Augmented Superfield Approach To Unique Nilpotent Symmetries For Complex Scalar Fields In QED

The derivation of the exact and unique nilpotent Becchi-Rouet-Stora-Tyutin (BRST)- and anti-BRST symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem in the framework of superfield approach to BRST formalism. These nilpotent symmetry transformations are deduced for the four (3 + 1)-dimensional (4D) complex scalar fields, coupled to the U(1) gauge field, in the framework of augmented superfield formalism. This interacting gauge theory (i.e. QED) is considered on a six (4, 2)-dimensional supermanifold parametrized by four even spacetime coordinates and a couple of odd elements of the Grassmann algebra. In addition to the horizontality condition (that is responsible for the derivation of the exact nilpotent symmetries for the gauge field and the (anti-)ghost fields), a new restriction on the supermanifold, owing its origin to the (super) covariant derivatives, has been invoked for the derivation of the exact nilpotent symmetry transformations for the matter fields. The geometrical interpretations for all the above nilpotent symmetries are discussed, too.Comment: LaTeX file, 17 pages, journal versio

From Trees to Loops and Back

We argue that generic one-loop scattering amplitudes in supersymmetric Yang-Mills theories can be computed equivalently with MHV diagrams or with Feynman diagrams. We first present a general proof of the covariance of one-loop non-MHV amplitudes obtained from MHV diagrams. This proof relies only on the local character in Minkowski space of MHV vertices and on an application of the Feynman Tree Theorem. We then show that the discontinuities of one-loop scattering amplitudes computed with MHV diagrams are precisely the same as those computed with standard methods. Furthermore, we analyse collinear limits and soft limits of generic non-MHV amplitudes in supersymmetric Yang-Mills theories with one-loop MHV diagrams. In particular, we find a simple explicit derivation of the universal one-loop splitting functions in supersymmetric Yang-Mills theories to all orders in the dimensional regularisation parameter, which is in complete agreement with known results. Finally, we present concrete and illustrative applications of Feynman's Tree Theorem to one-loop MHV diagrams as well as to one-loop Feynman diagrams.Comment: 52 pages, 17 figures. Some typos in Appendix A correcte

Lyapunov and Wirtinger inequalities

AbstractIn this paper, we prove the Lyapunov inequality for the second-order linear differential equation (r(t)φ(y′(t)))′+p(t)φ(y(t))=0, where(i)φ(s) = |s|αt-2s, α > 1 is a fixed real number(ii)r(t) and p(t) are integrable on [a, b] with r(t) > 0 on [a, b].On the other hand, a generalized Wirtinger inequality is also given

Tracing Ghost Cavities with Low Frequency Radio Observations

We present X-ray and multi-frequency radio observations of the central radio sources in several X-ray cavity systems. We show that targeted radio observations are key to determining if the lobes are being actively fed by the central AGN. Low frequency observations provide a unique way to study both the lifecycle of the central radio source as well as its energy input into the ICM over several outburst episodes.Comment: 6 pages, 4 figures, To appear in the Proceedings of "Heating vs. Cooling in Galaxies and Clusters of Galaxies", eds. H. Boehringer, P. Schuecker, G. W. Pratt & A. Finoguenov (ESO Astrophysics Symposia, Springer-Verlag), Garching (Germany), August 200

Effect of Boron substitution on the superconductivity of non-oxide perovskite MgCNi3

We report synthesis, structural and magnetic (DC and AC) properties of Boron substituted MgCNi3 superconductor. A series of polycrystalline bulk samples Mg1.2C1.6-xBxNi3 (x = 0.0, 0.08 and 0.16) is synthesized through standard solid-state reaction route, which are found to crystallize in cubic perovskite structure with space group Pm3m. Rietveld analysis of observed XRD data show that lattice parameters expand from a = 3.8106 (4) {\AA} for pure, to 3.8164 (2) {\AA} and 3.8173 (5) {\AA} for 5% and 10% Boron substituted samples respectively. DC magnetization exhibited superconducting transition (Tc) at around 7.3 K for pure sample, and the same decreases slightly with Boron substitution. The lower critical field (Hc1) at 2 K is around 150 Oe for pure sample, which increases slightly with Boron substitution. For pure sample the upper critical field (Hc2) being determined from AC susceptibility measurements is 11.6 kOe and 91.70 kOe with 50% and 90% diamagnetism criteria respectively, which decreases to 5.57 kOe and 42.5 kOe respectively for 10% Boron substituted sample. 10% Boron substitution at Carbon site has decreased both the Hc2 and Tc. On the other hand lower critical field (Hc1) at 2 K is slightly increased from around 150 Oe for pure sample, to 200 Oe for 10% Boron substituted sample. Seemingly, the Carbon site Boron substitution induced disorder though has increased slightly the Hc1 but with simultaneous decrease in superconducting transition temperature (Tc) and upper critical field (Hc2). The high relative proportion of Ni in studied MgCNi3 suggests that magnetic interactions are important and non-oxide perovskite structure make it interesting.Comment: 13 Pages Text + Figures: comments/suggestions ([email protected]

