Network representation of electromagnetic fields and forces using generalized bond graphs

We show that it is possible to describe electromagnetic (E-M) fields with a generalized network representation (generalized bond graphs). E-M fields inmoving matter, forces due to E-M fields (Lorentz force, ets.) and field transformations are included in the network description. The relations of these E-M phenomena with respect to each other are clearly represented by the bond graph. We also show that it is not possible to describe E-M phenomena in moving matter with conventional bond graphs, but that a generalized bond graph concept is required.\ud \ud The description of simple E-M devices with conventional bond graphs is based on rather drastic assumptions, i.e. quasi-static conditions (E-M radiation neglected), homogeneous fields, isotropic linear material, etc. These assumptions are not made in this paper

Generalized LFT-Based Representation of Parametric Uncertain Models

In this paper, we introduce a general descriptor-type linear fractional transformation (LFT) representation of rational parametric matrices. This is a generalized representation of arbitrary rationally dependent multivariate functions in LFT-form. As applications, we develop explicit LFT-realizations of the transfer-function matrix of a linear descriptor system whose state-space matrices depend rationally on a set of uncertain parameters. The resulting descriptor LFT-based uncertainty models generally have smaller orders than those obtained by using the standard LFT-based modelling approach. An example of an uncertain vehicle model illustrates the capability of the method

Generalized Pauli-Gursey transformation and Majorana neutrinos

We discuss a generalization of the Pauli-Gursey transformation, which is motivated by the Autonne-Takagi factorization, to an arbitrary $n$ number of generations of neutrinos using $U(2n)$ that defines general canonical transformations and diagonalizes symmetric complex Majorana mass matrices in special cases. The Pauli-Gursey transformation mixes particles and antiparticles and thus changes the definition of the vacuum and C. We define C, P and CP symmetries at each Pauli frame specified by a generalized Pauli-Gursey transformation. The Majorana neutrinos in the C and P violating seesaw model are then naturally defined by a suitable choice of the Pauli frame, where only Dirac-type fermions appear with well-defined C, P and CP, and thus the C symmetry for Majorana neutrinos agrees with the C symmetry for Dirac-type fermions. This fully symmetric setting corresponds to the idea of Majorana neutrinos as Bogoliubov quasi-particles. In contrast, the conventional direct construction of Majorana neutrinos in the seesaw model, where CP is well-defined but C and P are violated, encounters the mismatch of C symmetry for Majorana neutrinos and C symmetry for chiral fermions; this mismatch is recognized as the inevitable appearance of the singlet (trivial) representation of C symmetry for chiral fermions.Comment: 15 pages. Slightly expanded with some explanatory paragraphs added. This version is going to appear in Phys.Lett.

Representation theory of finite W algebras

In this paper we study the finitely generated algebras underlying $W$ algebras. These so called 'finite $W$ algebras' are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings of $sl_2$ into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finite $W$ algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finite $W$ symmetry. In the second part we BRST quantize the finite $W$ algebras. The BRST cohomology is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finite $W$ algebras in one stroke. Explicit results for $sl_3$ and $sl_4$ are given. In the last part of the paper we study the representation theory of finite $W$ algebras. It is shown, using a quantum version of the generalized Miura transformation, that the representations of finite $W$ algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finite $W$ algebras.Comment: 62 pages, THU-92/32, ITFA-28-9

Restoration of particle number as a good quantum number in BCS theory

As shown in previous work, number projection can be carried out analytically for states defined in a quasi-particle scheme when the states are expressed in a coherent state representation. The wave functions of number-projected states are well-known in the theory of orthogonal polynomials as Schur functions. Moreover, the functions needed in pairing theory are a particularly simple class of Schur functions that are easily constructed by means of recursion relations. It is shown that complete sets of states can be projected from corresponding quasi-particle states and that such states retain many of the properties of the quasi-particle states from which they derive. It is also shown that number projection can be used to construct a complete set of orthogonal states classified by generalized seniority for any nucleus.Comment: 21 pages, 2 figures, epsf.def style file for printing figure

Generalized Transformation for Decorated Spin Models

The paper discusses the transformation of decorated Ising models into an effective \textit{undecorated} spin models, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes $[-s,s]$ is used to obtain an analytical expression of the transformation. This kind of transformation is very useful to obtain the partition function of decorated systems. The method presented by Fisher is also extended, in order to obtain the correlation functions of the decorated Ising models transforming into an effective undecorated Ising models. We apply this transformation to a particular mixed spin-(1/2,1) and (1/2,2) square lattice with only nearest site interaction. This model could be transformed into an effective uniform spin-$S$ square lattice with nearest and next-nearest interaction, furthermore the effective Hamiltonian also include combinations of three-body and four-body interactions, particularly we considered spin 1 and 2.Comment: 16 pages, 4 figure

Generalized Jordan-Wigner Transformations

We introduce a new spin-fermion mapping, for arbitrary spin $S$ generating the SU(2) group algebra, that constitutes a natural generalization of the Jordan-Wigner transformation for $S=1/2$. The mapping, valid for regular lattices in any spatial dimension $d$, serves to unravel hidden symmetries in one representation that are manifest in the other. We illustrate the power of the transformation by finding exact solutions to lattice models previously unsolved by standard techniques. We also present a proof of the existence of the Haldane gap in $S=$1 bilinear nearest-neighbors Heisenberg spin chains and discuss the relevance of the mapping to models of strongly correlated electrons. Moreover, we present a general spin-anyon mapping for the case $d \leq 2$.Comment: 5 pages, 1 psfigur