Sh-Lie algebras Induced by Gauge Transformations

The physics of ``particles of spin $\leq 2$'' leads to representations of a Lie algebra $\Xi$ of gauge parameters on a vector space $\Phi$ of fields. Attempts to develop an analogous theory for spin $>2$ have failed; in fact, there are claims that such a theory is impossible (though we have been unable to determine the hypotheses for such a `no-go' theorem). This led BBvD [burgers:diss,BBvd:three,BBvD:probs] to generalize to `field dependent parameters' in a setting where some analysis in terms of smooth functions is possible. Having recognized the resulting structure as that of an sh-lie algebra ($L_\infty$-algebra), we have now reproduced their structure entirely algebraically, hopefully shedding some light on what is going on.Comment: Now 24 pages, LaTeX, no figures Extensively revised in terms of the applications and on shell aspects. In particular, a new section 8 analyzes Ikeda's 2D example from our perspective. His bracket is revealed as a generalized Kirillov-Kostant bracket. Additional reference

The Bastion Network Project

Workshop on Education in Computer Security (WECS) 6The Naval Postgraduate School’s Center for Information Systems Security Studies and Research (CISR) has developed a small, but realistic network lab—the Bastion Network—that is dedicated to educating students in the myriad elements involved in the secure operation of a computer network. This paper describes the rationale for this network lab, and offers an overview of a simple framework that could accommodate educational network interaction with other schools that have similar IA educational goals, and that have, or may soon acquire, similarly designated labs. The framework describes the essential elements of a memorandum of understanding, and twelve suggested inter-network cyber-exercise scenarios

The sh Lie structure of Poisson brackets in field theory

A general construction of an sh Lie algebra from a homological resolution of a Lie algebra is given. It is applied to the space of local functionals equipped with a Poisson bracket, induced by a bracket for local functions along the lines suggested by Gel'fand, Dickey and Dorfman. In this way, higher order maps are constructed which combine to form an sh Lie algebra on the graded differential algebra of horizontal forms. The same construction applies for graded brackets in field theory such as the Batalin-Fradkin-Vilkovisky bracket of the Hamiltonian BRST theory or the Batalin-Vilkovisky antibracket.Comment: 24 pages Latex fil

BRST Extension of Geometric Quantization

Consider a physical system for which a mathematically rigorous geometric quantization procedure exists. Now subject the system to a finite set of irreducible first class (bosonic) constraints. It is shown that there is a mathematically rigorous BRST quantization of the constrained system whose cohomology at ghost number zero recovers the constrained quantum states. Moreover this space of constrained states has a well-defined Hilbert space structure inherited from that of the original system. Treatments of these ideas in the Physics literature are more general but suffer from having states with infinite or zero "norms" and thus are not admissible as states. Also the BRST operator for many systems require regularization to be well-defined. In our more restricted context we show that our treatment does not suffer from any of these difficulties. This work was submitted for publication March 21,2006

Noether's variational theorem II and the BV formalism

We review the basics of the Lagrangian approach to field theory and recast Noether's Second Theorem formulated in her language of dependencies using a slight modernization of terminology and notation. We then present the Cattaneo-Felder sigma model and work out the Noether identities or dependencies for this model. We review the description of the Batalin-Vilkovisky formalism and show explicitly how the anti-ghosts encode the Noether identities in this example.Comment: 15 pages, submitted to the Proceedings of the 2002 Winter School ``Geometry and Physics'', Srni, Czech Republi

A Frame Bundle Generalization of Multisymplectic Momentum Mappings

This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to $L_VY$, the bundle of vertically adapted linear frames over the bundle of field configurations $Y$. Specifically, the generalized field momentum observables are vector-valued momentum mappings on the vertically adapted frame bundle generated from automorphisms of $Y$. The generalized symplectic geometry on $L_VY$ is a covering theory for multisymplectic geometry on the multiphase space $Z$, and it follows that the field momentum observables on $Z$ are generalized by those on $L_VY$. Furthermore, momentum observables on $L_VY$ produce conserved quantities along flows in $L_VY$. For translational and orthogonal symmetries of fields and reparametrization symmetry in mechanics, momentum is conserved, and for angular momentum in time-evolution mechanics we produce a version of the parallel axis theorem of rotational dynamics, and in special relativity, we produce the transformation of angular momentum under boosts.Comment: 23 page

Algebra Structures on Hom(C,L)

We consider the space of linear maps from a coassociative coalgebra C into a Lie algebra L. Unless C has a cocommutative coproduct, the usual symmetry properties of the induced bracket on Hom(C,L) fail to hold. We define the concept of twisted domain (TD) algebras in order to recover the symmetries and also construct a modified Chevalley-Eilenberg complex in order to define the cohomology of such algebras

Optimal Provisioning and Pricing of Differentiated Services Using QoS Class Promotion

This paper introduces a new method for optimally provisioning and pricing di#erentiated services, that maximizes profit and maintains a small blocking probability. Resources are provisioned per Quality of Service (QoS) class over the long-term (service level agreement duration), then priced based on user demand over the short-term. Unique to this method is the ability to dynamically promote tra#c from one QoS class to a higher QoS class, based on estimated demand statistics. This additional flexibility encourages better short-term utilization of the classes, resulting in higher profits while maintaining a low blocking probability. Experimental results will demonstrate QoS class promotion can obtain higher profits, as compared to other provisioning and allocation methods