On a different BRST constructions for a given Lie algebra

The method of the BRST quantization is considered for the system of constraints, which form a Lie algebra. When some of the Cartan generators do not imply any conditions on the physical states, the system contains the first and the second class constraints. After the introduction auxiliary bosonic degrees of freedom for these cases, the corresponding BRST charges with the nontrivial structure of nonlinear terms in ghosts are constructed.Comment: 10 Pages, LaTe

Symbolic Algebra and Renormalization of Gauge Theories

Symbolic algebra relevant to the renormalization of gauge theories can be efficiently performed by machine using modern packages. We devise a scheme for representing and manipulating the objects involved in perturbative calculations of gauge theories. This scheme is readily implemented using the general purpose package, Mathematica. The techniques discussed are used to calculate renormalization group functions for a non-abelian $SU(m)$ gauge theory with massless fermions in a representation R, in the two-loop approximation, and to simplify some expressions arising in electroweak calculations at the two loop level.Comment: 16 pages, LaTex, 2 diagrams drawn with FEYNMAN, uses cite.sty Entire manuscript available as a ps file at http://www.physics.adelaide.edu.au/theory/home.html Also available via anonymous ftp at ftp://adelphi.adelaide.edu.au/pub/theory/ADP-95-41.T193.ps Accepted for publication in Computer Physics Communicatio

Nonperturbative Contributions in an Analytic Running Coupling of QCD

In the framework of analytic approach to QCD the nonperturbative contributions in running coupling of strong interaction up to 4-loop order are obtained in an explicit form. For all $Q>\Lambda$ they are shown to be represented in the form of an expansion in inverse powers of Euclidean momentum squared. The expansion coefficients are calculated for different numbers of active quark flavors $n_f$ and for different number of loops taken into account. On basis of the stated expansion the effective method for precise calculation of the analytic running coupling can be developed.Comment: 9 pages, LaTeX, 1 table, 1 eps figur

RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses

In this paper the formulae are collected which are needed for the computation of the strong coupling constant and quark masses at different energy scales and for different number of active flavours. All equations contain the state-of-the-art QCD corrections up to three- and sometimes even four-loop order. For the practical implementation {\tt Mathematica} is used and a package containing useful procedures is provided.Comment: 32 pages, ps figures included, accepted for publication in Computer Physics Communication

Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme

We present in analytic form the matching conditions for the strong coupling constant alpha_s^(n_f)(mu) at the flavour thresholds to three loops in the modified minimal-subtraction scheme. Taking into account the recently calculated coefficient beta_3 of the Callan-Symanzik beta function of quantum chromodynamics, we thus derive a four-loop formula for alpha_s^(n_f)(mu) together with appropriate relationships between the asymptotic scale parameters Lambda^(n_f) for different numbers of flavours n_f.Comment: 10 pages (Latex), 3 figures (Postscript

Form Factors and QCD in Spacelike and Timelike Region

We analyze the basic hard exclusive processes: \pi\gamma*\gamma - transition, pion and nucleon electromagnetic form factors, and discuss the analytic continuation of QCD formulas from the spacelike q^2<0 to the timelike region q^2 >0 of the relevant momentum transfers. We describe the construction of the timelike version of the coupling constant \alpha_s. We show that due to the analytic continuation of the collinear logarithms each eigenfunction of the evolution equation acqiures a phase factor and investigate the resulting interference effects which are shown to be very small. We found no sources for the K-factor-type enhancements in the perturbative QCD contribution to the hadronic form factors. To study the soft part of the pion electromagnetic form factor, we use a QCD sum rule inspired model and show that there are non-canceling Sudakov double logarithms which result in a K-factor-type enhancement in the timelike region.Comment: 12 pages, LaTeX; a few typos corrected, references adde

Results and Techniques of Multi-Loop Calculations

In this review some recent multi-loop results obtained in the framework of perturbative Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED) are discussed. After reviewing the most advanced techniques used for the computation of renormalization group functions, we consider the decoupling of heavy quarks. In particular, an effective method for the evaluation of the decoupling constants is presented and explicit results are given. Furthermore the connection to observables involving a scalar Higgs boson is worked out in detail. We review the radiative corrections of a Higgs boson into gluons and quarks and present explicit results up to order $\alpha_s^4$ and $\alpha_s^3$, respectively. In this review special emphasis is put on the applications of asymptotic expansions. A method is described which combines expansion terms of different kinematical regions with the help of conformal mapping and Pad\'e approximation. This method allows us to proceed beyond the present scope of exact multi-loop calculations. As far as physical processes are concerned, we review the computation of three-loop current correlators in QCD taking into account the full mass-dependence. In a further application four-loop diagrams are considered which contribute to the order $\alpha^2$ QED corrections to the $\mu$ decay. Finally the calculation of the three-loop relation between the $\bar{\rm MS}$ and on-shell quark mass definitions is presented. To complete the presentation, some technical details are presented in the Appendix, where also explicit analytical results are listed.Comment: 125 pages, to appear in Physics Reports, eqs. (4.11), (4.77), (4.79) and (C.3) corrected, references and note adde

An overlooked cause of septic shock: Staphylococcal Toxic Shock Syndrome secondary to an axillary abscess

Staphylococcal Toxic Shock Syndrome (TSS) is characterized by rapid onset of fever, rash, hypotension, and multiorgan system involvement. Clinical manifestations of staphylococcal TSS include fever, chills, hypotension, and a diffuse macular erythroderma followed by desquamation one to two weeks later. The disease came to public attention in the 1980s with the occurrence of a series of menstrual-associated cases. However, the relative incidence of staphylococcal TSS not associated with menstruation has increased, and still, it remains an overlooked cause of septic shock. We present the case of a healthy 19-year-old male that presented with fever, chills, malaise, near-syncope, and a non-fluctuant, mobile nodule in the left armpit. The patient developed septic shock requiring critical care. He underwent extensive investigations resulting negative except for PCR for the detection of MRSA, raising the suspicion for STSS. For that reason, antibiotics for staphylococcal coverage were started, after which he started to improve. Ultimately, the mobile nodule evolved to fluctuant access. Incision and drainage was performed, and cultures confirmed the presence of Staphylococcus aureus