Spin and mass content of linearized Poincaré gauge theories

A unified gauge theory of massless and massive spin-2 fields is of considerable current interest. The Poincaré gauge theories with quadratic Lagrangian are linearized, and the conditions on the parameters are found which will lead to viable linear theories with massive gauge particles. As well as the 2+ massless gravitons coming from the translational gauge potential, the rotational gauge potentials, in the linearized limit, give rise to 2+ and 2− particles of equal mass, as well as a massive pseudoscalar.

Gauge Field Theories, Quantum Space-Time and Some Applications

In this thesis, the possibility of extending the Quantization Condition of Dirac for Magnetic Monopoles to noncommutative space-time is investigated. The three publications that this thesis is based on are all in direct link to this investigation. Noncommutative solitons have been found within certain noncommutative field theories, but it is not known whether they possesses only topological charge or also magnetic charge. This is a consequence of that the noncommutative topological charge need not coincide with the noncommutative magnetic charge, although they are equivalent in the commutative context. The aim of this work is to begin to fill this gap of knowledge. The method of investigation is perturbative and leaves open the question of whether a nonperturbative source for the magnetic monopole can be constructed, although some aspects of such a generalization are indicated. The main result is that while the noncommutative Aharonov-Bohm effect can be formulated in a gauge invariant way, the quantization condition of Dirac is not satisfied in the case of a perturbative source for the point-like magnetic monopole.

Observation of crack closure using a crack mouth opening displacement gauge

A crack mouth opening displacement (CMOD) gauge has been designed to estimate the crack length as well as the crack opening stress level in an automated fatigue crack propagation test programme. The CMOD gauge accurately predicts crack tip opening levels in K-controlled tests with constant K, K increasing or K decreasing. In all three K-controlled tests with a single 100% overload cycle, the CMOD gauge does not measure the crack tip opening stress level over a large range of crack lengths after the application of the overload. The CMOD gauge measures the stress level at which the overload plastic zone site opens. Caution should thus be exercised in using the crack opening stress level, estimated by the CMOD gauge, to explain fatigue crack propagation under arbitrary load sequences from the viewpoint of crack closure phenomena.

Gauge-invariant reformulation of theories with second-class constraints

Given a classical dynamical theory with second-class constraints, it is sometimes possible to construct another theory with first-class constraints, i.e., a gauge-invariant one, which is physically equivalent to the first theory. We identify some conditions under which this may be done, explaining the general principles and working out several examples. Field theoretic applications include the chiral Schwinger model and the non-linear sigma model. An interesting connection with the work of Faddeev and Shatashvili is pointed out.

Diaphragm-type sputtered platinum thin film strain gauge pressure transducer

A diaphragm-type pressure transducer with a sputtered platinum film strain gauge (sensing film) has been designed and fabricated. The various steps followed to prepare thin film strain gauges on the diaphragm are described. M-bond 450 adhesive (Measurements Group, USA) has been employed as the insulating layer. A detailed procedure to cure this layer is given. A d.c. sputtering method is employed to prepare the platinum films. This paper also includes details of the strain gauge pattern and its location on the diaphragm. A description of the output characteristics and overall behaviour of the platinum thin film pressure transducer is reported.

Phenomenological Ginzburg-Landau-like theory for superconductivity in the cuprates

