The Gaussian effective potential (GEP), a non-perturbative approach to study quantum field theory, is applied to scalar and scalar-fermion models. We study the scalar $\phi\sp6$ field coupled to fermions through g$\sb{\rm B}\phi\overline{\psi}\psi$ or g$\sb{\rm B}\phi\sp2\overline{\psi}\psi$ in 2 and 3 space-time dimensions. In addition, we derive the finite temperature (T $>$ 0) GEP from first principles and apply it to study these models at T $>$ 0. Also the Autonomous $\lambda\phi\sp4$, coupled to fermions through a Yukawa term (g$\sb{\rm B}\phi\overline{\psi}\psi$), is examined in 4 dimensions at T $>$ 0. In all these models, in order to obtain stable theories, it is found that g$\sb{\rm B}$ must vanish as 1/log(M$\sb{\rm uv}$), 1/M$\sb{\rm uv}$ or 1/M$\sbsp{\rm uv}{2}$ in 2, 3 or 4 dimensions respectively, M$\sb{\rm uv}$ being an ultraviolet cutoff which is sent to infinity. The contribution of fermions to the GEP, however, is nonvanishing. It is also found that for the class of theories discussed, symmetry, if broken, is restored above a critical temperature. The coupling constant parameter space for each model is studied carefully, and regions where symmetry breaking occurs are determined both at zero and finite temperature.

A polarized proton beam incident on a Beryllium target was used for inclusive $\Lambda$(1116 meV) production at beam momenta of 13.3 GeV and 18.5 GeV. The beam polarization was transverse to the beam direction with magnitude 0.63(0.40) at 13.3(18.5)GeV. The trigger condition favoured forward produced $\Lambda$'s with moderately high p$\sb{\rm T}$(p$\sb{\rm T}\sim$ 1GeV). The $\Lambda$ polarization was measured and found to be in agreement with results from earlier experiments which used unpolarized proton beams. Analyzing power (A) and depolarization (D$\sb{\rm NN}$) of the $\Lambda$'s were both measured and compared with a hyperon polarization model in which the polarization arises from a Thomas precession effect. There is good agreement with its predictions: A = 0 and D$\sb{\rm NN}$ = 0. In particular, our measurement of D$\sb{\rm NN}$ = $-$0.009 $\pm$ 0.015 supports the idea that the valence quarks carry all of the hadron spin, since this assumption is implicit in the model's use of SU(6) wave functions to form final state hadrons from beam fragments and sea quarks. The analyzing power of K$\sb{\rm s}$ was also measured at 13.3(18.5)GeV and found to be $-$0.094 $\pm$ 0.012($-$0.076 $\pm$ 0.015). We use the same model to predict A of K$\sb{\rm s}$, taking into account K$\sb{\rm s}$productgion from various sources (K$\sp\circ$, K$\sp\circ$ and K*) and find good agreement with the data. Finally a small sample of $\bar\Lambda$ was isolated from the 18.5GeV sample and was found to have A = 0.03 $\pm$ 0.1, consistent with the model's prediction of zero.

The present work concerns nonperturbative variational studies of the effective potential beyond the Gaussian effective potential (GEP) approximation. In the Hamiltonian formalism, we study the method of non-linear canonical transformations (NLCT) which allows one to perform variational calculations with non-Gaussian trial states, constructed by nonlinear unitary transformations acting on Gaussian states. We consider in detail a particular transformation that leads to qualitative as well as quantitative improvement over the Gaussian approximation. In particular we obtain a non-trivial correction to the Gaussian mass renormalization. For a general NLCT state, we present formulas for the expectation value of the $O(N)$-symmetric $\gamma(\phi\sp2)\sp2$ Hamiltonian, and also for the one-particle NLCT state energy. We also report on the development of a manifestly covariant formulation, based on the Euclidian path integral, to construct lower-bound approximations to $\Gamma\sb{1PI}$, the generating functional of one-particle-irreducible Green's functions. In the Gaussian approximation the formalism leads to the Gaussian effective action (GEA), as a natural variational bound to $\Gamma\sb{1PI}$. We obtain, non-trivially, the proper vertex functions at non-zero momenta, and non-zero values of the classical field. In general, the formalism allows improvement beyond the Gaussian approach, by applying nonlinear measure-preserving field transformations to the path integral. We apply this method to the $O(N)$-symmetric $\lambda(\phi\sp2)\sp2$ theory. In 4 dimensions, we consider two applications of the GEA. First, we consider the N = 1 $\lambda\phi\sp4$ theory, whose renormalized GEA seems to suggest that the theory undergoes SSB, but has noninteracting particles in its SSB phase. Second, we study the Higgs mechanism in scalar quantum electrodynamics (i.e., $O(2)$ $\lambda\phi\sp4$ coupled to a U(1) gauge field) in a general covariant gauge. In our variational scheme we can optimize the gauge parameter, leading to the Landau gauge as the optimal gauge. We derive optimization equations for the GEA and obtain the renormalized effective potential explicitly.

A steel-scintillator calorimeter has been designed to be used in a 250 GeV photon beam, and consists of approximately 10 nuclear absorption lengths of steel. Its sampling frequency is 1.5" and the sampling medium is 1/4" Kyowa SCSN-61T polystyrene based scintillator. Y7 Kyowa WLS was used to collect light into 8 Hamamatsu R2154 photomultipliers. A monitoring system has been built for the calorimeter. A LSI UV laser pumps a sample of SCSN-61T, which emits light that is subsequently shifted by Y7 and transported to the PM's via jacketted 1 mm acrylic fibers. It simulates the passage of a charged particle. A PIN photodiode also monitors the light output, for cross reference with the PM's. Interspersed among the steel and scintillator, there are 6 PWC's whose purpose is to discriminate between electromagnetic and hadronic showers. Some position information can be gathered. The PWC inter-wire spacing is approximately 1 cm. (Abstract shortened with permission of author.)

