Symplectic algorithm for systems with second-class constraints

The recently modified Faddeev-Jackiw formalism for systems having one chain of four levels of only second-class constraints is applied to the non-triviala=1 bosonized chiral Schwinger model in (1+1) dimensions as well as to one mechanical system. The sets of obtained constraints are in agreement with Dirac’s canonical formulation.     

Ward identities for interacting electronic systems

A Ward-Takahashi identity, as a consequence of gauge invariance and in a form that relates self-energy to the two-particle Bethe-Salpeter scattering kernel, was first derived by Vollhardt and Wölfle for a system of independent particles moving in a random medium. This is generalized to a class of interacting electronic systems in materials with or without random impurities, following a procedure previously used for classical wave transport in disordered media. This class of systems also possesses other symmetry properties such as invariance under time translations and local spin rotations, which imply local conservation laws for energy and spin current. They imply additional Vollhardt-Wölfle type identities. We present non-perturbative derivations of these identities, and consider the constraints they impose on the relationship between the self-energy and the two-particle scattering kernel.     

On computation of random response of a clamped plate

The free vibrations of elastically connected circular plate systems with elastically restrained edges and initial radial tensions are investigated analytically. By using the equations developed for the general n-plate system, the plate systems consisting of three and two identical plates with identical boundary conditions and a uniform radial tension are treated in detail. Both axisymmetric and non-axisymmetric vibrations are considered. Attention is directed to the influence of the radial tension and the elastic edge constraints on the first nine eigenvalues and the corresponding natural frequencies of the systems.     

Adaptive phase plates for optical encoding systems invariant to second-order aberrations

Certain optical aberrations of imaging systems yield low resolution images. Wavefront coding has proven to minimise this problem by means of hybrid optical-digital imaging systems. The optical part usually involves a phase plate described in terms of cubic polynomials whose shape is a linear combination of (x³ + y³) and (x²y + xy²). Optimization is achieved by seeking the most appropriate linear combination with respect to the optical system's constraints. Here, we propose the shape of two pairs of phase plates such that by means of relative rotations they allow for variation of the linear combination of the cubic terms. This will enable adaptive optimization of the cubic phase to the optical system's constraints when these vary in time. Results will be illustrated with numerical simulations.     

Supersymmetric quantum mechanics

We give a general construction for supersymmetric Hamiltonians in quantum mechanics. We find that N-extended supersymmetry imposes very strong constraints, and for N > 4 the Hamiltonian is integrable. We give a variety of examples, for one-particle and for many-particle systems, in different numbers of dimensions.     

Functional Analysis for Gauge Fields on the Front-Form and the Light-Cone Gauge

Constrained systems in quantum field theories call for a careful study of diverse classes of constraints and consistency checks over their temporal evolution. Here we study the functional structure of the free electromagnetic and pure Yang–Mills fields on the front-form coordinates with the null-plane gauge condition. It is seen that in this framework, we can deal with strictu sensu physical fields.     

Relativistic and separable classical hamiltonian particle dynamics

We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincaré invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincaré invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light.     

Conformal invariance and the six-dimensional formalism

Conformal invariance is discussed assuming the equations are well defined in arbitrary coordinate systems. This assumption leads to some constraints on scale dimensions of terms, and constraints on the introduction of ‘conformally invariant massive equations’. The six-dimensional formalism is then discussed, and is generalized to project to all conformally flat spaces. Finally the imbedding of Minkowski space equations is studied.SO(4, 2) breaking is seen to enter due to the presence of a non-invariant scalar field, and a non-invariant vector field. The theorem relating invariance of the six-space equations underSO(4, 2) to the invariance of their corresponding four-space equations under the conformal group is carefully stated and proved.     

Causality bounds for neutron-proton scattering

We consider the constraints of causality and unitarity for the low-energy interactions of protons and neutrons. We derive a general theorem that non-vanishing partial-wave mixing cannot be reproduced with zero-range interactions without violating causality or unitarity. We define and calculate interaction length scales which we call the causal range and the Cauchy-Schwarz range for all spin channels up to J = 3 . For some channels we find that these length scales are as large as 5fm. We investigate the origin of these large lengths and discuss their significance for the choice of momentum cutoff scales in effective field theory and universality in many-body Fermi systems.     

New limits on Primakoff production of hybrid mesons

I discuss constraints on properties of isoscalarJ ^PC =1^?+ exotic hybrid mesons, assuming their dominant decay mode is ηπ. This work expands on a similar study by the Rochester-Minnesota-Fermilab collaboration, which excluded ?π as the dominant decay channel for such hybrids. The experimental limits are based on Primakoff production of such states and on a VDM argument relating their radiative widths to their ?π decay modes. Using data on coherent production of ηπ⁺ systems in π⁺ collisions with nuclei, I obtain few percent limits on the ?π branching ratios for hybrid masses ?1.5 GeV.     

Dirac constraint analysis and symplectic structure of anti-self-dual Yang-Mills equations

We present the explicit form of the symplectic structure of anti-self-dual Yang-Mills (ASDYM) equations in Yang’s J- and K-gauges in order to establish the bi-Hamiltonian structure of this completely integrable system. Dirac’s theory of constraints is applied to the degenerate Lagrangians that yield the ASDYM equations. The constraints are second class as in the case of all completely integrable systems which stands in sharp contrast to the situation in full Yang-Mills theory. We construct the Dirac brackets and the symplectic 2-forms for both J- and K-gauges. The covariant symplectic structure of ASDYM equations is obtained using the Witten-Zuckerman formalism. We show that the appropriate component of the Witten-Zuckerman closed and conserved 2-form vector density reduces to the symplectic 2-form obtained from Dirac’s theory. Finally, we present the Bäcklund transformation between the J- and K-gauges in order to apply Magri’s theorem to the respective two Hamiltonian structures.     

