A unified approach to the gauging of space-time and internal symmetries

The properties of the manifold of a Lie groupG, fibered by the cosets of a sub-groupH, are exploited to obtain a geometrical description of gauge theories in space-timeG/H. Gauge potentials and matter fields are pullbacks of equivariant fields onG. Our concept of a connection is more restricted than that in the similar scheme of Ne'eman and Regge, so that its degrees of freedom are just those of a set of gauge potentials forG, onG/H, with no redundant components. The ldquotranslationalrdquo gauge potentials give rise in a natural way to a nonsingular tetrad onG/H. The underlying groupG to be gauged is the groupG of left translations on the manifoldG and is associated with a ldquotrivialrdquo connection, namely the Maurer-Cartan form. Gauge transformations are all those diffeomorphisms onG that preserve the fiber-bundle structure.

Symmetries and constraints in generalized Hamiltonian dynamics

A general analysis of symmetries and constraints for singular Lagrangian systems is given. It is shown that symmetry transformations can be expressed as canonical transformations in phase space, even for such systems. The relation of symmetries to generators, constraints, commutators, and Dirac brackets is clarified.

Non-periodic tilings in 2-dimensions with 4, 6, 8, 10 and 12-fold symmetries

The two dimensional plane can be filled with rhombuses, so as to generate non-periodic tilings with 4, 6, 8, 10 and 12-fold symmetries. Some representative tilings constructed using the rule of inflation are shown. The numerically computed diffraction patterns for the corresponding tilings are also shown to facilitate a comparison with possible X-ray or electron diffraction pictures.

Non-periodic tilings in 2-dimensions: 4- and 7-fold symmetries

By inflating basic rhombuses, with a self-similarity principle, non-periodic tiling of 2-d planes is possible with 4, 5, 6, 7, 8, … -fold symmetries. As examples, non-periodic tilings with crystallographically allowed 4-fold symmetry and crystallographically forbidden 7-fold symmetry are presented in detail. The computed diffraction patterns of these tilings are also discussed.

Exact entanglement studies of strongly correlated systems: role of long-range interactions and symmetries of the system

We study the bipartite entanglement of strongly correlated systems using exact diagonalization techniques. In particular, we examine how the entanglement changes in the presence of long-range interactions by studying the Pariser-Parr-Pople model with long-range interactions. We compare the results for this model with those obtained for the Hubbard and Heisenberg models with short-range interactions. This study helps us to understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions. To better understand the behavior of long-range interactions and why the DMRG works well with it, we study the entanglement spectrum of the ground state and a few excited states of finite chains. We also investigate if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, we make an interesting observation on the entanglement profiles of different states (across the energy spectrum) in comparison with the corresponding profile of the density of states. We use isotropic chains and a molecule with non-Abelian symmetry for these numerical investigations.

Poincare invariant quantum field theories with twisted internal symmetries

Following up the work of 1] on deformed algebras, we present a class of Poincare invariant quantum field theories with particles having deformed internal symmetries. The twisted quantum fields discussed in this work satisfy commutation relations different from the usual bosonic/fermionic commutation relations. Such twisted fields by construction are nonlocal in nature. Despite this nonlocality we show that it is possible to construct interaction Hamiltonians which satisfy cluster decomposition principle and are Lorentz invariant. We further illustrate these ideas by considering global SU(N) symmetries. Specifically we show that twisted internal symmetries can provide a natural-framework for the discussion of the marginal deformations (beta-deformations) of the N = 4 SUSY theories.

Evolution of multivariant microstructures with anisotropic misfit: A phase field study

We study, in two dimensions, the effect of misfit anisotropy on microstructural evolution during precipitation of an ordered beta phase from a disordered alpha matrix; these phases have, respectively, 2- and 6-fold rotation symmetries. Thus, precipitation produces three orientational variants of beta phase particles, and they have an anisotropic (and crystallographically equivalent) misfit strain with the matrix. The anisotropy in misfit is characterized using a parameter t = epsilon(yy)/epsilon(xx), where epsilon(xx) and epsilon(yy) are the principal components of the misfit strain tensor. Our phase field, simulations show that the morphology of beta phase particles is significantly influenced by 1, the level of misfit anisotropy. Particles are circular in systems with dilatational misfit (t = 1), elongated along the direction of lower principal misfit when 0 < t < 1 and elongated along the invariant direction when - 1 <= t <= 0. In the special case of a pure shear misfit strain (t = - 1), the microstructure exhibits star, wedge and checkerboard patterns; these microstructural features are in agreement with those in Ti-Al-Nb alloys.

Gauge theory of a group of diffeomorphisms. I. General principles

Any (N+M)-parameter Lie group G with an N-parameter subgroup H can be realized as a global group of diffeomorphisms on an M-dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space-time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Spontaneous symmetry breaking in twisted noncommutative quantum theories

We analyze aspects of symmetry breaking for Moyal spacetimes within a quantization scheme which preserves the twisted Poincare´ symmetry. Towards this purpose, we develop the Lehmann-Symanzik- Zimmermann (LSZ) approach for Moyal spacetimes. The latter gives a formula for scattering amplitudes on these spacetimes which can be obtained from the corresponding ones on the commutative spacetime. This formula applies in the presence of spontaneous breakdown of symmetries as well. We also derive Goldstone’s theorem on Moyal spacetime. The formalism developed here can be directly applied to the twisted standard model.

