Canonical Quantization of Systems with Time-Dependent Constraints

The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion for a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for the relativistic particle in a plane wave lead us to obtain the canonical phase space coordinates without using any gauge fixing condition. As a result of the quantization, we get the Klein-Gordon theory for a particle in a plane wave. The path integral quantization for this system is obtained using the canonical path integral formulation method.     

Quantization of the O（N） Nonlinear Sigma Model

The Hamilton-Jacobi method of quantizing singular systems is discussed.The equations of motion are obtained as total differential equations in many variables.It is shown that if the system is integrable,one can obtain the canonical phase space coordinates and set of canonical Hamilton-Jacobi partial differential equations without any need to introduce unphysical auxiliary fields.As an example we quantize the O(2) nonlinear sigma model using two different approaches:the functional Schrodinger method to obtain the wave functionals for the ground and the exited state and then we quantize the same model using the canonical path integral quantization as an integration over the canonical phase-space coordinates.     

Hamilton–Jacobi Quantization of Constrained Systems with Second-Order Lagrangians

We investigate the path-integral quantization of constrained systems with second-order Lagrangians using the Hamilton-Jacobi method. The path-integral quantization for two models is obtained using the canonical path-integral method.     

Canonical Path Integral Quantization of Einstein's Gravitational Field

The connection between the canonical and the path integral formulations of Einstein's gravitational field is discussed using the Hamilton Jacobi method. Unlike conventional methods, its shown that our path integral method leads to obtain the measure of integration with no -functions, no need to fix any gauge and so no ambiguous determinants will appear.     

Hamilton–Jacobi and Symplectic Analysis of a Particle Constrained on a Circle

Hamilton-Jacobi and modified Faddeev-Jackiw methods were applied to investigate the motion of a particle moving on a circle. The results of both methods were found to be equivalent with those of Dirac's formalism. Besides, the importance of the Lagrange multipliers was analyzed and the action of the second-class constrained system was given.     

The CP^1 nonlinear sigma model with ChernSimons term in the Faddeev-Jachiw quantization formalism

Using the Faddeev-Jackiw （FJ） quantization method, this paper treats the CP^1nonlinear sigma model with ChernSimons term. The generalized FJ brackets are obtained in the framework of this quantization method, which agree with the results obtained by using the Dirac＇s method.     

Quantization of constrained systems: A comparative look at three methods

Constrained Hamiltonian systems are investigated using three different methods: Hamilton-Jacobi, Batalin-Fradkin-Tyutin and gauge unfixing methods. The abelian Proca model is analyzed and the involutive Hamiltonian is obtained by the three methods.     

Quantal Symmetries in the Nonlinear Sigma Model with Maxwell–Chern–Simons Term

The quantal symmetry property in the CP¹ nonlinear sigma model with Abelian–Maxwell–Chern–Simons (AMCS) term in 2 + 1 dimensions is studied. In the Coulomb gauge, the system is quantized in the Faddeev–Senjanovic (FS) path-integral formalism. The canonical Ward identities for proper vertices under local gauge transformation are derived. Based on the quantal symmetries of a constrained Hamiltonian system, the fractional spin at the quantum level of this system is also presented as those of the system without Maxwell term.     

Investigation of Constrained Systems with Singular Higher-Order Lagrangians

Constrained Hamiltonian systems with singular higher-order Lagrangians are investigated by using two methods: the Dirac's and the Hamilton-Jacobi methods. Three examples are studied and it is shown that the equations of motion which are obtained by these two methods are in exact agreement.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian hasstrict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory.Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar fieldminimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian forscalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressedby gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian has strict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory. Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar field minimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian for scalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressed by gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

Front-Form Hamiltonian, Path Integral, and BRST Formulations of the Nonlinear Sigma Model

The nonlinear sigma model in one-space one-time dimension is considered on the light-front. The front-form theory is seen to possess a set of three first-class constraints and consequently it possesses a local vector gauge symmetry. This is in contrast to the usual instant-form theory, which is well known to be a gauge noninvariant theory possessing a set of four second-class constraints. The front-form Hamiltonian, path integral, and BRST formulations of this theory are investigated under some specific gauge choices.     

