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The Polymer Optical interconnect Technology (POINT) is a collaborative program among GE, Honeywell, AMP, AlliedSignal, Columbia University and University of California at San Diego (UCSD), sponsored by ARPA, in developing affordable optoelectronic packaging and interconnect technologies for board- and backplane-level optical interconnect applications. The POINT program leverages on the existing electronic design, processing, fabrication and MCM packaging technologies to optoelectronic packaging. The POINT program also incorporates several state-of-the-art optoelectronic technologies that include: high speed VCSEL for multi-channel data transmission; flexible optical polymer waveguides and low-loss polymers for board and backplane interconnects; low-cost diffractive optical elements (DOE) for board-to-backplane interconnect; and use of molded MT-type connectors to reduce weight and size. In addition, to further reduce design and fabrication cycle times, CAD tools for multimode optical waveguide modelling, and for mechanical modelling of optoelectronic packaging will be employed to aid the technology development.

We developed a statistical model of the passive alignment process. This model allows us to calculate the distribution of VCSEL to waveguide alignment tolerances for laser micromachining of the waveguide and pedestal alignment features. Using this distribution as input for the optical model, the distribution of optical coupling efficiencies for the packaging tolerances was calculated. The coupling efficiencies for the passively aligned waveguides to the VCSEL array sources were measured and compared to the simulation results.

The technical approach and progress achieved under the Polymer Optical Interconnect Technology (POINT) program are described in this paper. The POINT program is a collaborative effort among GE, Honeywell, AMP, AlliedSignal, Columbia University, and University of California at San Diego (UCSD), sponsored by DARPA/ETO, to develop affordable optoelectronic packaging and interconnect technologies for board and backplane applications. Specifically, progress is reported on (a) development of batch-operated plastic VCSEL array packaging technology using planar fabrication, (b) demonstration of high-density optical interconnects for board and backplane applications using polymer waveguides to a length of 50 cm at an I/O density of 250 channels per inch, (c) development of low-loss optical polymer waveguides with loss less than 0.1 dB/cm at 850 nm, and (d) development of passive alignment processes for efficient coupling between a VCSEL array and polymer waveguides. Significant progress has also been made under the POINT program at Columbia University, in applying CAD tools to simulate multimode-guided wave systems and, at UCSD, to assist mechanical and thermal design in optoelectronic packaging.

Due to the explosive growth in high speed network communication and the rapid advance in the processor speed and processing power, data transfer bandwidths between chips, modules, board, backplane and cabinets have increased drastically. The required interconnect bandwidths for efficient data communication across different platforms have increased accordingly. The optical backplane offers a much higher data bandwidth and interconnect density with minimum cross-talk. However, in order to successfully deploy optical interconnect in complex electronic systems such as board and backplane and offer performance/cost comparable of superior to electronic solutions, the development of optoelectronic interconnect devices, components, packaging and processing technologies must be compatible with the existing electronic interconnect counterparts. In this work, we report the recent development of high density optical interconnect technology using VCSEL and polymer waveguides for board and backplane level applications.

This paper describes the technical approach and progresses of the POINT (Polymer Optical Interconnect Technology) program. This project is a collaborative effort among GE, Honeywell, AMP, AlliedSignal, Columbia University and University of California at San Diego (UCSD), sponsored by DARPA/ETO to develop affordable optoelectronic packaging and interconnect technologies for board and backplane applications. In this paper, we describe the recent development under this program in the following areas: (a) a high density optical interconnect for board and backplane applications using polymer waveguides (Polyguide) to demonstrate high I/O density (100 /spl mu/m channel spacing) and high speed (/spl sim/1 Gbps) interconnect with an interconnect distance to 280 mm, (b) a high density and high speed VCSEL array packaging technology that employs planar and batch fabrication processes scaleable to large volume, low-cost manufacturing, (c) passive alignment techniques for reducing the recurrent cost in an optoelectronic assembly, (d) low-loss optical polymers for board and backplane level interconnects, and (e) CAD tools for modeling multimode guided wave systems and assisting optoelectronic packaging mechanical design.