We propose and develop here a phenomenological Ginzburg-Landau-like theory of cuprate high-temperature superconductivity. The free energy of a cuprate superconductor is expressed as a functional F of the complex spin-singlet pair amplitude psi(ij) equivalent to psi(m) = Delta(m) exp(i phi(m)), where i and j are nearest-neighbor sites of the square planar Cu lattice in which the superconductivity is believed to primarily reside, and m labels the site located at the center of the bond between i and j. The system is modeled as a weakly coupled stack of such planes. We hypothesize a simple form FDelta, phi] = Sigma(m)A Delta(2)(m) + (B/2)Delta(4)(m)] + C Sigma(< mn >) Delta(m) Delta(n) cos(phi(m) - phi(n)) for the functional, where m and n are nearest-neighbor sites on the bond-center lattice. This form is analogous to the original continuum Ginzburg-Landau free-energy functional; the coefficients A, B, and C are determined from comparison with experiments. A combination of analytic approximations, numerical minimization, and Monte Carlo simulations is used to work out a number of consequences of the proposed functional for specific choices of A, B, and C as functions of hole density x and temperature T. There can be a rapid crossover of from small to large values as A changes sign from positive to negative on lowering T; this crossover temperature T-ms(x) is identified with the observed pseudogap temperature T*(x). The thermodynamic superconducting phase-coherence transition occurs at a lower temperature T-c(x), and describes superconductivity with d-wave symmetry for positive C. The calculated T-c(x) curve has the observed parabolic shape. The results for the superfluid density rho(s)(x, T), the local gap magnitude , the specific heat C-v(x, T) (with and without a magnetic field), as well as vortex properties, all obtained using the proposed functional, are compared successfully with experiments. We also obtain the electron spectral density as influenced by the coupling between the electrons and the correlation function of the pair amplitude calculated from the functional, and compare the results successfully with the electronic spectrum measured through angle resolved photoemission spectroscopy (ARPES). For the specific heat, vortex structure, and electron spectral density, only some of the final results are reported here; the details are presented in subsequent papers.

Bound states of two spin-1/2 fermions in a synthetic non-Abelian gauge field

We study the bound states of two spin-1/2 fermions interacting via a contact attraction (characterized by a scattering length) in the singlet channel in three-dimensional space in presence of a uniform non-Abelian gauge field. The configuration of the gauge field that generates a Rashba-type spin-orbit interaction is described by three coupling parameters (lambda(x),lambda(y),lambda(z)). For a generic gauge field configuration, the critical scattering length required for the formation of a bound state is negative, i.e., shifts to the ``BCS side'' of the resonance. Interestingly, we find that there are special high-symmetry configurations (e.g., lambda(x) = lambda(y) = lambda(z)) for which there is a two-body bound state for any scattering length however small and negative. Remarkably, the bound-state wave functions obtained for such configurations have nematic spin structure similar to those found in liquid He-3. Our results show that the BCS-BEC (Bose-Einstein condensation) crossover is drastically affected by the presence of a non-Abelian gauge field. We discuss possible experimental signatures of our findings both at high and low temperatures.

Conjectures about phase turbulence in the complex Ginzburg-Landau equation

In the complex Ginzburg-Landau equation, we consider possible ''phase turbulent'' regimes, where asymptotic correlations are controlled by phase fluctuations rather than by topological defects. Conjecturing that the decay of such correlations is governed by the Kardar-Parisi-Zhang (KPZ) model of growing interfaces, we derive the following results: (1) A scaling ansatz implies that equal-time spatial correlations in 1d, 2d, and 3d decay like e(-Ax2 zeta), where A is a nonuniversal constant, and zeta=1/2 in 1d. (2) Temporal correlations decay as exp(-t(2 beta)h(t/L(z))), with the scaling law <(beta)over bar> = <(zeta)over bar>/z, where z = 3/2, 1.58..., and 1.66..., for d = 1,2, and 3 respectively. The scaling function h(y) approaches a constant as y --> 0, and behaves like y(2(beta-<(beta)over bar>)), for large y. If in 3d the associated KPZ model turns out to be in its weak-coupling (''smooth'') phase, then, instead of the above behavior, the CGLE exhibits rotating long-range order whose connected correlations decay like 1/x in space or 1/t(1/2) in time. (3) For system sizes, L, and times t respectively less than a crossover length, L(c), and time, t(c), correlations are governed by the free-field or Edwards-Wilkinson (EW) equation, rather than the KPZ model. In 1d, we find that L(c) is large: L(c) similar to 35,000; for L < L(c) we show numerical evidence for stretched exponential decay of temporal correlations with an exponent consistent with the EW value beta(EW)= 1/4.