HABEAS CORPUS-FEDERAL COURTS-EXHAUSTION OF STATE REMEDIES

Petitioner\u27s writ of habeas corpus, alleging denial of due process of law in violation of the Fourteenth Amendment, was quashed on the merits by an inferior Florida court whose action was affirmed without opinion by the Florida Supreme Court. It was impossible to ascertain whether the affirmance was on the merits or on the ground that, under Florida law, habeas corpus was not the proper procedure to raise the due process issue. A later decision by the Florida Supreme Court clearly established that the prior case had been decided on the merits of the constitutional question, and that habeas corpus was available in Florida to raise the due process issue. Petitioner did not seek review of the Florida court\u27s decision by certiorari to the United States Supreme Court, but later instituted habeas corpus proceedings in a federal district court which ordered his release. On certiorari to the United States Supreme Court, held, the district court had properly exercised its discretion to issue the writ. Four justices dissented on the ground that, because petitioner had failed to exhaust his state remedies, the constitutional question was not properly before the court. Wade v. Mayo, 334 U.S. 672, 68 S.Ct. 1270 (1948)

Improved lattice operators for non-relativistic fermions

In this work I apply a recently proposed improvement procedure, originally conceived to reduce finite lattice spacing effects in transfer matrices for dilute Fermi systems, to tuning operators for the calculation of observables. I construct, in particular, highly improved representations for the energy and the contact, as a first step in an improvement program for finite-temperature calculations. I illustrate the effects of improvement on those quantities with a ground-state lattice calculation at unitarity.Comment: 11 pages, 7 figures; replaced with published versio

Recursive Construction of Generator for Lagrangian Gauge Symmetries

We obtain, for a subclass of structure functions characterizing a first class Hamiltonian system, recursive relations from which the general form of the local symmetry transformations can be constructed in terms of the independent gauge parameters. We apply this to a non-trivial Hamiltonian system involving two primary constraints, as well as two secondary constraints of the Nambu-Goto type.Comment: 10 pages, Late

Thermal Quantum Fields in Static Electromagnetic Backgrounds

We present and discuss, at a general level, new mathematical results on the spatial nonuniformity of thermal quantum fields coupled minimally to static background electromagnetic potentials. Two distinct examples are worked through in some detail: uniform (parallel and perpendicular) background electric and magnetic fields coupled to a thermal quantum scalar field.Comment: 22 page

Hamiltonian Embedding of SU(2) Higgs Model in the Unitary Gauge

Following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin (BFT), we embed the second-class non-abelian SU(2) Higgs model in the unitary gauge into a gauge invariant theory. The strongly involutive Hamiltonian and constraints are obtained as an infinite power series in the auxiliary fields. Furthermore, comparing these results with those obtained from the gauged second class Lagrangian, we arrive at a simple interpretation for the first class Hamiltonian, constraints and observables.Comment: 13 pages, Latex, no figure

Resonance ionization spectroscopy of thorium isotopes - towards a laser spectroscopic identification of the low-lying 7.6 eV isomer of Th-229

In-source resonance ionization spectroscopy was used to identify an efficient and selective three step excitation/ionization scheme of thorium, suitable for titanium:sapphire (Ti:sa) lasers. The measurements were carried out in preparation of laser spectroscopic investigations for an identification of the low-lying Th-229m isomer predicted at 7.6 +- 0.5 eV above the nuclear ground state. Using a sample of Th-232, a multitude of optical transitions leading to over 20 previously unknown intermediate states of even parity as well as numerous high-lying odd parity auto-ionizing states were identified. Level energies were determined with an accuracy of 0.06 cm-1 for intermediate and 0.15 cm-1 for auto-ionizing states. Using different excitation pathways an assignment of total angular momenta for several energy levels was possible. One particularly efficient ionization scheme of thorium, exhibiting saturation in all three optical transitions, was studied in detail. For all three levels in this scheme, the isotope shifts of the isotopes Th-228, Th-229, and Th-230 relative to Th-232 were measured. An overall efficiency including ionization, transport and detection of 0.6 was determined, which was predominantly limited by the transmission of the mass spectrometer ion optics

The Complexity of Computing Minimal Unidirectional Covering Sets

Given a binary dominance relation on a set of alternatives, a common thread in the social sciences is to identify subsets of alternatives that satisfy certain notions of stability. Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory. Brandt and Fischer [BF08] proved that it is NP-hard to decide whether an alternative is contained in some inclusion-minimal upward or downward covering set. For both problems, we raise this lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and provide a Sigma_{2}^{p} upper bound. Relatedly, we show that a variety of other natural problems regarding minimal or minimum-size covering sets are hard or complete for either of NP, coNP, and Theta_{2}^{p}. An important consequence of our results is that neither minimal upward nor minimal downward covering sets (even when guaranteed to exist) can be computed in polynomial time unless P=NP. This sharply contrasts with Brandt and Fischer's result that minimal bidirectional covering sets (i.e., sets that are both minimal upward and minimal downward covering sets) are polynomial-time computable.Comment: 27 pages, 7 figure

A New Look at the Axial Anomaly in Lattice QED with Wilson Fermions

By carrying out a systematic expansion of Feynman integrals in the lattice spacing, we show that the axial anomaly in the U(1) lattice gauge theory with Wilson fermions, as determined in one-loop order from an irrelevant lattice operator in the Ward identity, must necessarily be identical to that computed from the dimensionally regulated continuum Feynman integrals for the triangle diagrams.Comment: 1 figure, LaTeX, 18 page

Feynman-Schwinger representation approach to nonperturbative physics

The Feynman-Schwinger representation provides a convenient framework for the cal culation of nonperturbative propagators. In this paper we first investigate an analytically solvable case, namely the scalar QED in 0+1 dimension. With this toy model we illustrate how the formalism works. The analytic result for the self energy is compared with the perturbative result. Next, using a $\chi^2\phi$ interaction, we discuss the regularization of various divergences encountered in this formalism. The ultraviolet divergence, which is common in standard perturbative field theory applications, is removed by using a Pauli-Villars regularization. We show that the divergence associated with large values of Feynman-Schwinger parameter $s$ is spurious and it can be avoided by using an imaginary Feynman parameter $is$.Comment: 26 pages, 9 figures, minor correctio