Thesis--Wisconsin. / Vita. Includes bibliographical references (leaf 57).

Thesis (Ph. D.)--University of Missouri-Columbia, 1998. / Typescript. Vita. Includes bibliographical references (leaves 84-85). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1998. / Typescript. Vita. Includes bibliographical references (leaves 84-85). Also available on the Internet.

Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / A technique capable of describing in detail the various phenomena arising in the limit of low energy photons because of the polarization of the vacuum is obtained by quantizing the gauge invariant effective interaction Lagrangian. This approach then permits the use of the standard covariant calculational tools of Quantum Electro-dynamics. We first apply this technique to the computation of the differential cross section for low energy photon-photon scattering. The well known Euler cross section is thereby derived in a direct manner. As a second example, the probability of the triple breakup of a free photon because of vacuum polarization is explicitly shown to vanish. This, however, is primarily due to the kinematics of the photon breakup. For a third application we calculate the differential cross section for the scattering of a low energy photon from the Coulomb field of a nucleus, that is, Delbruck scattering. Here the exact low energy differential cross section is obtained. However, though the present technique determines completely the angular dependence, it is necessary to introduce a momentum cutoff in the Coulomb field in order to obtain a finite value for the coefficient in front of the angular dependence. A comparison of the resulting expression for the cross section with that for forward scattering given by Rohrlich and Gluckstern (1952) gives the numerical value of this coefficient. A brief comparison between the angular distribution for Delbruck scattering and that for a combination of an electric and magnetic dipole radiator is presented. / 2031-01-01

Quantum gravity is one of the interesting fields in contemporary physics which is still in progress. The purpose of quantum gravity is to present a quantum description for spacetime at 10 33cm or find the `quanta' of gravitational interaction.. At present, the most viable theory to describe gravitational interaction is general relativity which is a classical theory. Semi-classical quantum gravity or quantum field theory in curved spacetime is an approximation to a full quantum theory of gravity. This approximation considers gravity as a classical field and matter fields are quantized. One interesting phenomena in semi-classical quantum gravity is Hawking radiation. Hawking radiation was derived by Stephen Hawking as a thermal emission of particles from the black hole horizon. In this thesis we obtain the spectrum of Hawking radiation using a new method. Vacuum is defined as the possible lowest energy state which is filled with pairs of virtual particle-antiparticle. Vacuum polarization is a consequence of pair creation in the presence of an external field such as an electromagnetic or gravitational field. Vacuum polarization in the vicinity of a black hole horizon can be interpreted as the cause of the emission from black holes known as Hawking radiation. In this thesis we try to obtain the Hawking spectrum using this approach. We re-examine vacuum polarization of a scalar field in a quasi-local volume that includes the horizon. We study the interaction of a scalar field with the background gravitational field of the black hole in the desired quasi-local region. The quasi-local volume is a hollow cylinder enclosed by two membranes, one inside the horizon and one outside the horizon. The net rate of particle emission can be obtained as the difference of the vacuum polarization from the outer boundary and inner boundary of the cylinder. Thus we found a new method to derive Hawking emission which is unitary and well defined in quantum field theory. / ix, 109 leaves : ill. ; 29 cm

Vacuum polarization by electric fields is a well established fact. Assuming that anti-matter has negative gravitational properties, the fluctating electric dipoles from the quantum vacuum may also have gravitational dipolar properties. A model is developed that describes how electric fields could gravitationally polarize the vacuum causing gravitational screening or anti-screening effects. This leads to a violation of the Weak Equivalence Principle or a general mass change most notabily for elementary particles, such as the electron or positron, below but close to measured boundaries. Also a gravitational vacuum torque is predicted to act on a charged capacitor perpendicular to a gravitational field. The predictions could be verified by future laboratory experiments that could contribute on our understanding of the gravitational properties of anti-matter.

