This dissertation is concerned with variational problems whose field variables are functions on a product manifold M x G of two manifolds M and G. These field variables transform as type (0,1) tensor fields on M and are denoted by ψ(h)ᵅ (h = 1, ..., n = dim M, α = 1, ..., r = dim G). The dependence of ψ(h)ᵅ on the coordinates of G is given by a generalized gauge transformation that depends on a local map h:M → G. The requirement that a Lagrangian that is defined in terms of these field variables be independent of the coordinates of G and the choice of the map h endows G with a local Lie group structure. The class of Lagrangians that exhibits this type of invariance may be characterized by three invariance identities. These identities, together with an arbitrary solution of a system of partial differential equations, may be used to define field strengths associated with the ψ(h)ᵅ as well as connection and curvature forms on M. The former may be used to express the Euler-Lagrange equations in a particularly simple form. An energy-momentum tensor may also be defined in the usual manner; however additional conditions must be imposed in order to guarantee the existance of conservation laws resulting from this tensor. The above analysis may be repeated for the case that the field variables behave as type (0,2) tensor fields under coordinate transformations on M. For these field variables, the Euler-Lagrange expressions may be expressed as a product of a covariant divergence with the components λʰ of a type (1,0) vector field on M. An unexpected consequence of this construction is the fact that the Euler-Lagrange equations that result for the vector field λʰ are satisfied whenever the Euler-Lagrange equations associated with the field variables are satisfied.

International Telemetering Conference Proceedings / October 25-28, 1993 / Riviera Hotel and Convention Center, Las Vegas, Nevada / Transducers whose outputs are characterized as a charge require signal conditioning to convert the charge produced to a voltage or current for use in instrumentation systems. Blast gauges, in particular, require processing which preserves the transient nature of the data and very fast risetimes, which would otherwise be degraded by long cable runs and parasitic capacitances. A charge amplifier which amplifies and converts a charge to a low-impedance voltage suitable for driving coaxial lines is described, along with theory of operation. Charge amplifiers of the type described are relatively unaffected by temperature and power supply variations, and occupy less than two square inches of printed circuit board space per channel.

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Fases topológicas da matéria são caracterizadas por terem uma degenerescên- cia do estado fundamental que depende da topologia da variedade em que o sistema físico é definido, além disso apresentam estados excitados no interior do sistema que são interpretados como sendo quase-partículas com estatística de tipo anyonica. Estes sistemas apresentam também excitações sem gap de energia em sua borda. Fases topologicamente ordenadas distintas não podem ser distinguidas pelo esquema usual de quebra de simetria de Ginzburg-Landau. Nesta dissertação apresentamos como exemplo o modelo mais simples de um sistema com Ordem Topológica, a saber, o Toric Code (TC), introduzido originalmente por A. Kitaev em [1]. O estado fundamental deste modelo ap- resenta degenerescência igual a 4 quando incorporado à superfície de um toro. As excitações elementares são interpretadas como sendo quase-partículas com estatística do tipo anyonica. O TC é um caso especial de uma classe mais geral de models chamados de Quantum Double Models (QDMs), estes modelos podem ser entendidos como sendo uma implementação de Teorias de gauge na rede em (2 + 1) dimensões na formulação Hamiltoniana, em que os graus de liberdade vivem nas arestas da rede e são elementos do grupo de gauge G. Nós generalizamos estes modelos com a inclusão de campos de matéria nos vértices da rede. Também apresentamos uma construção detalhada de tais modelos e mostramos que eles são exatamente solúveis. Em particular, exploramos o modelo que corresponde à escolher o grupo de gauge como sendo o grupo cíclico Z2 e os graus de liberdade de matéria como sendo elementos de um espaço vetorial bidimensional V2. Além disso, mostramos que a degenerescência do estado fundamental não depende da topologia da variedade e obtemos os estados excitados mais elementares deste modelo. / Topological phases of matter are characterized for having a topologically dependent ground state degeneracy, anyonic quasi-particle bulk excitations and gapless edge excitations. Different topologically ordered phases of matter can not be distinguished by te usual Ginzburg-Landau scheme of symmetry breaking. Therefore, a new mathematical framework for the study of such phases is needed. In this dissertation we present the simplest example of a topologically ordered system, namely, the \\Toric Code (TC) introduced by A. Kitaev in [1]. Its ground state is 4-fold degenerate when embedded on the surface of a torus and its elementary excited states are interpreted as quasi-particle anyons. The TC is a particular case of a more general class of lattice models known as Quantum Double Models (QDMs) which can be interpreted as an implementation of (2+1) Lattice Gauge Theories in the Hamiltonian formulation with discrete gauge group G. We generalize these models by the inclusion of matter fields at the vertices of the lattice. We give a detailed construction of such models, we show they are exactly solvable and explore the case when the gauge group is set to be the abelian Z_2 cyclic group and the matter degrees of freedom to be elements of a 2-dimensional vector space V_2. Furthermore, we show that the ground state degeneracy is not topologically dependent and obtain the most elementary excited states.