As CDs continue to shrink, lithographers are moving more towards using off-axis illumination schemes to increase their CD budget. There have been several papers over the last few years describing various custom illumination profiles designed for application specific optimization. These include various annular and quadrupole illumination schemes including weak quadrupole, CQUEST, and QuasarTM. Diffractive optics, if incorporated into the design of the illumination system, can be used to create arbitrary illumination profiles without the associated light loss, thus maintaining throughput while optimizing system performance. Diffractive optical elements used to generate efficient illumination profiles for 248 nm and 193 nm excimer laser-source scanners, have been reported and realized in fused silica. The fabrication of such elements in calcium fluoride (CaF2), for use in 157 nm wavelength lithographic projection tools has been developed and is presented in this paper. Three different categories of elements are shown: large-diagonal-cluster diffusers, medium- and small-rectangular-cluster diffusers. The diffusers were fabricated as binary phase devices, in order to determine calcium fluoride processing capabilities.

Almost all lattice work on confinement has been carried out for an SU (2) gauge group. This is a good starting point. Confinement is caused by glue and every physicist believes that there is no essential physical difference in the confining properties of glue for SU (N), for arbitrary N. Despite this, in confinement by topological objects, questions arise for SU (3) which have no SU (2) analog. We discuss two of these. The first involves the fact that the formulation of the maximal abelian gauge (MAG) is more subtle for SU (3) than it is for SU (2). Calculations with the simplest form give poor results for the string tension (Sec. (3)). A generalized form which appears more natural is suggested (Sec. (4)). The second question has to do with the subgroup structure of monopoles, and their relation to P-vortices. There are strong arguments that monopoles should be associated with SU (2) subgroups of SU (3). There is also good evidence from our SU (3) lattice calculations that P-vortices pass through monopoles. This appears to be paradoxical at first, since P-vortices carry only center flux. We show how these two properties can coexist (Sec. (5)). We begin with a general discussion of gauge-fixing and projection (Sec. (2)).

We present results for the fundamental string tension in SU(2) lattice gauge theory after projection to maximal abelian and direct maximal center gauges. We generate 20 Gribov copies/configuration. Abelian and center projected string tensions slowly decrease as higher values of the gauge functionals are reached., 3 pages, latex, 1 postscript figure, presented at Lattice 2000(Topology and Vacuum)

We present results for the heavy quark potential computed in SU(3) from magnetic monopoles and from center vortices. The monopoles are identified after fixing SU(3) lattice configurations to the maximal abelian gauge. The center vortices are identified after using an indirect center gauge fixing scheme which we describe for SU(3). Z(3) center vortices are extracted and used to compute the potential. The values of the string tensions from monopoles and vortices are compared to the full SU(3) string tension., Lattice 2000 (Topology and Vacuum), 4 pages, latex, 2 postscript figures

Graded index fiber has a limited bandwidth due to defects introduced in the fiber manufacturing process. In this paper, an alternative launch technique is presented using a diffractive element to excite specific modes in a fiber to maximize the bandwidth of graded index fiber.

Bioinspired copper-model-complexes that react with O2 provide an opportunity to probe biological reactivity at a small-molecule level of detail. Biological structural information combined with appropriate ligand design has proven sufficient to create Cu:O2 complexes capable of external substrate oxidation. Most notable developments during the review period are the bioinspired catalysts capable of aerobic alcohol-oxidation. The extension of this oxidative reactivity to other important organic transformations beyond the scope of the inspiring system completes a modeling paradigm.

An alternative method is presented for launching light into graded index fiber. This approach utilizes a diffractive element to match the phase of the launched light into specific modes of the graded index fiber.

