lightning arresters and to arrester-protected extended objects at different arrangements of the arresters.     

Measurement of displacement vector fields of extended objects

The main effort in laser metrology during the last 15 years has been focussed on the development of high precision phase measurement techniques, since the phase is the primary quantity for interferometrical testing. However, the phase distribution gives only a first impression of the deformation of the surface. In practice, the three-dimensional displacement components are required if the mechanical behaviour of the object under load is to be investigated. To calculate displacement components some further quantities are necessary, e.g. the three coordinates of the object points. Although the contour measurement can also be reduced to a phase measurement problem, the measurement of three-dimensional displacements is more complex than a high precision phase evaluation. From the practical point of view, four main tasks have to be performed: planning of the experiment, design of the interferometer, acquisition of data and evaluation of data. This paper deals with a discussion of the theoretical background of the last three procedures concerning the state of the art and describes some general rules as well as some problems remaining to be solved for the investigation of extended specimens.     

Perturbative expansion of quantum states of extended objects

We construct an effective Hamiltonian at fixed momentum which can be used to calculate higher-order corrections to quantum states of localized classical solutions of scalar field theories in 1 + 1 dimensions. We use the quantization scheme discussed first by Creutz and also by Rothe and one of the present authors (J.B.). The effective Hamiltonian is similar to, but nevertheless different from the one obtained in the collective coordinate method. The agreement of the energy corrections at the two-loop level has been checked.     

Areal objects and the problem of the λ term in the theory of gravitation

The following areal objects are considered: an ether thread contracting two material points and a multidimensional ether fibre in the pseudo-Euclidean world of events. An ether space-time model with an arbitrarily determined Riemannian metric is constructed and the problem of the λ term in Einstein equations is discussed in this regard.