General coding method of address code for optical code division multiple access passive optical network – (F,K, λa, λc) optical orthogonal code

Since the importance of address code of OCDMA passive optical network (PON) diversity and lacking of general coding method until now, in this paper, we present a general coding method of (F, K, λ_a, λ_c) optical orthogonal code (OOC) based on block design. Through the discussion of block, difference sets and cyclic permutation of perfect distance (CPPD), cyclic permutation of imperfect distance (CPID) is defined and applied to realize the coding method. Simulations results demonstrated that it is possible to construct (F, K, λ_a, λ_c) OOCs with arbitrary code length, code weight, auto-correlation constraints and co-correlation constraints based on the same general coding method.     

Resolution of Chern–Simons–Higgs Vortex Equations

It is well known that the presence of multiple constraints of non-Abelian relativisitic Chern–Simons–Higgs vortex equations makes it difficult to develop an existence theory when the underlying Cartan matrix K of the equations is that of a general simple Lie algebra and the strongest result in the literature so far is when the Cartan subalgebra is of dimension 2. In this paper we overcome this difficulty by implicitly resolving the multiple constraints using a degree-theorem argument, utilizing a key positivity property of the inverse of the Cartan matrix deduced in an earlier work of Lusztig and Tits, which enables a process that converts the equality constraints to inequality constraints in the variational formalism. Thus this work establishes a general existence theorem that settles a long-standing open problem in the field regarding the general solvability of the equations.     

Geometry of the quantum complex projective spaceCP q (N)

We study the constraints from theb→sγ decay in the parameter space of effective supergravities from orbifold string theory and with minimal supesymmetric particle content. Both the general dilaton-dominated universal scenario as well as a non-universal scenario for the soft terms are investigated. It is found that the recently reported CLEO upper and lower bounds constrain the parameter space of the models under scrutiny. In particular we find constraints on the values of the parameter tanβ and the gluino masses. In this class of string scenarios the negative sign of the Higgs mixing parameterμ, is phenomenologically preferred.     

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.     

Quantization of relativistic systems with boson and fermion first- and second-class constraints

The general solution for the S matrix of an arbitrary Hamilton system with boson and fermion first- and second-class constraints of general form is obtained. Additional diagrams arise securing unitary and gauge invariance of the theory: the many-particle interaction of fermion and boson ghosts. The generalized Ward identities are obtained.     

Instanton constraints and renormalization

The renormalization is investigated of one-loop quantum fluctuations around a constrained instanton in ?⁴-theory with negative coupling. It is found that the constraint should be renormalized also. This indicates that in general only renormalizable constraints are permitted.     

Symmetries in constrained Hamiltonian systems

We derive an algorithm for the construction of all the gauge generators of a constrained hamiltonian theory. Dirac's conjecture that all secondary first-class constraints generate symmetries is revisited and replaced by a theorem. The algorithm is applied to Yang-Mills theories and metric gravity, and we find generators which operate on the complete set of canonical variables, thus producing the correct transformation laws also for the unphysical coordinates. Finally we discuss the general structure of the Hamiltonian for constrained theories. We show how in most cases one can read off the first-class constraints directly from the Hamiltonian.     

Pion and kaon form factors and heavy vector mesons

A zero parameter model of analytic pion and kaon form factors with supplementary dynamical constraints is presented. Contrary to the general belief the predicted form factors have a t^?2 behaviour and fit the pion space-like data excellently. Some properties of heavy vector mesons are predicted and discussed.     

Electroweak interactions within a five quark model

We discuss the 5 quark model of Peskin and Tye. We derive the general form of the weak currents. The phenomenology of FCNC puts severe constraints on the mixing angles. When these constraints are fulfilled the model can hardly be distinguished from the standard model. A possible experimental test is radiative decay of theB ⁰ meson. In this model it is about an order of magnitude bigger. We also analyzed if the smallness of the mixing angles could be understood in a natural way. Using discrete symmetries we failed in finding a solution in agreement with all present data.     

Collective hamiltonians with Kac-Moody algebraic conditions

We describe the general framework for constructing collective-theory hamiltonians whose hermiticity requirements imply a Kac-Moody algebra of constraints on the associated jacobian. We give explicit examples for the algebras sl(2)_k and sl(3)_k. The reduction to W_n-constraints, relevant to n-matrix models, is described for the jacobians.     

Bianchi-I Universe with Decaying Vacuum Energy Density and Time Varying Gravitational Constant

Anisotropic Locally Rotationally Symmetric Bianchi-I (LRSBI) cosmological model is investigated with variable gravitational and cosmological constants in the framework of Einstein’s general relativity. The shear scalar is considered to be proportional to the expansion scalar. The dynamics of the anisotropic universe with variable G and Λ are discussed. Our calculations for the Supernova constraints concerning the luminosity distance provide reasonable results.     

Conformal geometrodynamics regained: Gravity from duality

There exist several ways of constructing general relativity from ‘first principles’: Einstein’s original derivation, Lovelock’s results concerning the exceptional nature of the Einstein tensor from a mathematical perspective, and Hojman–Kucha?-Teitelboim’s derivation of the Hamiltonian form of the theory from the symmetries of space–time, to name a few. Here I propose a different set of first principles to obtain general relativity in the canonical Hamiltonian framework without presupposing space–time in any way. I first require consistent propagation of scalar spatially covariant constraints (in the Dirac picture of constrained systems). I find that up to a certain order in derivatives (four spatial and two temporal), there are large families of such consistently propagated constraints. Then I look for pairs of such constraints that can gauge-fix each other and form a theory with two dynamical degrees of freedom per space point. This demand singles out the ADM Hamiltonian either in (i) CMC gauge, with arbitrary (finite, non-zero) speed of light, and an extra term linear in York time, or (ii) a gauge where the Hubble parameter is conformally harmonic.     