Standard laser welding practices are limited by the intensity profile of the beam and spot size. The introduction of Diffractive Optical Elements (DOE) to the welding process allows for new beam shapes that are better suited to the welding process. A particular problem in laser welding is the joining of dissimilar materials. Because these materials have different material properties including different melting temperatures, it is difficult to synchronize the welding process using a single spot. Additionally, significant thermal stresses are introduced by the welding process because of the keyhole weld shape formed by a gaussian beam. By using a power splitting DOE, two spots of unequal intensity distributions may be projected onto each side of the weld joint. This paper discusses the use of DOEs in laser welding and joining of dissimilar materials. Results are presented from the testing of several candidate aerospace materials.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Silicon v-groove structures have been utilized for passive positioning of optical fiber for fiber optic and opto- electronic applications. In this paper, we will present our results of using micro-machined silicon v-groove arrays to passively align optical fiber arrays to micro rod optics. We will also demonstrate the integration of N fiber arrays bonded into the silicon v-groove with a 1xN micro lens array, which is composed of a 2 inch-phase level diffractive optics. For the assembly of 1x6 fiber array and lens array with 16 phase level diffractive optics, the experimental results indicated that total insertion loss per link is typically 1.5-2.0 dB/channel.

Does media endorsement for catharsis produce a self-fulfilling or a self-defeating prophecy? In Study 1, participants who read a procatharsis message (claiming that aggressive action is a good way to relax and reduce anger) subsequently expressed a greater desire to hit a punching bag than did participants who read an anticatharsis message. In Study 2, participants read the same messages and then actually did hit a punching bag. This exercise was followed by an opportunity to engage in laboratory aggression. Contrary to the catharsis hypothesis and to the self-fulfilling prophecy prediction, people who read the procatharsis message and then hit the punching bag were subsequently more aggressive than were people who read the anticatharsis message.

We review GaAs Fabry-Perot vertical cavity multiple quantum well (MQW) spatial light modulators (SLMs) developed at Sanders, a Lockheed Martin Company, and demonstrate their use in optical image correlation. These MQW SLMs are reflective- mode modulators using electrically-tunable absorption to modulate the reflected intensity. The operation of the MQW SLMs with a newly-developed Labview graphical user interface is described. A compact Vander-Lugt image correlator is described which was configured using MQW SLMs: binary 128 X 128 pixel image input with a binary filter plane. In addition, the architecture of 8-bit gray-scale MQW-SLM module developed at Sanders is discussed. The performance of the image correlator was characterized using amplitude-encoded binary phase-only filters and various test targets including test imagery supplied by US Army AMCOM, and is compared with simulations for peak-to-secondary efficiencies on these data. Finally, high-speed (250,000 frames per second) target recognition of 128 X 128 pixels binary input imagery is demonstrated.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Lockheed Martin Sanders' Integrated Optoelectronics Group makes flexible smart-pixel devices for a variety of applications.

We review GaAs Fabry-Perot vertical cavity electro-optical devices constructed at Lockheed Martin Sanders, with particular attention to spatial light modulators and discuss a number of their applications. Our manufacturing processes enable the construction of large format, highly-uniform optical modulator and smart pixel arrays integrated with silicon CMOS VLSI circuitry. These devices can be used for a wide variety of applications including: optical computing for target recognition and signal processing, optical data routing, optical interconnect systems, and optical memory storage and access.

