Gauge-fixing, semiclassical approximation and potentials for graded Chern-Simons theories

We perform the Batalin-Vilkovisky analysis of gauge-fixing for graded Chern-Simons theories. Upon constructing an appropriate gauge-fixing fermion, we implement a Landau-type constraint, finding a simple form of the gauge-fixed action. This allows us to extract the associated Feynman rules taking into account the role of ghosts and antighosts. Our gauge-fixing procedure allows for zero-modes, hence is not limited to the acyclic case. We also discuss the semiclassical approximation and the effective potential for massless modes, thereby justifying some of our previous constructions in the Batalin-Vilkovisky approach.Comment: 46 pages, 4 figure

Local realizations of contact interactions in two- and three-body problems

Mathematically rigorous theory of the two-body contact interaction in three dimension is reviewed. Local potential realizations of this proper contact interaction are given in terms of Poschl-Teller, exponential and square-well potentials. Three body calculation is carried out for the halo nucleus 11Li using adequately represented contact interaction.Comment: submitted to Phys. Rev.

Effective Lagrangian for strongly coupled domain wall fermions

We derive the effective Lagrangian for mesons in lattice gauge theory with domain-wall fermions in the strong-coupling and large-N_c limits. We use the formalism of supergroups to deal with the Pauli-Villars fields, needed to regulate the contributions of the heavy fermions. We calculate the spectrum of pseudo-Goldstone bosons and show that domain wall fermions are doubled and massive in this regime. Since we take the extent and lattice spacing of the fifth dimension to infinity and zero respectively, our conclusions apply also to overlap fermions.Comment: 26 pp. RevTeX and 3 figures; corrected error in symmetry breaking scheme and added comments to discussio

Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments

A large number of treatments of the meson spectrum have been tried that consider mesons as quark - anti quark bound states. Recently, we used relativistic quantum "constraint" mechanics to introduce a fully covariant treatment defined by two coupled Dirac equations. For field-theoretic interactions, this procedure functions as a "quantum mechanical transform of Bethe-Salpeter equation". Here, we test its spectral fits against those provided by an assortment of models: Wisconsin model, Iowa State model, Brayshaw model, and the popular semi-relativistic treatment of Godfrey and Isgur. We find that the fit provided by the two-body Dirac model for the entire meson spectrum competes with the best fits to partial spectra provided by the others and does so with the smallest number of interaction functions without additional cutoff parameters necessary to make other approaches numerically tractable. We discuss the distinguishing features of our model that may account for the relative overall success of its fits. Note especially that in our approach for QCD, the resulting pion mass and associated Goldstone behavior depend sensitively on the preservation of relativistic couplings that are crucial for its success when solved nonperturbatively for the analogous two-body bound-states of QED.Comment: 75 pages, 6 figures, revised content

A Modal µ-Calculus and a Proof System for Value Passing Processes

A first-order modal ¯-calculus is introduced as a convenient logic for reasoning about processes with value passing. For this logic we present a proof system for model checking sequential processes defined in the value passing CCS. Soundness of the proof system is established. The use of the system is demonstrated on two small but instructive examples. 1 Introduction The propositional modal ¯-calculus is a particularly expressive logic for reasoning about branching-time properties of communicating systems. Many other logics, like dynamic logic and CTL, have uniform encodings in this logic [11]. Over the last decade, many proof systems for checking validity of formulae of this logic w.r.t. particular states (or sets of states) of particular models have been proposed. Since the semantics of the logic is given w.r.t. labelled transition systems (LTS), some of these proof systems [1,4,6,7,15] refer directly to LTS, while other, compositional approaches [2,8] refer to descriptions in some ..

The photophysical and metal coordination properties of the N-CH3 substituted porphyrins: H(N-CH3)TPP vs H(CH3)OEP

The effect of N-methyl substitution on photophysical and metal coordination properties of the respective derivatives of octaethylporphyrin (H2OEP) and tetraphenylporphyrin (H2TPP) was studied by means of steady-state and time-resolved optical spectroscopies combined with semi-empirical quantum-chemical calculations and coordination chemistry methods. In case of H2TPP, the insertion of the methyl substituent into the center of the porphyrin macrocycle leads to noticeable nonplanar distortions of the molecule and is accompanied by changes of its photophysical and physicochemical properties towards those manifested by "classical" nonplanar porphyrins. Contrasting to that, N-methyl substituted H2OEP does not undergo significant nonplanar distortions and possesses photophysical characteristics mainly similar to unsubstituted H2OEP, except for the long-wavelength shift of the absorption and emission bands. The Zn coordination/Zn complex dissociation and macrocycle thermal stability parameters were also determined for both N-methyl substituted and parent unsubstituted macrocycles, which correlate well with a higher degree of nonplanarity of the N-methyl substituted H2TPP as compared to H2OEP. Basing on the results of this study the conclusion postulated is that N-methyl substitution has a different effect on the photophysical and coordination properties of H2TPP vs. H2OER Copyright (c) 2005 Society of Porphyrins & Phthalocyanines

Modern Trends of Organic Chemistry in Russian Universities

This review is devoted to the scientific achievements of the departments of organic chemistry in higher schools of Russia within the past decade. © 2018, Pleiades Publishing, Ltd