Renormalization of Lorentz non-invariant actions and manifest T-duality

We study general two-dimensional σ-models which do not possess manifest Lorentz invariance. We show how demanding that Lorentz invariance is recovered as an emergent on-shell symmetry constrains these σ-models. The resulting actions have an underlying group-theoretic structure and resemble Poisson–Lie T-duality invariant actions. We consider the one-loop renormalization of these models and show that the quantum Lorentz anomaly is absent. We calculate the running of the couplings in general and show, with certain non-trivial examples, that this agrees with that of the T-dual models obtained classically from the duality invariant action. Hence, in these cases solving constraints before and after quantization are commuting operations.     

Role of surface integrals in the Hamiltonian formulation of general relativity

It is shown that if the phase space of general relativity is defined so as to contain the trajectories representing solutions of the equations of motion then, for asymptotically flat spaces, the Hamiltonian does not vanish but its value is given rather by a nonzero surface integral. If the deformations of the surface on which the state is defined are restricted so that the surface moves asymptotically parallel to itself in the time direction, then the surface integral gives directly the energy of the system, prior to fixing the coordinates or solving the constraints. Under more general conditions (when asymptotic Poincaré transformations are allowed) the surface integrals giving the total momentum and angular momentum also contribute to the Hamiltonian. These quantities are also identified without reference to a particular fixation of the coordinates. When coordinate conditions are imposed the associated reduced Hamiltonian is unambiguously obtained by introducing the solutions of the constraints into the surface integral giving the numerical value of the unreduced Hamiltonian. In the present treatment there are therefore no divergences that cease to be divergences after coordinate conditions are imposed. The procedure of reduction of the Hamiltonian is explicity carried out for two cases: (a) Maximal slicing, (b) ADM coordinate conditions.A Hamiltonian formalism which is manifestly covariant under Poincaré transformations at infinity is presented. In such a formalism the ten independent variables describing the asymptotic location of the surface are introduced, together with corresponding conjugate momenta, as new canonical variables in the same footing with the g_ij, π^ij. In this context one may fix the coordinates in the “interior” but still leave open the possibility of making asymptotic Poincaré transformations. In that case all ten generators of the Poincaré group are obtained by inserting the solution of the constraints into corresponding surface integrals.     

On the existence of perturbed robertson-walker universes

Solutions of the full nonlinear field equations of general relativity near the Robertson-Walker universes are examined, together with their relation to linearized perturbations. A method due to Choquet-Bruhat and Deser is used to prove existence theorems for solutions near Robertson-Walker constraint data of the constraint equations on a spacelike hypersurface. These theorems allow one to regard the matter fluctuations as independent quantities, ranging over certain function spaces. In the k = ?1 case the existence theory describes perturbations which may vary within uniform bounds throughout space. When k = +1 a modification of the method leads to a theorem which clarifies some unusual features of these constraint perturbations. The k = 0 existence theorem refers only to perturbations which die away at large distances. The connection between linearized constraint solutions and solutions of the full constraints is discussed. For k = ±1 backgrounds, solutions of the linearized constraints are analyzed using transverse-traceless decompositions of symmetric tensors. Finally the time-evolution of perturbed constraint data and the validity of linearized perturbation theory for Robertson-Walker universes are considered.     

Supercovariant derivatives,super-Weyl groups,and N = 2 supergravity

We analyze the kinematic constraints for N = 2 Poincaré supergravity within the context of “superconformal symmetry breakdown”. We find that N = 2 supergravity is described in terms of two independent supertensors: W_αβij and T_αi. We also discuss general properties of superspace covariant derivatives to derive the relation of superspace to component approaches.     

General approach to deep inelastic scattering

Due to preliminary indications of a possible scaling violation, it is interesting to clarify which of the parton light-cone results are indeed the consequences of a more general scheme. We consider the constraints imposed by the general ideas of duality (absence of exotics in the t-channel) applied to deep inelastic single-particle distributions. This provides a restrictive scheme, although it allows for a larger set of diagrams than that of the parton model. However, in a particular kinematical region where the diffractive component of the total deep inelastic cross section can be neglected, all the algebraic results of the parton model are recovered by this scheme.     

Quark recombination in deuteron fragmentation

Low-P _T production off deuteron in the fragmentation region is studied on the basis of a six-quark picture of deuteron. It is argued that all the six valence quarks participate equally in the hadronization processes associated with meson and baryon productions. Thex-distribution of the inclusive cross sections is studied in the framework of a quark recombination model. Fit with experimental data leads to a determination of the valence and sea quark distributions in deuteron. Probabilistic arguments applied to a general recombination picture are shown to lead to some experimentally verifiable constraints on baryon multiplicities. Possibilities of determining the various recombination probabilities are also discussed.     

Bounds on elastic absorptive parts

We reduce the general problem of obtaining bounds on elastic absorptive parts of a scattering amplitude subject to unitarity restrictions and any number of constraints involving partial wave amplitudes linearly to a form where it can be directly applied to any such problem. A series of bounds on absorptive parts for positive momentum transfer square t, within the Lehmann-Martin ellipse, is derived. These involve a knowledge of the first few momentum transfer derivatives of the absorptive part in the forward direction, i.e., t = 0. Upper and lower bounds on the higher t-derivatives of the absorptive part at t = 0 are also given.