JohnAlfredTrezzaJeffry S. Powell, Charles Garvin, Keith Kang, Richard StackSanders, A Lockheed Martin Company, 65 Spit Brook Road, NHQ6-1551, Nashua, NH 03060Vertical cavity optoelectronic modulators are the key component for future real-time electro-opticalsignal processing, computing, optical memory access, free-space optical interconnect, informationprocessing, laser printing, and data conversion systems. Here we will discuss the operation and operatingprinciples of our optical devices, the integration of these devices into large arrays, the experimentalcharacteristics of large arrays of devices, and the use of the arrays.The quantum well device arrays that we produce are comprised of "MED pixels". These are surfacenormal devices constructed (by molecular beam epitaxy) out ofthe 111-V semiconductor material system.MED pixels are so called because they:1) Modulate light: The devices can be operated in a mode in which they alter either the amplitude (onor off), the phase (0° to 360°), or the direction (either unimpeded, or altered by simple reflection).2) Emit light: The devices can be operated as resonant cavity light emitting diodes, providing outputlight that, while not coherent, is spatially collimated and spectrally confined.3) lletect light: The devices can be operated as detectors for incident light.A given pixel can perform all three of these types of operations (though one typically chooses eitherphase or amplitude modulation as one of the three properties); the type of behavior that a given MEDpixel exhibits at any one time is determined by the control signal which is applied at any given moment.When such arrays consist of close-packed pure modulating or light emitting pixels, they are referred toas 'spatial light modulator' (SLM) or 'spatial light emitter' (SLE) arrays respectively. We typicallycombine optical chips containing large (up to 1x2048 and 256 x 256) arrays of GaAs MED pixels withcustom SRAM CMOS chips. The GaAs optical and silicon driver chips are combined by placing solderbumps on the chips and then using these bumps as electrical contacts between individual optical pixelsand silicon transistor circuits. The resultant hybrid electro optical chip is then sealed, wirebonded intoan IC package, and hermetically contained. We have used this 'flip-chip' bonding technology to connectpixelated GaAs devices to silicon drivers on chips over 2 square centimeters in size, containing as manyas 307,000 pixels with pixel yields of 99.98% uncorrected and 99.998% with electrical correction. TheSRAM chips (currently 2 x 65k) can store data bits and output data optically through the optical chip.These arrays, then, are ultra-fast electrical to optical (and optical to electrical) transducers where hugeparallelism exists.Electrical data input into our 256x256 array is through a series of 256 input lines, each of which isclocked in parallel into the array. Thus, the array takes 256 clocks to load an image (our 128x128 arrayhandles 128 input lines and takes 128 clocks to load). The CMOS SRAM driver chip allows two fullframes of binary mode data can be stored at any one time. Electronic data is loaded into the CMOS's'back buffer page' while another page of memory is displayed through the optical chip. When the back

The technical approach and progress achieved under the Polymer Optical Interconnect Technology (POINT) program are described in this paper. The POINT program is a collaborative effort among GE, Honeywell, AMP, AlliedSignal, Columbia University, and University of California at San Diego (UCSD), sponsored by DARPA/ETO, to develop affordable optoelectronic packaging and interconnect technologies for board and backplane applications. Specifically, progress is reported on (a) development of a plastic VCSEL array packaging technology using batch and planar fabrication, (b) demonstration of high-density optical interconnects for board and backplane applications using polymer waveguides to a length of 50 cm at an I/O density of 250 channels per inch, (c) development of low-loss optical polymer waveguides with loss less than 0.1 dB/cm at 850 nm, and (d) development of passively alignment processes for efficient coupling between a VCSEL array and polymer waveguides. Significant progress has also been made under the POINT program at Columbia University, in applying CAD tools to simulate multi-mode-guided wave systems and, at UCSD, to assist mechanical and thermal design in optoelectronic packaging. Because of space limitations, these results will be described elsewhere in future publications.

Optical connectors utilize microlens elements for coupling light into and out of fibers. Typically, these lenses are based on sapphire ball lenses or Gradient Index lens elements.However, lenses that are on the same scale as the single-mode fiber itself have not been previously realized. This paper introduces an optical lens element that fits into the single-mode optical ferrule, without any modifications to the connector package. This approach offers substantial performance and cost benefits over other methods.Both theoretical and experimental results are presented.

