Fermion Condensate and Vacuum Current Density Induced by Homogeneous and Inhomogeneous Magnetic Fields in (2+1)-Dimensions

We calculate the condensate and the vacuum current density induced by external static magnetic fields in (2+1)-dimensions. At the perturbative level, we consider an exponentially decaying magnetic field along one cartesian coordinate. Non-perturbatively, we obtain the fermion propagator in the presence of a uniform magnetic field by solving the Schwinger-Dyson equation in the rainbow-ladder approximation. In the large flux limit, we observe that both these quantities, either perturbative (inhomogeneous) and non-perturbative (homogeneous), are proportional to the external field, in agreement with early expectations.Comment: 8 pages, 2 figures. Accepted for publication in Phys. Rev.

Massive Dirac fermions and the zero field quantum Hall effect

Through an explicit calculation for a Lagrangian in quantum electrodynamics in (2+1)-space--time dimensions (QED$_3$), making use of the relativistic Kubo formula, we demonstrate that the filling factor accompanying the quantized electrical conductivity for massive Dirac fermions of a single species in two spatial dimensions is a half (in natural units) when time reversal and parity symmetries of the Lagrangian are explicitly broken by the fermion mass term. We then discuss the most general form of the QED$_3$ Lagrangian, both for irreducible and reducible representations of the Dirac matrices in the plane, with emphasis on the appearance of a Chern-Simons term. We also identify the value of the filling factor with a zero field quantum Hall effect (QHE).Comment: 15 pages. Accepted in Jour. Phys.

Analisis Kewajiban Deposito sebagai Jaminan Reklamasi dan Pascatambang

Sesuai dengan Undang-Undang Nomor 32 Tahun 2009 tentang Perlindungan dan Pengelolaan Lingkungan Hidup menyebutkan bahwa dalam rangka melestarikan fungsi lingkungan hidup, maka setiap orang wajib untuk melindungi lingkungan. Undang-Undang Nomor 4 tahun 2009 tentang Mineral dan Batubara, mengatur mengenai izin USAha pertambangan. Perusahaan diwajibkan menyetor deposito untuk menjamin reklamasi dan pascatambang. Objek tulisan ini terkait dengan kewajiban deposito sebagai jaminan reklamasi dan pascatambang, dengan menggunakan metode yuridis normatif. Hasil penelitian menunjukkan bahwa setiap Perusahaan diwajibkan melakukan kegiatan pertambangan agar dapat melestarikan fungsi lingkungan hidup dan mencegah terjadinya pencemaran dan/ atau kerusakan lingkungan

Chiral and Parity Symmetry Breaking for Planar Fermions: Effects of a Heat Bath and Uniform External Magnetic Field

We study chiral symmetry breaking for relativistic fermions, described by a parity violating Lagrangian in 2+1-dimensions, in the presence of a heat bath and a uniform external magnetic field. Working within their four-component formalism allows for the inclusion of both parity-even and -odd mass terms. Therefore, we can define two types of fermion anti-fermion condensates. For a given value of the magnetic field, there exist two different critical temperatures which would render one of these condensates identically zero, while the other would survive. Our analysis is completely general: it requires no particular simplifying hierarchy among the energy scales involved, namely, bare masses, field strength and temperature. However, we do reproduce some earlier results, obtained or anticipated in literature, corresponding to special kinematical regimes for the parity conserving case. Relating the chiral condensate to the one-loop effective Lagrangian, we also obtain the magnetization and the pair production rate for different fermion species in a uniform electric field through the replacement $B\to-iE$.Comment: 9 pages, 10 figure

Free Form of the Foldy-Wouthuysen Transformation in External Electromagnetic Fields

We derive the exact Foldy-Wouthuysen transformation for Dirac fermions in a time independent external electromagnetic field in the basis of the Ritus eigenfunctions, namely the eigenfunctions of the operator $(\gamma \cdot \Pi)^2$, with $\Pi^\mu = p^\mu - e A^\mu$. In this basis, the transformation acquires a free form involving the dynamical quantum numbers induced by the field.Comment: 8 pages. Accepted in J. Phys. A: Math. and Theo. (Fast Track Communication

Pseudoscalar mesons: Light front wave functions, GPDs, and PDFs

We develop a unified algebraic model which satisfactorily describes the internal structure of pion and kaon as well as heavy quarkonia (ηc and ηb). For each of these mesons, we compute their generalized parton distributions (GPDs), built through the overlap representation of their light front wave function, tightly constrained by the modern and precise knowledge of their quark distribution amplitudes. From this threedimensional knowledge of mesons, we deduce parton distribution functions (PDFs) as well as electromagnetic form factors and construct the impact parameter space GPDs. The PDFs for mesons formed with light quarks are then evolved from the hadronic scale of around 0.3 to 5.2 GeV, probed in experiments. We make explicit comparisons with experimental results available and with earlier theoretical predictions.L. A. acknowledges the FAPESP Postdoctoral Fellowship Grant No. 2018/17643-5. The research of L. A. and I. M. H.-A. was also supported by CONACyT through the national fellowship program. A. B. wishes to thank CIC of UMSNH for the Research Grant No. 4.10