Dirac quantization of open p-brane

We give the scheme of Dirac quantization of open p-brane in the D-brane background. Treating the mixed boundary conditions as primary constraints, we get a set of secondary constraints, then the constraints conditions are shown to be equivalent to orbifold conditions imposed on normal p-brane modes.     

The Source Galerkin method: fermionic formulation

We present a new deterministic, numerical method to solve fermion field theories. The Source Galerkin approach is based on finding solutions Z [ J] to the lattice functional equations for field theories in the presence of an external source J. Using Grassmann polynomial expansions for the generating functional Z, we calculate propagators for systems of interacting fermions. These calculations are straightforward to perform and are executed rapidly compared to Monte Carlo. The bulk of the computation involves a single matrix inversion. Because it is not based on a statistical technique, it does not have many of the difficulties often encountered when simulating fermions. Since no determinant is ever calculated, solutions to problems with dynamical fermions are handled more easily. This approach is very flexible, and can be tailored to specific problems based on convenience and computational constraints. We present simple examples to illustrate the method. More general schemes are desirable for more complicated systems.     

Reconstruction of dynamic contrast enhanced magnetic resonance imaging of the breast with temporal constraints

A number of methods using temporal and spatial constraints have been proposed for reconstruction of undersampled dynamic magnetic resonance imaging (MRI) data. The complex data can be constrained or regularized in a number of different ways, for example, the time derivative of the magnitude and phase image voxels can be constrained separately or jointly. Intuitively, the performance of different regularizations will depend on both the data and the chosen temporal constraints. Here, a complex temporal total variation (TV) constraint was compared to the use of separate real and imaginary constraints, and to a magnitude constraint alone. Projection onto Convex Sets (POCS) with a gradient descent method was used to implement the diverse temporal constraints in reconstructions of DCE MRI data. For breast DCE data, serial POCS with separate real and imaginary TV constraints was found to give relatively poor results while serial/parallel POCS with a complex temporal TV constraint and serial POCS with a magnitude-only temporal TV constraint performed well with an acceleration factor as large as R=6. In the tumor area, the best method was found to be parallel POCS with complex temporal TV constraint. This method resulted in estimates for the pharmacokinetic parameters that were linearly correlated to those estimated from the fully-sampled data, with K^trans,R=6=0.97 K^trans,R=1+0.00 with correlation coefficient r=0.98, k_ep,R=6=0.95 k_ep,R=1+0.00 (r=0.85). These results suggest that it is possible to acquire highly undersampled breast DCE-MRI data with improved spatial and/or temporal resolution with minimal loss of image quality.     

Description of composite systems in the spectral integration technique: The gauge invariance and analyticity constraints for the radiative decay amplitudes

The constraints following from gauge invariance and analyticity are considered for the amplitudes of radiative transitions of composite systems, when composite systems are treated in terms of spectral integrals. We discuss gauge-invariant amplitudes for the transitions S → γS and V → γS, with scalar S and vector V mesons being two-particle composite systems of scalar (or pseudoscalar) constituents, and we demonstrate the mechanism of cancellation of false kinematical singularities. Furthermore, we explain how to generalize this consideration for quark-antiquark systems, in particular, for the reaction φ(1020) → γf₀(980). Here, we also consider in more detail the quark-model nonrelativistic approach for this reaction.     

Hadronization of quark systems

Hadronization in simple models of quark systems is discussed with emphasis on the combinatorial aspects. The numberN of quarks and the numberN _c of colours are the relevant variables. In onedimension and in the meson and baryon sector the problem is completely soluble. When multiquark hadrons are included an iterative procedure still allows a complete solution. Higher dimensions are difficult to treat but global hadronization, without dimensionality constraints, is again soluble. As a general result the baryon/meson ratio is, for large quark densities, rather large, ?1/3 and may grow without limit asN→∞.     

Axially symmetric time-dependent Hartree-Fock study of the 208Pb + 208Pb reaction

A time-dependent Hartree-Fock calculation assuming axial and reflection symmetry constraints is performed for the head-on collision of ²⁰⁸Pb + ²⁰⁸Pb systems at E_lab≈1600 MeV. The calculation suggests the excitation of surface modes in the reaction and the energy loss characteristic of a deep inelastic process. An estimate of neck-radius and neck-formation time is given.     

Transition to special canonical coordinates for systems with constraints

When using the Dirac hamiltonization of Lagrange systems with constraints, it is convenient to perform a canonical transformation such that the constraints become linear combinations of only a subset of the new variables, while the primary constraints can be identified with some of the variables belonging to this subset. We prove the existence of such canonical transformation, as well as the possibility of separation of first-class constraints.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 93–97, August, 1983.     

Dirac Canonical Quantization of Composite Fermions QED

Composite Fermions QED is quantized by using the Dirac’s canonical formalism for constrained systems. As a strategy, we first work out the constraints (including primary and secondary constraints), combine two first-class constraints, introduce Coulomb gauge and its stationary as gauge conditions, and then quantize, replacing the Dirac brackets with quantum commutators.