GaAs asymmetric Fabry-Perot vertical cavity modulators are useful in a wide variety of applications. Vertical cavity devices have employed amplitude or phase modulation for optical switching. Amplitude modulators have been demonstrated in large format arrays. Additional uses for the pixels include directional modulation, detection, and light- emitting capability. When arrays of these deices are integrated with electronic circuits - most significantly silicon CMOS VLSI - at the pixel level, large, complex optical spatial light modulators, detectors, transceivers, computation devices, and emitters can be created for a wide variety of applications. These applications range from target recognition to SAR radar processing, to optical data routing, to optical interconnect systems, to optical memory access.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

We apply smoothing to SU(2) lattice field configurations in 3+1 dimensions before fixing to the maximally Abelian gauge. The Abelian projected string tension is shown to be stable under this, whilst the monopole string tension declines by O(30%). Blocking of the SU(2) fields reduces this effect, but the use of extended monopole definitions does not. We discuss these results in the context of additional confining excitations in the U(1) vacuum., Comment: LATTICE98(confine)

This paper describes the technical approach and progresses of the POINT program. This project is a collaborative effort among GE, Honeywell, AMP, AlliedSignal, Columbia University and University of California at San Diego, sponsored by DARPA/ETO to develop affordable optoelectronic packaging and interconnect technologies for board and backplane applications. In this paper, we report the development of a backplane interconnect structure using polymer waveguides to an interconnect length of 280 mm to demonstrate high density and high speed interconnect, and the related technical development efforts on: (a) a high density and high speed VCSEL array packaging technology that employs planar fabrication and batch processing for low-cost manufacturing, (b) passive alignment techniques for reducing recurrent cost in optoelectronic assembly, (c) low-cost optical polymers for board and backplane level interconnects, and (d) CAD tools for modeling multimode guided wave systems and assisting optoelectronic packaging mechanical design.

We present results suggesting that magnetic monopoles can account for chiral symmetry breaking in abelian gauge theory. Full U(1) configurations from a lattice simulation are factorized into magnetic monopole and photon contributions. The expectation is computed using the monopole configurations and compared to results for the full U(1) configurations. It is shown that excellent agreement between the two values of is obtained if the effect of photons, which "dress" the composite operator psibarpsi, is included. This can be estimated independently by measurements of the physical fermion mass in the photon background., Comment: 14 pages REVTeX, including 5 figures

The phase diagram is investigated for SU(2) lattice gauge theory in d=3, coupled to adjoint scalars. For small values of the quartic scalar coupling, lambda, the transition separating Higgs and confinement phases is found to be first-order, in agreement with earlier work by Nadkarni. The surface of second-order transitions conjectured by Nadkarni, however, is shown instead to correspond to crossover behaviour. This conclusion is based on a finite size analysis of the scalar mass and susceptibility. The nature of the phase transition at the termination of first-order behaviour is investigated and we find evidence for a critical point at which the scalar mass vanishes. The photon mass and confining string tension are measured and are found to be negligibly small in the Higgs phase. This is correlated with the very small density of magnetic monopoles in the Higgs phase. The string tension and photon mass rise rapidly as the crossover is traversed towards the symmetric phase., LaTeX. Replaced with version to be published in Physics Letters B. Minor changes only

The coupling of a vertical cavity surface emitting laser (VCSEL) array into an array of multimode polymer waveguides through a 45 degree endface mirror is investigated. A coupling model for the VCSEL and waveguide interface is developed and compared with our experimental results.

The Polymer Optical Interconnect Technology (POINT) represents a major collaborative effort among GE, Honeywell, AMP, AlliedSignal, Columbia University and the University of California at San Diego (UCSD), sponsored by ARPA, in developing affordable optoelectronic module packaging and interconnect technologies for board- and backplane- level optical interconnect applications for a wide range of military and commercial applications. The POINT program takes a novel development approach by fully leveraging the existing electronic design, processing, fabrication and module packaging technologies to optoelectronic module packaging. The POINT program further incorporates several state-of-the-art optoelectronic technologies that include high-speed VCSEL for multichannel array data TM transmission; flexible optical polymers such as Polyguide or coupling of device-to-fiber using a passively alignment process; a low-loss polymer for backplane interconnect to provide a high I/O density; low-cost diffractive optical elements (DOE) for board-to-backplane interconnect; and use of molded MT array ferrule to reduce overall system size, weight, and cost. In addition to further reducing design and fabrication cycle times, computer simulation tools for optical waveguide and mechanical modeling will be advanced under the POINT program.

