Exact electromagnetic duality

This talk, given at several conferences and meetings, explains the background leading to the formulation of the exact electromagnetic duality conjecture believed to be valid in N=4 supersymmetric SU(2) gauge theory

Representations of the Canonical group, (the semi-direct product of the Unitary and Weyl-Heisenberg groups), acting as a dynamical group on noncommuting extended phase space

The unitary irreducible representations of the covering group of the Poincare group P define the framework for much of particle physics on the physical Minkowski space P/L, where L is the Lorentz group. While extraordinarily successful, it does not provide a large enough group of symmetries to encompass observed particles with a SU(3) classification. Born proposed the reciprocity principle that states physics must be invariant under the reciprocity transform that is heuristically {t,e,q,p}->{t,e,p,-q} where {t,e,q,p} are the time, energy, position, and momentum degrees of freedom. This implies that there is reciprocally conjugate relativity principle such that the rates of change of momentum must be bounded by b, where b is a universal constant. The appropriate group of dynamical symmetries that embodies this is the Canonical group C(1,3) = U(1,3) *s H(1,3) and in this theory the non-commuting space Q= C(1,3)/ SU(1,3) is the physical quantum space endowed with a metric that is the second Casimir invariant of the Canonical group, T^2 + E^2 - Q^2/c^2-P^2/b^2 +(2h I/bc)(Y/bc -2) where {T,E,Q,P,I,Y} are the generators of the algebra of Os(1,3). The idea is to study the representations of the Canonical dynamical group using Mackey's theory to determine whether the representations can encompass the spectrum of particle states. The unitary irreducible representations of the Canonical group contain a direct product term that is a representation of U(1,3) that Kalman has studied as a dynamical group for hadrons. The U(1,3) representations contain discrete series that may be decomposed into infinite ladders where the rungs are representations of U(3) (finite dimensional) or C(2) (with degenerate U(1)* SU(2) finite dimensional representations) corresponding to the rest or null frames.Comment: 25 pages; V2.3, PDF (Mathematica 4.1 source removed due to technical problems); Submitted to J.Phys.

Diagnosing disagreements:The authentication of the positron 1931–1934

This paper bridges a historiographical gap in accounts of the prediction and discovery of the positron by combining three ingredients. First, the prediction and discovery of the positron are situated in the broader context of a period of ‘crystallisation’ of a research tradition. Second, the prediction and discovery of the positron are discussed in the context of the 'authentication’ of the particle. Third, the attitude of the relevant scientists to both prediction and discovery are conceptualised in terms of the idea of 'perspectives’. It will be argued that by examining the prediction and discovery of the positron in the context of authentication within a period of crystallisation, we can better understand disagreements regarding the positron between relevant scientists (Dirac, Bohr, and Pauli) in the period 1931-34

Assessing the Risk due to Software Faults: Estimates of Failure Rate versus Evidence of Perfection.

In the debate over the assessment of software reliability (or safety), as applied to critical software, two extreme positions can be discerned: the ‘statistical’ position, which requires that the claims of reliability be supported by statistical inference from realistic testing or operation, and the ‘perfectionist’ position, which requires convincing indications that the software is free from defects. These two positions naturally lead to requiring different kinds of supporting evidence, and actually to stating the dependability requirements in different ways, not allowing any direct comparison. There is often confusion about the relationship between statements about software failure rates and about software correctness, and about which evidence can support either kind of statement. This note clarifies the meaning of the two kinds of statement and how they relate to the probability of failure-free operation, and discusses their practical merits, especially for high required reliability or safety

Translational invariance in bag model

In this thesis, we investigate the effect of restoring the translational invariance to an approximation to the MIT bag model on the calculation of deep in elastic structure functions. In chapter one, we review the model, its major problems and we outline Dirac's method of quantisation. This method is used in chapter two to quantise a two-dimensional complex scalar bag and formal expressions for the form factor and the structure functions are obtained. In chapter three, we try to study the expression for the structure function away from the Bjorken limit . The corrections to the L(_o) - approximation to the structure function i s calculated in chapter four and it is shown to be large. Finally , in chapter five, we introduce a bag-like model for kinematic corrections to structure functions and obtain agreement with data between 2 and 6 (GeV/C)(^2

A Study of Sufficient Conditions for Hamiltonian Cycles

A graph G is Hamiltonian if it has a spanning cycle. The problem of determining if a graph is Hamiltonian is well known to be NP-complete. While there are several necessary conditions for Hamiltonicity, the search continues for sufficient conditions. In their paper, On Smallest Non-Hamiltonian Regular Tough Graphs (Congressus Numerantium 70), Bauer, Broersma, and Veldman stated, without a formal proof, that all 4-regular, 2-connected, 1-tough graphs on fewer than 18 nodes are Hamiltonian. They also demonstrated that this result is best possible. Following a brief survey of some sufficient conditions for Hamiltonicity, Bauer, Broersma, and Veldman\u27s result is demonstrated to be true for graphs on fewer than 16 nodes. Possible approaches for the proof of the n=16 and n=17 cases also will be discussed

Solitons in supersymmetric models

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