Assignment of the 1H and 13C Spectra of 5-Methylthio-4H-1-(p-R1-phenyl)-3a-(p-R2-Phenyl)-3a, 4-dihydro (1,2,4) oxadiazolo(4,5-a), 1, 5-benzodiazepines Using 2D NMR Spectroscopy

The ¹H NMR spectra of the title benzodiazepines derivatives is highly congested because all the protons are in aromatic environment so many proton signals remain overlap even 300 MHz or higher fields. With this in mind, the assignment of the ¹H and ¹³C spectra of these compounds obtained using COSY, NOESY, HMQC and HMBC experiments is reported.     

Assignment of the 1H and 13C Spectra of 5-Methylthio-4H-1-(p-R1-phenyl)-3a-(p-R2-phenyl)-3a,4-dihydro (1,2,4) oxadiazolo(4,5-a), 1,5-benzodiazepines using 2D NMR Spectroscopy.

The ¹H NMR spectra of the title benzodiazepines derivatives is highly congested because all the protons are in aromatic enviroment so many proton signals remain overlap even 300 MHz or higher fields. With this in mind, the assignment of the ¹H and ¹³C spectra of these compounds obtained using COSY, NOESY, HMQC and HMBC experiments is reported.     

A Poincaré lemma for sigma models of AKSZ type

For a sigma model of AKSZ type, we show that the local BRST cohomology is isomorphic to the cohomology of the target space differential when restricted to coordinate neighborhoods both in the base and in the target. An analogous result is shown to hold for the cohomology in the space of functional multivectors. Applications of these latter cohomology classes in the context of the inverse problem of the calculus of variation for general gauge systems are also discussed.     

The Proton NMR Assignment of 1-Aminocyclo-propane-1-carboxylic Acid

The two sets of diastereomeric hydrogen atoms cis and trans to the carboxylate of 1-aminocyclopropane-1-carboxylic acid (ACC) were differentiated by a ¹H-nmr study. The measurement of the ¹H-nmr spectrum of ACC at pH 3.8 during the successive addition of non-chiral lanthanide reagents such as Eu(NO₃)₃, Pr(NO₃)₃ or Gd(NO₃)₃ demonstrated that the hydrogen atoms cis to the carboxylate function of ACC resonate at δ=1.42 and that the hydrogen atoms trans to the carboxylate function of ACC resonate at δ=1.20. The mono-substituted cyclopropanes, cyclo-propanecarboxylic acid (CPC) and cyclopropyl-amine (CPA) were used in complementary lanthanide-reagent shift titrations along with the back titration of an ACC-Eu⁺⁺⁺ complex with DCl to further substantiate the assignment. This assignment allows for the non-destructive, nonisotopic diluting analysis of various biosynthetically derived deuterated ACC's formed from the corresponding deuterated S-adenosyl-L-methionine.     

Complete Analysis of the 1H and 13C NMR Spectra of 5-Isopropylsulfonyl-2-Norbornenes Through the Application of Two-Dimensional NMR Techniques

Total assignment of ¹³C and ¹H NMR spectra of the 5-isopropylsulfonyl-2-norbornenes 2 was achieved using the concerted application of two-dimensional homonuclear and heteronuclear chemical shift correlations. The stereochemistry of both the diastereoisomers endo 2a and exo 2b have been established using the magnitude of the proton coupling constants.     

1H NMR Studies of 1-Ethylimidazole Binding to Cytochrome C

Abstract

Kinetic and equilibrium data for 1-EtIm binding to cyt c at temperature range of 303–319K have been determined at pH 7.0 by using ¹HNMR method. Thermodynamic values (ΔH°=39.5 kJ mol^?1, ΔS° = 154 J mol^?1K^?1 and Ea = 142 kJ mol^?1) are obtained from Van't Hoff and Arrhenius's relations. Some hyperfine shifted resonances of l-EtIm cyt c have been assigned for the first time using 1D saturation transfer experiments. The origin of the asymmetric spin density distribution in heme groups of 1-EtIm cyt c and the reason of low affinity of cytochrome c for 1-EtIm are also discussed move toward upfield from original position. However, Te-2, 4 substituents in cyt c are more electron withdrawing than the propionic acid side chains, which lead to the 5-methyl group going toward downfield.