We resolve a discrepancy between the SU(2) spacial string tension at finite temperature, and the value obtained by monopoles in the maximum Abelian gauge. Previous work had incorrectly omitted a term due to Dirac sheets. When this term is included, the monopole and full SU(2) determinations of the spacial string tension agree to within the statistical errors of the monopole calculation., Comment: 8 pages, Latex files: msum.tex,msum.aux packaged with uufiles

Confinement via 't Hooft-Mandelstam monopoles is studied for the positive plaquette model in SU(2) lattice gauge theory. Positive plaquette model configurations are projected into the maximum abelian gauge and the magnetic current extracted. The resulting magnetic current is used to compute monopole contributions to Wilson loops and extract a monopole contribution to the string tension. As was previously found for the Wilson action, the monopole contribution to the string tension agrees with the string tension calculated directly from the SU(2) links. The fact that the positive plaquette model suppresses Z2 monopoles and vortices is discussed., Comment: 8 pages, one Postscript figure, Latex, uses psfig files: posplaq.tex,posplaq.aux,pp_1_3.ps packaged with uufiles

The axis for Figure 2 was wrong. It has been fixed and the postscript file replaced (The file was called comp.ps)., Comment: (22 pages latex (revtex); 2 figures appended as postscript files - search for mono.ps and comp.ps. Figures mailed on request--send a note to rwensley@stmarys-ca.edu) Preprint ILL-(TH)-94-#14

We calculate the heavy quark potential from the magnetic current due to monopoles in four dimensional $U(1)$ lattice gauge theory. The magnetic current is found from link angle configurations using the DeGrand-Toussaint identification method. The link angle configurations are generated in a cosine action simulation on a $24^4$ lattice. The magnetic current is resolved into large loops which wrap around the lattice and simple loops which do not. Wrapping loops are found only in the confined phase. It is shown that the long range part of the heavy quark potential, in particular the string tension, can be calculated solely from the large, wrapping loops of magnetic current., Comment: 15 pages (Latex file plus 3 postscript files appended), Univeristy of Illinois Preprint ILL-(TH)-93-\#15

Using Monte Carlo methods and the icosahedral approximation to SU(2), the heavy quark potential has been determined for SU(2) lattice gauge theory. The range of distances covered is 0.05 fm to 1 fm for a string tension of 400 MeV. The results are compared to perturbation theory, string theory, and the phenomenological potential of Martin. A simple Coulomb plus linear form gives a good overall representation of the potential.

We study the effect of vortices of different size on the long range heavy quark potential. Under certain simplifying assumptions, we find that the subdominant term in the potential at long range is controlled by the distribution of vortices of large size.

The iterative discrete on-axis (IDO) method1 is a computer generated hologram (CGH) encoding algorithm that employs iterative optimization routines such as simulated annealing. The IDO method has been used for the optimization of large 2-D even numbered, spot arrays for optical interconnect applications. Even numbered spot arrays have several performance advantages including low sensitivity to fabrication errors, and reduced computational complexity. Binary and multiple phase level CGHs have been designed and fabricated. Intensity and/or phase of the individual output pixels can be controlled. Methods to decrease the computation time, similar to the recursive mean squares error function described in Ref. 2, have been developed for this use. Diffraction efficiencies of up to 84% have been achieved for generating spot arrays with 100–1024 points.

A hybrid-algorithm has been developed that uses the concept of a rapid recursive mean-squared-error (RMSE) function combined with the annealed, multiphase, on-axis capabilities of iterative discrete on-axis (IDO) encoding. High diffraction efficiency and computational speed are obtained through the use of the RMSE algorithm with a constant weighting coefficient in the error function and an iterative initial process for determining phase codes in the output plane. Results for large even spot arrays are presented, and comparisons are made for diffraction efficiency, spot uniformity, and computation speed between the original IDO and the RMSE-based IDO encoding.

Mesons with heavy quarks are modeled by putting fermions on the ends of a string. The spin dependence of the fermion potential over large distances is found by solving for the classical motion of a rotating string. Some general remarks about such theories of “heavy” strings are also made.

