On the maslov index

In this paper we give four definitions of Maslov index and show that they all satisfy the same system of axioms and hence are equivalent to each other. Moreover, relationships of several symplectic and differential geometric, analytic, and topological invariants (including triple Maslov indices, eta invariants, spectral flow and signatures of quadratic forms) to the Maslov index are developed and formulae relating them are given. The broad presentation is designed with a view to applications both in geometry and in analysis. © 1994 John Wiley & Sons, Inc.     

Topological quantum field theory

A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments in topology of low dimensional manifolds; the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally. The model may also be interesting from a physical viewpoint; it is in a sense a generally covariant quantum field theory, albeit one in which general covariance is unbroken, there are no gravitons, and the only excitations are topological.On leave from Department of Physics, Princeton University. Research supported in part by NSF Grants No. 80-19754, 86-16129, 86-20266     

Charged Particle Emission and Detection Sources in Quantum Field Theory and Infrared Photons

A study is carried out of the fundamental roles played by emission and detection sources of charged particles in quantum field theory by incorporating the unavoidable fact that charged particles feel the presence of each other even when they are widely separated at the emission and detection sites due to the long range effect of the electromagnetic interaction. It is shown that the emission and detection sources as amplitudes of emission and detection of charged particles are to have given specific coupling dependent phase factors for a correct formulation of the problem. Composite sources are introduced for emitting and detecting “clusters” of charged particles. Finally a complete cancellation of the so-called relativistic Dalitz phase factor occurs prior to computing transition rates and probabilities. This work generalizes our earlier work (Fortschr. Phys. 34 , 835 (1986)) dealing with the non-relativistic Coulomb problem.     

Global gravitational anomalies

A general formula for global gauge and gravitational anomalies is derived. It is used to show that the anomaly free supergravity and superstring theories in ten dimensions are all free of global anomalies that might have ruined their consistency. However, it is shown that global anomalies lead to some restrictions on allowed compactifications of these theories. For example, in the case of O(32) superstring theory, it is shown that a global anomaly related to ₇(O(32)) leads to a Dirac-like quantization condition for the field strength of the antisymmetric tensor field.Related to global anomalies is the question of the number of fermion zero modes in an instanton field. It is argued that the relevant gravitational instantons are exotic spheres. It is shown that the number of fermion zero modes in an instanton field is always even in ten dimensional supergravity.Supported in part by NSF Grant No. PHY80-19754     

Equivalence of vacuum Yang-Mills gravitation and vacuum Einstein gravitation

In the Yang-Mills formulation of gravitational dynamics based uponSL(2,C) spin transformations acting on Dirac spinors, the vacuum field equations are R +C R = 0 and and . HereR is the Ricci curvature andC is the Weyl conformal curvature; is a coupling constant. We show the equivalence between solutions of these equations and the vacuum Einstein equationsR = 0. The proof uses the Newman-Penrose formalism.Supported by a NATO fellowship.Supported by a SRC fellowship.     

Quantum electrodynamic corrections to the 23S1 → 11S0 + one photon transition rate in helium and helium-like lons

The order (Zα)⁵, α(Zα)⁴, and α(Zα)⁴ log(Zα) energy denominator and recoil corrections to the leading order (Zα)⁴ decay amplitude for the 2³S₁ → 1¹S₀ + one photon transition are considered. It is found that order α(Zα)⁴ terms arise in the individual diagrams but exactly cancel upon summation. In view of the results of this and other recent theoretical work it is concluded that the rates predicted by pure quantum electrodynamics are known to considerable precision. The recent discrepancy between theory and experiment in the decay rate for several helium-like ions appears to have been resolved by placing the detector farther downstream from the foil where the metastable states are produced. At present, all the experimental values are in good agreement with the theory.     

Vibrational characterization of carbon monoxide oxidation on the Pt(111) surface

The surface reaction between coadsorbed carbon monoxide and atomic oxygen has been characterized using high resolution electron energy loss spectroscopy, coupled with temperature programmed reaction spectroscopy on a Pt(111) surface characterized using Auger electron spectroscopy and low energy electron diffraction. Preferential oxidation of bridge bonded CO is not observed despite the fact that bridge bonded CO is adsorbed less vigorously than linearly bound CO. Saturation of the Pt(111) surface with one quarter of a monolayer of atomic oxygen completely suppresses the adsorption of bridge bonded CO. However, substantial coverages of bridge bonded CO can be coadsorbed if the Pt(111) surface is only partially saturated with atomic oxygen. The vibrational data for reaction of coadsorbed CO and atomic oxygen is consistent with a reaction mechanism involving reaction of mobile CO along oxygen island perimeters.     

Effect of age on detection of gaps in speech and nonspeech markers varying in duration and spectral symmetry

Gap detection thresholds for speech and analogous nonspeech stimuli were determined in younger and older adults with clinically normal hearing in the speech range. Gap detection thresholds were larger for older than for younger listeners in all conditions, with the size of the age difference increasing with stimulus complexity. For both ages, gap detection thresholds were far smaller when the markers before and after the gap were the same (spectrally symmetrical) compared to when they were different (spectrally asymmetrical) for both speech and nonspeech stimuli. Moreover, gap detection thresholds were smaller for nonspeech than for speech stimuli when the markers were spectrally symmetrical but the opposite was observed when the markers were spectrally asymmetrical. This pattern of results may reflect the benefit of activating well-learned gap-dependent phonemic contrasts. The stimulus-dependent age effects were interpreted as reflecting the differential effects of age-dependent losses in temporal processing ability on within- and between-channel gap detection.     

Uniform Field Re-entrant Cylindrical TE$$_{01\text {U}}$$ Cavity for Pulse Electron Paramagnetic Resonance Spectroscopy at Q-band

Uniform field (UF) resonators create a region-of-interest, where the sample volume receives a homogeneous microwave magnetic field (\(B_1\)) excitation. However, as the region-of-interest is increased, resonator efficiency is reduced. In this work, a new class of uniform field resonators is introduced: the uniform field re-entrant cylindrical TE\(_{\text {01U}}\) cavity. Here, a UF cylindrical TE\(_{\text {01U}}\) cavity is designed with re-entrant fins to increase the overall resonator efficiency to match the resonator efficiency maximum of a typical cylindrical TE\(_{011}\) cavity. The new UF re-entrant cylindrical TE\(_{\text {01U}}\) cavity is designed for Q-band (34 GHz) and is calculated to have the same electron paramagnetic resonance (EPR) signal intensity as a TE\(_{011}\) cavity, a 60% increase in average resonator efficiency \(\Lambda _\mathrm{ave}\) over the sample, and has a \(B_1\) profile that is 79.8% uniform over the entire sample volume (98% uniform over the region-of-interest). A new H-type T-junction waveguide coupler with inductive obstacles is introduced that increases the dynamic range of a movable short coupler while reducing the frequency shift by 43% during over-coupling. The resonator assembly is fabricated and tested both on the bench and with EPR experiments. This resonator provides a template to improve EPR spectroscopy for pulse experiments at high frequencies.