New symmetries for Abelian gauge theory in superfield formulation

We show the existence of some new local, covariant and continuous symmetries for the BRST invariant Lagrangian density of a free two ($1 + 1$)-dimensional (2D) Abelian U(1) gauge theory in the framework of superfield formalism. The Noether conserved charges corresponding to the above local continuous symmetries find their geometrical origin as the translation generators along the odd (Grassmannian)- and even (bosonic) directions of the four ($2 + 2)$-dimensional compact supermanifold. Some new discrete symmetries are shown to exist in the superfield formulation. The logical origin for the existence of BRST- and co-BRST symmetries is shown to be encoded in the Hodge decomposed versions (of the 2D fermionic vector fields) that are consistent with the discrete symmetries of the theory.Comment: LaTeX, 12 pages, no figures, Eqns. (3.10),(4.6),(4.7) correcte

Nilpotent Symmetries for QED in Superfield Formalism

In the framework of superfield approach, we derive the local, covariant, continuous and nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations on the U(1) gauge field $(A_\mu)$ and the (anti-)ghost fields $((\bar C)C)$ of the Lagrangian density of the two $(1 + 1)$-dimensional QED by exploiting the (dual-)horizontality conditions defined on the four $(2 + 2)$-dimensional supermanifold. The long-standing problem of the derivation of the above symmetry transformations for the matter (Dirac) fields $(\bar\psi, \psi)$ in the framework of superfield formulation is resolved by a new set of restrictions on the $(2 + 2)$-dimensional supermanifold. These new physically interesting restrictions on the supermanifold owe their origin to the invariance of conserved currents of the theory. The geometrical interpretation for all the above transformations is provided in the framework of superfield formalism.Comment: LaTeX file, 12 pages, title slightly changed, text altered, typos corrected, minor changes in equations (3.1), (3.7), (3.8) and (3.9), journal-ref give

Phase Separation in Lix_xFePO4_4 Induced by Correlation Effects

We report on a significant failure of LDA and GGA to reproduce the phase stability and thermodynamics of mixed-valence Li$_x$FePO$_4$ compounds. Experimentally, Li$_x$FePO$_4$ compositions ($0 \leq x \leq 1$) are known to be unstable and phase separate into Li FePO$_4$ and FePO$_4$. However, first-principles calculations with LDA/GGA yield energetically favorable intermediate compounds an d hence no phase separation. This qualitative failure of LDA/GGA seems to have its origin in the LDA/GGA self-interaction which de localizes charge over the mixed-valence Fe ions, and is corrected by explicitly considering correlation effects in this material. This is demonstrated with LDA+U calculations which correctly predict phase separation in Li$_x$FePO$_4$ for $U-J \gtrsim 3.5$eV. T he origin of the destabilization of intermediate compounds is identified as electron localization and charge ordering at different iron sites. Introduction of correlation also yields more accurate electrochemical reaction energies between FePO$_4$/Li$_x$FePO$_ 4$ and Li/Li$^+$ electrodes.Comment: 12 pages, 5 figures, Phys. Rev. B 201101R, 200

Modularisation strategies in the AEC industry:a comparative analysis

Many industries have benefited from modularisation; while in the architecture, engineering and construction (AEC) industry, the concept of modularisation is associated with dimensional coordination. This has added to an already extensive list of challenges due to market size and the concept of economies of scale in AEC industry, to name but a few. Moreover, there is a myth that the AEC industry is bound to stay associated with build-to-order or made-to-order approach caused the AEC industry to restrict modularisation to the component level. This changes the balance in favour of what this paper calls a bottom-up approach. On the other hand, a valid alternative strategy–referred to in this study as top-down strategy–remains very much underexploited. The clients, therefore, do not have a neutral means by which they can assess which strategy is in their best interest. Likewise, if a construction company plans to make a strategic move towards the principles of modularisation and off-site manufacturing, they do not have clear decision support tools. This study investigates these two main modularisation strategies in the AEC industry to provide some examples of successful cases regarding how, when and where such strategy have been applied by different construction companies in different cases. The collected and collated empirical data and the results from the interviews will help clients and companies to analyse their own cases and make operational decisions on how, when and where to best utilise the bottom-up and top-down modularisation techniques while considering the pros and cons of such decisions

Noncommutative Dipole Field Theories And Unitarity

We extend the argument of Gomis and Mehen for violation of unitarity in field theories with space-time noncommutativity to dipole field theories. In dipole field theories with a timelike dipole vector, we present 1-loop amplitudes that violate the optical theorem. A quantum mechanical system with nonlocal potential of finite extent in time also shows violation of unitarity.Comment: typos corrected, more details added in Sec 5, version to appear in JHE