We study the instanton in the nonlinear two-dimensional < or = model and show that it can be interpreted, in Minkowski space, as a tunneling process through a potential barrier between two vacuums. In this case the process carries nontrivial winding number. We then show, using this interpretation, that the sigma-model vacuum is nevertheless unique by demonstrating that two such vacuums may also be connected by processes that carry zero winding number and which do not require tunneling through a barrier. Some geometrical aspects of instanton solutions are also given.

The string tension is calculated using magnetic monopoles in three-dimensional U(1) lattice gauge theory. The monopoles are identified in configurations of link angles generated in a simulation on a 32{sup 3} lattice. Wilson-loop values are determined by the monopoles' flux through the loop. The string-tension results are in excellent agreement with a semiclassical analytic formula.

Using Monte Carlo methods and the icosahedral approximation to SU(2), the heavy quark potential has been determined for SU(2) lattice gauge theory. The range of distances covered is 0.05 fm to 1 fm for a string tension of 400 MeV. The results are compared to perturbation theory, string theory, and the phenomenological potential of Martin. A simple Coulomb plus linear form gives a good overall representation of the potential.

Monte Carlo calculations have been carried out on Z/sub 2/ lattice gauge theories in d=3 and d=4 space-time dimensions. For d=3, for the gauge-Higgs system, the results show a phase diagram in which the Higgs and confined regions are smoothly connected. There are lines of phase transitions surrounding the unconfined region; first-order behavior occurs on and near the self-dual line. For d=4, for the pure gauge system, we confirm the results of Creutz et al., that the transition between confined and unconfined regions is first order.

The results of a high statistics calculation of the SU(3) heavy quark potential are presented. The validity of scaling is tested quantitatively. New results are given for the string tension and the strength of the long-range Coulomb term in the potential.

We report on a pure gauge SU(3) lattice theory computation performed on an array of 64 microprocessors interconnected as a 2/sup 6/ hypercube and having the cumulative power of approximately eight VAX11/780's. The availability of a substantial number of computer cycles, coupled with an improvement in the algorithm, made possible a high-statistics determination of the heavy-quark potential on a 12/sup 3/ x 16 lattice.

We examine the calculation of O ( α S ) corrections to Drell-Yan pair production and find that off-shell and on-shell methods for regulating infrared divergences, when properly applied, lead to the same cross section. We show further that the on-shell quark-antiquark cross section is the relevant quantity for the calculation of corrections to the Drell-Yan process, in spite of the fact that hadrons contain off-shell constituents.

We analyze 't Hooft's method for evaluating Gaussian fluctuations around semiclassical field configurations and also propose a new approximate method. The analysis of 't Hooft's method starts from a soluble quantum-mechanical tunneling problem involving a double-well potential. In addition, we analyze in an appendix a one-dimensional example first proposed by Patrascioiu. The example has infrared structure similar to that encountered in calculating Gaussian fluctuations around an instanton in non-Abelian gauge theory. We find in general that 't Hooft's method, which expresses a functional determinant in terms of products of discrete eigenvalues, is valid, provided the correct eigenvalues are used, and certain zero-mode normalization factors are handled with care. In the calculation of fluctuations around a gauge-theory instanton, we confirm Patrascioiu's result that the individual partial-wave determinants are infrared divergent. We show that these divergences cancel and yield 't Hooft's finite answer for the full determinant if 't Hooft's regulators with spatially varying masses are used. However, it is pointed out that the variable-mass regulators always suppress all dependence on the infrared cutoff, so they are in fact acting as regulators in both ultraviolet and infrared regions. A convincing demonstration of infrared finiteness for the full determinant calculated with fixed-mass regulatorsmore » is still lacking. The approximate method we propose should be useful in handling cases where the semiclassical field configuration is more general than a single instanton. The method combines Weinberg's quasiparticle technique in potential scattering with a convenient way of extracting ultraviolet divergences.« less