Gauge independence for noncovariant supergauges

Previous work on noncovariant gauge choices within the superfield formalism was restricted to renormalization problems. Here we show the gauge independence and (global) supersymmetry for theS-matrix with suitably defined on-shell physical sources.     

Covariant gauges and point sources in general relativity

The tree graph contributions to the vacuum expectation value of the quantized gravitational field produced by a point mass source are found to diverge. These divergences can be removed only by giving the source a finite extension, and it is first necessary to analyze the corresponding classical situation before making a comparison with the quantum theory. In this paper, the model for such an extended particle is taken to be a spherical shell of initially static pressure-free dust. Without solving the Einstein equations explicity, a coordinate-independent mass renormalization formula can be derived, valid at the moment of time symmetry, which relates the total mass of the system to the bare mass of the source and its invariant radius. The equations are then solved for various choices of coordinate systems, allowing the invariant radius of the shell to be expressed in terms of its coordinate dependent extension. The results are in agreement with those obtained previously by Arnowitt, Deser, and Misner. The work of these authors is generalized to include coordinate frames for which the metric is discontinuous across the shell. Aside from any intrinsic interest, such a generalization is necessary since the most convenient coordinate system for the quantum calculations, namely the covariant de Donder (harmonic) gauge, falls into this category. By expanding the total mass of the source in terms of its bare mass and harmonic coordinate extension, the classical Schwarzschild solution may be cast into a form which facilitates a direct comparison with the quantum theory in the de Donder gauge.     

Some remarks on radiation gauges in general relativity

We prove that it is possible to specify the shift vector field for a given foliation in such a way as to provide automatically the transverse-traceless part of the second fundamental form K associated with the slices of the foliation. We interpret this particular specification as providing a simple way for characterizing the dynamical degrees of freedom of the gravitational field. The resulting gauge is not the minimal distortion gauge devised by Smarr and York. In numerical relativity it permits the maintenance in time of the difference equations associated with the divergence constraint.     

A renormalization prescription for massless quantum electrodynamics

An alternative proof of the Ward-Takahashi identity for perturbative quantum electrodynamics is given which makes no use of a gauge invariant regularization such as the Pauli-Villars loop subtraction or dimensional regularization. Instead, it is shown, in the presence of an arbitrary high momentum cutoff, that the exact W-T identity holds with an error ofO(1) with 0<<1. The proof involves a perturbative analysis of the Euclidean functional integral for QED by the tree expansion method.Research supported by the Natural Sciences and Engineering Research Council     

A new approach to radial and axial gauges

We develop a new path integral formulation of QCD in radial and axial gauges. This formalism yields free propagators which are free of gauge poles. We find that radial gauges are ghost free. In axial gauges ghosts cannot generally be excluded from the formalism due to the need to fix the residual gauge freedom.     

Generalized coulomb gauges for the free photon field

We point out that the classical notion of gauge transformations can be interpreted in two different ways in the quantum theory. Beside the transformation of the field operator appearing in the Gupta-Bleuler theory, the gauge transformations can be viewed as acting on the wave functions in a generalization of the Coulomb gauge.     

A prescription for removing centre-of-mass effects from the bag model

We assume that the state of the MIT bag model describes a hadron which itself is confined to a spherical region of certain size. By demanding that the low energy levels of the quark system and that of the confined hadron coincide we determine selfconsistently all relevant parameters and calculate the Roper resonance mass.     

A general model for jet fragmentation

We present a general condition on quark fragmentation which gives a hadron distribution satisfying Lorentz invariance and causality. The hadronization can be described as an iterative cascade process, symmetric with respect to iteration from the quark and the antiquark ends. The possible particle distributions are strongly restricted, with few free parameters related to the total multiplicity and corelations in rapidity. These parameters can be given an appealing interpretation in terms of the expected area and perimeter dependence of Wilson loop integrals.     

A general scheme for microscopic theories

We discuss from an operational point of view some fundamental concepts of the micro-scopic physical theories, with the aim of providing a background for a successive investigation of the microscopic space-time structure. We consistently develop the remark that a frame of reference is determined by physical objects which may interact with the objects under investigation. As it is not clear that a state can be prepared by means of physical operations, we do not use the concept of physical state for the foundation of the theory. In our approach, the primitive concepts are the measurement procedures, following which one gets a numerical result, and the transformation procedures, which have the aim of building a frame of reference. We discuss several rules which allow us to define new procedures in terms of known procedures. The statistical laws of physics are formulated in terms of an order relation between measurement procedures, which defines also an equivalence relation. The equivalence classes of measurement procedures are called measurements. We define also equivalence classes of transformation procedures, called transformations. The mathematical structure of the set of measurements and of the set of transformations is discussed in detail. We consider measurements with an arbitrary finite number of possible results, as this enables us to give a rigorous definition of compatibility. Finally, we point out that all the physical theories necessarily contain ideal measurements and transformations which do not correspond to any known physical procedure. The introduction of these ideal objects permits a considerable simplification of the mathematical structure of the theory, but reduces its physical content.