The action semantics of object-oriented languages

Action Semantics is a framework for defining the semantics of languages. It is intended to be accessible to a wider audience of Computer Scientists than traditional semantics frameworks (such as Denotational Semantics). There has been little work carried out to date on the techniques required to define object-oriented languages with Action Semantics. The work presented in this thesis examines four potential approaches to defining the Action Semantics of object-oriented languages. In order to illustrate the four approaches a simple language EIL (Example Inheritance Language) is given, and described using these four approaches. The language Smalltalk-80 has been selected for a case study of a practical application of one of the techniques described above. It is important to be able to relate Action Semantics definitions of object-oriented languages to similar definitions given in other frameworks. It is described how this can be achieved. An example is given for the Action Semantics and Denotational Semantics of Smalltalk. This thesis concludes that it is feasible to produce Action Semantics definitions of object-oriented languages

Electron Mass Anomalous Dimension at O(1/N^2_f) in Quantum Electrodynamics

The critical exponent corresponding to the renormalization of the composite operator $\bar{\psi}\psi$ is computed in quantum electrodynamics at O(1/\Nf^2) in arbitrary dimensions and covariant gauge at the non-trivial zero of the $\beta$-function in the large \Nf expansion and the exponent corresponding to the anomalous dimension of the electron mass which is a gauge independent object is deduced. Expanding in powers of $\epsilon$ $=$ $2$ $-$ $d/2$ we check it is consistent with the known three loop perturbative structure and determine the subsequent coefficients in the coupling constantComment: 12 pages (latex), 1 figure (available from author on request), LTH-31

Three loop gauge beta-function for the most general single gauge-coupling theory

We calculate the three loop contribution to the beta-function of the gauge coupling constant in a general, anomaly-free, renormalisable gauge field theory involving a single gauge coupling using the background field method in the MSbar scheme.Comment: 10 latex page

Quark, Gluon and Ghost Anomalous Dimensions at O(1/N_f) in Quantum Chromodynamics

By considering the scaling behaviour of various Feynman graphs at leading order in large \Nf at the non-trivial fixed point of the $d$-dimensional $\beta$-function of QCD we deduce the critical exponents corresponding to the quark, gluon and ghost anomalous dimensions as well as the anomalous dimensions of the quark-quark-gluon and ghost-ghost-gluon vertices in the Landau gauge. As the exponents encode all orders information on the perturbation series of the corresponding renormalization group functions we find agreement with the known three loop structure and, moreover, we provide new information at all subsequent orders.Comment: 13 pages latex plus 3 figures (available from author on request), LTH-31

Three loop QCD MOM beta-functions

We present the full expressions for the QCD beta-function in the MOMggg, MOMq and MOMh renormalization schemes at three loops for an arbitrary colour group in the Landau gauge. The results for all three schemes are in very good agreement with the SU(3) numerical estimates provided by Chetyrkin and Seidensticker.Comment: 9 latex page

QCD and QED renormalization group functions - a large N_f approach

The large N_f self-consistency programme is reviewed. As an application the QCD beta-function is computed at O(1/N_f) and the anomalous dimensions of polarized twist-2 singlet operators are determined at the same order.Comment: Talk given at DESY workshop QCD and QED in higher order; 8 pages latex plus 1 figur

Multibeam Maser Survey of methanol and excited OH in the Magellanic clouds: new detections and maser abundance estimates

‘The definitive version is available at www.blackwell-synergy.com.’ Copyright Blackwell Publishing DOI: 10.1111/j.1365-2966.2008.12888.xPeer reviewe

Anomalous Dimension of Non-Singlet Wilson Operators at O(1/N_f) in Deep Inelastic Scattering

We use the large N_f self consistency formalism to compute the $O(1/N_f)$ critical exponent corresponding to the renormalization of the flavour non-singlet twist two Wilson operators which arise in the operator product expansion of currents in deep inelastic processes. Expanding the $d$-dimensional expression in powers of $\epsilon$ $=$ $(4-d)/2$ the coefficients of $\epsilon$ agree with the known two loop structure of the corresponding renormalization group function and we deduce analytic expressions for all moments, $n$, at three and higher orders in perturbation theory in the \overline{\mbox{MS}} scheme at $O(1/N_f)$.Comment: 13 Latex pages, 1 figure (available from author on request), LTH-32

A determination of <A^2> and the non-perturbative vacuum energy of Yang-Mills theory in the Landau gauge

We discuss the 2-point-particle-irreducible (2PPI) expansion, which sums bubble graphs to all orders, in the context of SU(N) Yang-Mills theory in the Landau gauge. Using the method we investigate the possible existence of a gluon condensate of mass dimension two, , and the corresponding non-zero vacuum energy. This condensate gives rise to a dynamically generated mass for the gluon.Comment: 12 pages, 3 eps figures; v2 : wrong use of "enhancement" instead of "suppression" corrected; v3: version accepted for publication in Phys.Lett.

Computation of quark mass anomalous dimension at O(1/N_f^2) in quantum chromodynamics

We present the formalism to calculate d-dimensional critical exponents in QCD in the large N_f expansion where N_f is the number of quark flavours. It relies in part on demonstrating that at the d-dimensional fixed point of QCD the critical theory is equivalent to a non-abelian version of the Thirring model. We describe the techniques used to compute critical two and three loop Feynman diagrams and as an application determine the quark wave function, eta, and mass renormalization critical exponents at O(1/N_f^2) in d-dimensions. Their values when expressed in relation to four dimensional perturbation theory are in exact agreement with the known four loop MSbar results. Moreover, new coefficients in these renormalization group functions are determined to six loops and O(1/N_f^2). The computation of the exponents in the Schwinger Dyson approach is also provided and an expression for eta in arbitrary covariant gauge is given.Comment: 41 latex pages, 17 postscript figure