Canonical Quantization of the Self-Dual Model coupled to Fermions

This paper is dedicated to formulate the interaction picture dynamics of the self-dual field minimally coupled to fermions. To make this possible, we start by quantizing the free self-dual model by means of the Dirac bracket quantization procedure. We obtain, as result, that the free self-dual model is a relativistically invariant quantum field theory whose excitations are identical to the physical (gauge invariant) excitations of the free Maxwell-Chern-Simons theory. The model describing the interaction of the self-dual field minimally coupled to fermions is also quantized through the Dirac bracket quantization procedure. One of the self-dual field components is found not to commute, at equal times, with the fermionic fields. Hence, the formulation of the interaction picture dynamics is only possible after the elimination of the just mentioned component. This procedure brings, in turns, two new interaction terms, which are local in space and time while non-renormalizable by power counting. Relativistic invariance is tested in connection with the elastic fermion-fermion scattering amplitude. We prove that all the non-covariant pieces in the interaction Hamiltonian are equivalent to the covariant minimal interaction of the self-dual field with the fermions. The high energy behavior of the self-dual field propagator corroborates that the coupled theory is non-renormalizable. Certainly, the self-dual field minimally coupled to fermions bears no resemblance with the renormalizable model defined by the Maxwell-Chern-Simons field minimally coupled to fermions.Comment: 16 pages, no special macros, no corrections in the pape

On the constrained structure of duality symmetric Maxwell theory

The constrained structure of the duality invariant form of Maxwell theory is considered in the Hamiltonian formulation of Dirac as well as from the symplectic viewpoint. Compared to the former the latter approach is found to be more economical and elegant. Distinctions from the constrained analysis of the usual Maxwell theory are pointed out and their implications are also discussed.Comment: Latex, 12 page

Cointegration in Panel Data with Breaks and Cross-Section Dependence

The power of standard panel cointegration statistics may be affected by misspecification errors if proper account is not taken of the presence of structural breaks in the data. We propose modifications to allow for one structural break when testing the null hypothesis of no cointegration that retain good properties in terms of empirical size and power. Response surfaces to approximate the finite sample moments that are required to implement the statistics are provided. Since panel cointegration statistics rely on the assumption of cross-section independence, a generalisation of the tests to the common factor framework is carried out in order to allow for dependence among the units of the panel.Panel cointegration, structural break, common factors, cross-section dependence

Batalin-Tyutin Quantization of the Self-Dual Massive Theory in Three Dimensions

We quantize the self-dual massive theory by using the Batalin-Tyutin Hamiltonian method, which systematically embeds second class constraint system into first class one in the extended phase space by introducing the new fields. Through this analysis we obtain simultaneously the St\"uckelberg scalar term related to the explicit gauge-breaking effect and the new type of Wess-Zumino action related to the Chern-Simons term.Comment: 17 pages, SOGANG-HEP 191/9

Cointegration in panel data with breaks and cross-section dependence

The power of standard panel cointegration statistics may be affected by misspecification errors if proper account is not taken of the presence of structural breaks in the data. We propose modifications to allow for one structural break when testing the null hypothesis of no cointegration that retain good properties in terms of empirical size and power. Response surfaces to approximate the finite sample moments that are required to implement the statistics are provided. Since panel cointegration statistics rely on the assumption of cross-section independence, a generalisation of the tests to the common factor framework is carried out in order to allow for dependence among the units of the panel. JEL Classification: C12, C22common factors, cross-section dependence, Panel Cointegration, structural break

Komar energy and Smarr formula for noncommutative Schwarzschild black hole

We calculate the Komar energy $E$ for a noncommutative Schwarzschild black hole. A deformation from the conventional identity $E=2ST_H$ is found in the next to leading order computation in the noncommutative parameter $\theta$ (i.e. $\mathcal{O}(\sqrt{\theta}e^{-M^2/\theta})$) which is also consistent with the fact that the area law now breaks down. This deformation yields a nonvanishing Komar energy at the extremal point $T_{H}=0$ of these black holes. We then work out the Smarr formula, clearly elaborating the differences from the standard result $M=2ST_H$, where the mass ($M$) of the black hole is identified with the asymptotic limit of the Komar energy. Similar conclusions are also shown to hold for a deSitter--Schwarzschild geometry.Comment: 5 pages Late

Approximations from Anywhere and General Rough Sets

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present author in her earlier papers. From the practical perspective, a few (as opposed to one) theoretical frameworks may be suitable for formulating the problem itself. \emph{Granular operator spaces} have been recently introduced and investigated by the present author in her recent work in the context of antichain based and dialectical semantics for general rough sets. The nature of the inverse problem is examined from number-theoretic and combinatorial perspectives in a higher order variant of granular operator spaces and some necessary conditions are proved. The results and the novel approach would be useful in a number of unsupervised and semi supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings, Springe

Dual Projection and Selfduality in Three Dimensions

We discuss the notion of duality and selfduality in the context of the dual projection operation that creates an internal space of potentials. Contrary to the prevailing algebraic or group theoretical methods, this technique is applicable to both even and odd dimensions. The role of parity in the kernel of the Gauss law to determine the dimensional dependence is clarified. We derive the appropriate invariant actions, discuss the symmetry groups and their proper generators. In particular, the novel concept of duality symmetry and selfduality in Maxwell theory in (2+1) dimensions is analysed in details. The corresponding action is a 3D version of the familiar duality symmetric electromagnetic theory in 4D. Finally, the duality symmetric actions in the different dimensions constructed here manifest both the SO(2) and $Z_2$ symmetries, contrary to conventional results.Comment: 20 pages, late