Computer simulation is used to study the ability of a proposed silicon-scintillating fiber tracking system for SDC to correctly interpret $Z\sp\prime\to e\sp+e\sp-$ events. Two versions of the Lund Monte Carlo model for inelastic non-diffractive events are compared to existing data and then evaluated at $\sqrt{s}=40$ TeV. We use the two versions to generate the associated particles in $Z\sp\prime\to e\sp+e\sp-$ events and find that the predicted occupancy in the proposed tracking system varies by $\approx$50% between the two versions. The tracking system is able to reconstruct the $e\sp+e\sp-$ tracks with nearly 100% efficiency in either case. We find that the leptonic asymmetry, $A\sb{fb}$ can be accurately measured for $.5\le M\sb{Z\sp\prime}\le 7$ TeV.

We calibrated a leadglass Pb-scintillator photon detector with a positron beam of 30 GeV. The detector consisted of a segmented leadglass counter in front and a Pb-scintillator sandwich counter in the back. The response of the sandwich counter exhibited an exponential dependence on the position of the incident particle. The calibration constants of the leadglass segments were obtained by an iterative method. The results of our analysis showed an energy resolution of $\sigma ({\rm E})\over {\rm E}$ = 24%/$\surd$E. A monitoring system using LED and $\sp{241}$Am sources regularly checked the stability of all modules. A typical photomultiplier's gain factor deviated no more than 6% from the mean value at any time during a period of three months.

The Spin Muon Collaboration was formed to measure the spin dependent structure function $g\sb1$ of both the proton and the neutron. This was done by scattering polarized muons off of polarized protons or deuterons. The results provided a test of three sum rules: the Ellis-Jaffe sum rule for the proton, the Ellis-Jaffe sum rule for the neutron, and the Bjorken sum rule. Two polarimeters were used to measure the beam polarization. The polarimeter discussed in this thesis used elastic scattering from polarized electrons to measure the muon beam polarization. It gave a result in agreement with both the previous measurement using muon decay and a simulation of the beamline. These measurements helped reduce the systematic error on the measurement and improve the measurements of the sum rules. The results from the experiment showed that both Ellis-Jaffe sum rules were violated while the Bjorken sum rule was confirmed.

As part of an eventual experiment to measure the gravitational acceleration of the antiproton, we have designed, constructed and tested an extended-length, harmonic Penning-type ion trap. A distributed-electrode design allows the radial inside dimension to be kept at a minimum (1 $cm$) while extending the axial length to 15 $cm$. In-flight capture of 10-$keV$ protons from a continuous-beam ion source has been achieved. A storage time decay constant of 4.78 $\pm$ 1.25 $s$ has been observed and is shown to be dominated by losses due to collision with the residual gas. Resonant excitation of the axial motion of the trapped ions has demonstrated the harmonicity of the trap in both the linewidth of the resonance and the agreement between observed and calculated frequency of axial motion for protons in the harmonic well. The harmonic quality factor $Q$ = $f$/$\Delta f$ is observed to be 120. Systematic uncertainties allow for agreement of the observed capture efficiency with the expected 100%, although future work will be necessary. Possible future improvements to the system, some already implemented, are mentioned.

Jets produced in high transverse energy proton-nucleus collisions at 400 GeV/c were recorded in a calorimeter study at Fermilab. The jets were identified with two different jet-finding algorithms; the results from the two algorithms agree. For the eight nuclear targets with atomic number, A, ranging from 1 to 207 (H$\sb2$, He, Be, C, Al, Cu, Sn and Pb), the cross section increases as A$\sp{1.35\pm0.01}$ over mean jet pair transverse momentum of 4 to 8 GeV/c. The enhancement, however, depends on the class of jets selected; for example the cross section increases as A$\sp1$ for highly planar high-transverse-momentum jet events and as A$\sp{1.65}$ for non-planar high-transverse-momentum events. Jet properties were studied as a function of jet transverse momentum and A. In general as A increases, the number of particles in the jets increases while their collimation and coplanarity decrease. Also with increasing A, the proton transfers more of its energy into the target fragmentation region instead of the forward or central regions. Multiple scattering models describe nuclear enhancement, however fits to our data require negative coefficients in the higher order terms of the expansion, presenting a challenge to simple multiple scattering models.

We have measured, for the first time, the atomic number dependence of photon-nucleus collisions at high transverse energy. The measurements were made at FNAL by using a large acceptance calorimeter with 50-400 GeV photons incident on LH$\sb2,$ LD$\sb2,$ Be, C, Al, Cu, Sn and Pb targets. The cross section is parameterized as $\sigma\sb{\gamma A} = \sigma\sb{\gamma p}A\sp\alpha,$ where $\alpha$ is found to increase from 0.9 to 1.1 when the total transverse energy $E\sb{T}$ is increased from roughly 6 GeV to 12 GeV; $\alpha$ is also found to increase with the photon energy at fixed $x\sb{T}\equiv E\sb{T}/\sqrt{s},$ but depends only weakly on the photon energy at fixed $E\sb{T}.$ The increase of $\alpha$ with total transverse energy is qualitatively consistent with previous measurements from the hadron-nucleus collisions, but our $\alpha$ values are somewhat lower. At high transverse energy, photon induced collisions are found to be more jet-like than pion induced collisions, revealing the point-like nature of the photons at high $E\sb{T}.$ The mean planarity in $\gamma A$ collisions is independent of A in the kinematic range covered by this experiment.