Origin of Antifields in the Batalin-Vilkovisky Lagrangian Formalism

The antifields of the Batalin-Vilkovisky Lagrangian quantization are standard antighosts of certain collective fields. These collective fields ensure that Schwinger-Dyson equations are satisfied as a consequence of the gauge symmetry algebra. The associated antibracket and its canonical structure appear naturally if one integrates out the corresponding ghost fields. An analogous Master Equation for the action involving these ghosts follows from the requirement that the path integral gives rise to the correct Schwinger-Dyson equations.Comment: 36 pages, LaTeX, CERN--TH-6788/9

Local spectral properties of Luttinger liquids: scaling versus nonuniversal energy scales

Motivated by recent scanning tunneling and photoemission spectroscopy measurements on self-organized gold chains on a germanium surface we reinvestigate the local single-particle spectral properties of Luttinger liquids. In the first part we use the bosonization approach to exactly compute the local spectral function of a simplified field theoretical low-energy model and take a closer look at scaling properties as a function of the ratio of energy and temperature. Translational invariant Luttinger liquids as well as those with an open boundary (cut chain geometry) are considered. We explicitly show that the scaling functions of both setups have the same analytic form. The scaling behavior suggests a variety of consistency checks which can be performed on measured data to experimentally verify Luttinger liquid behavior. In a second part we approximately compute the local spectral function of a microscopic lattice model---the extended Hubbard model---close to an open boundary using the functional renormalization group. We show that as a function of energy and temperature it follows the field theoretical prediction in the low-energy regime and point out the importance of nonuniversal energy scales inherent to any microscopic model. The spatial dependence of this spectral function is characterized by oscillatory behavior and an envelope function which follows a power law both in accordance with the field theoretical continuum model. Interestingly, for the lattice model we find a phase shift which is proportional to the two-particle interaction and not accounted for in the standard bosonization approach to Luttinger liquids with an open boundary. We briefly comment on the effects of several one-dimensional branches cutting the Fermi energy and Rashba spin-orbit interaction.Comment: 19 pages, 5 figures, version as accepted for publication in J. Phys.:Condensed Matte

The Microcanonical Functional Integral. I. The Gravitational Field

The gravitational field in a spatially finite region is described as a microcanonical system. The density of states $\nu$ is expressed formally as a functional integral over Lorentzian metrics and is a functional of the geometrical boundary data that are fixed in the corresponding action. These boundary data are the thermodynamical extensive variables, including the energy and angular momentum of the system. When the boundary data are chosen such that the system is described semiclassically by {\it any} real stationary axisymmetric black hole, then in this same approximation $\ln\nu$ is shown to equal 1/4 the area of the black hole event horizon. The canonical and grand canonical partition functions are obtained by integral transforms of $\nu$ that lead to "imaginary time" functional integrals. A general form of the first law of thermodynamics for stationary black holes is derived. For the simpler case of nonrelativistic mechanics, the density of states is expressed as a real-time functional integral and then used to deduce Feynman's imaginary-time functional integral for the canonical partition function.Comment: 29 pages, plain Te

A Note on AdS/CFT Dual of SL(2,Z) Action on 3D Conformal Field Theories with U(1) Symmetry

In this letter, we elaborate on the SL(2,Z) action on three dimensional conformal field theories with U(1) symmetry introduced by Witten, by trying to give an explicit verification of the claim regarding holographic dual of the S operation in AdS/CFT correspondence. A consistency check with the recently proposed prescription on boundary condition of bulk fields when we deform the boundary CFT in a non-standard manner is also discussed.Comment: LaTex, 1+15 pages, 1 figure, v2: discussion in terms of deformation theory is adde

Measuring brain atrophy with a generalized formulation of the boundary shift integral

AbstractBrain atrophy measured using structural magnetic resonance imaging (MRI) has been widely used as an imaging biomarker for disease diagnosis and tracking of pathologic progression in neurodegenerative diseases. In this work, we present a generalized and extended formulation of the boundary shift integral (gBSI) using probabilistic segmentations to estimate anatomic changes between 2 time points. This method adaptively estimates a non-binary exclusive OR region of interest from probabilistic brain segmentations of the baseline and repeat scans to better localize and capture the brain atrophy. We evaluate the proposed method by comparing the sample size requirements for a hypothetical clinical trial of Alzheimer's disease to that needed for the current implementation of BSI as well as a fuzzy implementation of BSI. The gBSI method results in a modest but reduced sample size, providing increased sensitivity to disease changes through the use of the probabilistic exclusive OR region

The Extended Wronskian Determinant Approach and the Iterative Solutions of One-Dimensional Dirac Equation

An approximation method, namely, the Extended Wronskian Determinant Approach, is suggested to study the one-dimensional Dirac equation. An integral equation which can be solved by iterative procedure to find the wave functions is established. We employ this approach to study the one-dimensional Dirac equation with one-well potential, and give the energy levels and wave functions up to the first order iterative approximation. For double-well potential, the energy levels up to the first order approximation are given.Comment: 3 figures, 21 page