We present and explore a new formulation of perturbative QCD based not on the renormalised coupling but on the dimensional transmutation parameter of the theory and the property of asymptotic scaling. The approach yields a continued function, the iterated function being that involved in the solution of the two-loop β-function equation. In the so-called large-b limit the continued function reduces to a continued fraction and the successive approximants are diagonal Padé approximants. We investigate numerically the convergence of successive approximants using the leading-b approximation, motivated by renormalons, to model the all-orders result. We consider the Adler D-function of vacuum polarisation, the Polarised Bjorken and Gross-Llewellyn Smith sum rules, the (unpolarised) Bjorken sum rule, and the Minkowskian quantities R(_r) and the R-ratio of e(^+)e(^-) annihilation. In contrast to diagonal Fade approximants the truncated continued function method gives remarkably stable large-order approximants in cases where infra-red renormalon effects are important. We also use the new approach to determine the QCD fundamental parameters from the R(_r) and the R-ratio measurements, where we find Ā(^(3))(_MS)=516±48 MeV (which yields a(_s)(µ=m(_r))=0.360(^+0.021)(_=0.020)), and Ā(^(5))(_MS)=299(^+6)(_-7) MeV (which yields a(_s)(µ=m(_zo)=0.1218±0.0004), respectively. The evolution of the former value to the m(_zo) energy results in a(_s)(µ= m(_zo)) = 0.123 ± 0.002. These values are in line with other determinations available in the literature. We implement the Complete Renormalisation Group Improvement (CORGI) scheme throughout all the calculations. We report on how the mathematical concept of Stieltjes series can be used to assess the convergence of Padé approximants of perturbative series. We find that the combinations of UV renormalons which occur in perturbative QCD may or may not be Stieltjes series depending on the renormalisation scheme used.

In the present work the vacuum polarization and the circular dichroism of hydrogen-like atoms are studied. We derive equations for the Fourier transforma- tion of the vacuum expectation value of the charge density. We use it to derive Uehling potential and calculate energy shifts caused by it. Then we discuss effects of vacuum polarization in higher orders of α. In second part we define circular dichroism and we express it in terms of reduced matrix elements. Then we derive the formula for parity vilating potential which is generated by weak interaction and together with other results we use it to find the expression for circular dichro- ism in terms of hydrogen radial functions. 1

The thesis is divided into two parts. The first part deals with radiative cor- rections in muonic hydrogen. The effect of vacuum polarization is studied, and the simplified derivation of the Wichmann-Kroll potential is presented. The en- ergy shift caused by vacuum polarization to the Lamb shift in muonic hydrogen is calculated and it agrees with results in literature. Further, the concept of the extended Bethe logarithm is introduced and its advantages are shown and used to calculate the combined self-energy vacuum polarization contribution to the Lamb shift in muonic hydrogen. The results given here are more accurate and somewhat different from others given in literature. In the second part, the ground-state en- ergy splitting due to the tunneling in a two-dimensional double-well potential is calculated. A systematic WKB expansion of the energy splitting is given. An in- terplay between curvature of the classical tunneling path and quantum nature of motion is observed. A series is found that describes systems with strong coupling like the proton transfer in malonaldehyde. The results show a strong sensitivity of the splitting on slight variations of the parameters entering the Hamiltonian linearly. This indicates a presence of quantum chaos in this problem. 1

The scalar mesons have caused much debate amongst hadronic physicists for many years. Even today the number of scalars is hotly contested, and there is almost no agreement on the composition of any of the experimentally observed states, except perhaps for the K*(_0) (1430). This thesis attempts to shed light on both of these problems via the application of analyticity to two different quantities. Recently a number of authors have proposed the existence of a light, strange, scalar meson known as the k. We perform a direct search of the best available πK scattering data to determine whether or not this resonance exists. This is done by constructing contour integrals from these data and determining the number of poles present inside the contour. We do not need to model either the internal dynamics of the state nor the form of the background scattering. The number of poles found tells us the number of resonances present and their positions allow us to estimate the resonance parameters. We find that there is only one resonance in scalar πK scattering below 1800 MeV and this is identified with the established K*(_0)(1430). We find no evidence for the k. Secondly, applying Cauchy's Theorem to the vacuum polarisation function leads to a relation between experimental and theoretical integrals known as a Finite Energy Sum Rule (FESR). FESRs are used to explore the scalar, isoscalar non-strange current and allow us to determine which of the experimentally observed scalar, isoscalar mesons is most likely to be the uũ + dd state. We find that the lightest scalar, isoscalar uũ dd state is not the fo(980) as suggested by some authors, but is rather the light, broad object known as the fo(400 - 1200). We are also able to estimate the average light quark mass and find m(_q)(l GeV(^2)) = 4.7 ± 0.9 MeV which is consistent with the recent estimates of this quantity from unquenched lattice QCD.