Stereochemical studies on cyclic peptides. XIII. Energy minimization studies on cyclic hexapeptides having hydrogen bonds

The basic cyclic hexapeptide conformations which accommodate hydrogen bonded β and γ turns in the backbone have been worked out using stereochemical criteria and energy minimization procedures. It was found that cyclic hexapeptides can be made up of all possible combinations of 4 ± 1 hydrogen bonded types I, I', II and II' β turns, giving rise to symmetric conformations having twofold and inversion symmetries as well as nonsymmetric structures. Conformations having exclusive features of 3 ± 1 hydrogen bonded γ turns were found to be possible in threefold and S6 symmetric cyclic hexapeptides. The results show that the cyclic hexapeptides formed by the linking of two β turn tripeptide fragments differ mainly in (a) the hydrogen bonding scheme present in the β turn tripeptides and (b) the conformation at the α-carbon atoms where the two tripeptide fragments link. The different hydrogen bonding schemes found in the component β turns are: 1) a β turn with only a 4 ± 1 hydrogen bond, 2) a type I or I' β turn with 4 ± 1 and 3 ± 1 hydrogen bonds occurring in a bifurcated form and 3) a type II or II' β turn having both the 4 ± 1 and the 3 ± 1 hydrogen bonds with the same acceptor oxygen atom. The conformation at the linking α-carbon atoms was found to lie either in the extended region or in the 3 ± 1 hydrogen bonded γ turn or inverse γ turn regions. Further, the threefold and the S6 symmetric conformations have three γ turns interleaved by three extended regions or three inverse γ turns, respectively. The feasibility of accommodating alanyl residues of both isomeric forms in the CHP minima has been explored. Finally, the available experimental data are reviewed in the light of the present results.

ESR studies of non-silicate inorganic glasses through their glass transformation ranges

ESR spectra of three inorganic glasses doped with Mn2+ and Fe3+ have been studied through their glass transition temperatures (Tg). Spectral features in each case have been discussed with reference to site symmetries. The intensity of the ESR signal has been bound to decrease in the region of Tg. An attempt has been made to explain this interesting feature on the basis of a two-state model.

Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.

A phase space approach to generalized Hamilton–Jacobi theory

Generalizations of H–J theory have been discussed before in the literature. The present approach differs from others in that it employs geometrical ideas on phase space and classical transformation theory to derive the basic equations. The relation between constants of motion and symmetries of the generalized H–J equations is then clarified. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Structure of polyamidoamide dendrimers up to limiting generations: A mesoscale description

The polyamidoamide (PAMAM) class of dendrimers was one of the first dendrimers synthesized by Tomalia and co-workers at Dow. Since its discovery the PAMAMs have stimulated many discussions on the structure and dynamics of such hyperbranched polymers. Many questions remain open because the huge conformation disorder combined with very similar local symmetries have made it difficult to characterize experimentally at the atomistic level the structure and dynamics of PAMAM dendrimers. The higher generation dendrimers have also been difficult to characterize computationally because of the large size (294852 atoms for generation 11) and the huge number of conformations. To help provide a practical means of atomistic computational studies, we have developed an atomistically informed coarse-grained description for the PAMAM dendrimer. We find that a two-bead per monomer representation retains the accuracy of atomistic simulations for predicting size and conformational complexity, while reducing the degrees of freedom by tenfold. This mesoscale description has allowed us to study the structural properties of PAMAM dendrimer up to generation 11 for time scale of up to several nanoseconds. The gross properties such as the radius of gyration compare very well with those from full atomistic simulation and with available small angle x-ray experiment and small angle neutron scattering data. The radial monomer density shows very similar behavior with those obtained from the fully atomistic simulation. Our approach to deriving the coarse-grain model is general and straightforward to apply to other classes of dendrimers.

Hanle-Zeeman redistribution matrix. I. Classical theory expressions in the laboratory frame

Polarized scattering in spectral lines is governed by a 4; 4 matrix that describes how the Stokes vector is scattered and redistributed in frequency and direction. Here we develop the theory for this redistribution matrix in the presence of magnetic fields of arbitrary strength and direction. This general magnetic field case is called the Hanle- Zeeman regime, since it covers both of the partially overlapping weak- and strong- field regimes in which the Hanle and Zeeman effects dominate the scattering polarization. In this general regime, the angle-frequency correlations that describe the so-called partial frequency redistribution (PRD) are intimately coupled to the polarization properties. We develop the theory for the PRD redistribution matrix in this general case and explore its detailed mathematical properties and symmetries for the case of a J = 0 -> 1 -> 0 scattering transition, which can be treated in terms of time-dependent classical oscillator theory. It is shown how the redistribution matrix can be expressed as a linear superposition of coherent and noncoherent parts, each of which contain the magnetic redistribution functions that resemble the well- known Hummer- type functions. We also show how the classical theory can be extended to treat atomic and molecular scattering transitions for any combinations of quantum numbers.