Quantization of bosonic fields with two mass and spin states

We investigate bosonic fields possessing two mass and spin states. The density matrix in the first order formalism is obtained. The quantization of fields in the first order formulation is performed and propagators are found.Comment: 9 page

Kalb-Ramond fields in the Petiau-Duffin-Kemmer formalism and scale invariance

Kalb-Ramond equations for massive and massless particles are considered in the framework of the Petiau-Duffin-Kemmer formalism. We obtain $10\times10$ matrices of the relativistic wave equation of the first-order and solutions in the form of density matrix. The canonical and Belinfante energy-momentum tensors are found. We investigate the scale invariance and obtain the conserved dilatation current. It was demonstrated that the conformal symmetry is broken even for massless fields.Comment: 9 pages, no figure

Analisis Koordinasi dan Setting Over Current Relay (Ocr) pada Pemakaian Daya Sendiri Pltu SMS Energy Menggunakan Software Etap 12.6.0

Penelitian ini bertujuan untuk mengetahui besaran settingan OCR Motor Pump, Grading Time OCR Motor Pump, koordinasi OCR Motor Pump dan OCR auxiliary pada PLTU SMS Energi di kawasan industri Bolok.  Penelitian diawali dengan mengumpulkan data kelistrikan PLTU SMS Energy berupa data sekunder. Data-data tersebut digunakan  untuk membuat single line diagram, simulasi dan analisis menggunakan  ETAP 12.6.0. Hasil Penelitian mendapatkan Settingan OCR dengan parameter nilai arus hubung singkat sebagai berikut. Setting Rele Bus 1 FCP dengan Ip = 3 A dan TMS = 0,1 s,  Setting Rele Bus Auxiliary I dengan Ip = 2 A dan TMS = 0,21 s, Setting Rele Bus OutGoing 1 dengan Ip = 0,6666 A dan TMS = 0,30 s dan Setting Rele Bus G1 dengan Ip = 1 A dan TMS = 0,45 s. TMS OCR pada motor Pump disetting lebih cepat karena letak OCR paling hilir dengan ganguan hubung singkat lebih kecil. Dari koordinasi kurva didapatkan Grading Time yang sudah sesuai dengan standar IEEE 242-yakni 0.2 – 0.4 detik.  Kata Kunci: Over Current Relay, Koordinasi OCR, Grading time, Settingan OCR, ETAP 12.6.

ANALISIS KOORDINASI DAN SETTING OVER CURRENT RELAY (OCR) PADA PEMAKAIAN DAYA SENDIRI PLTU SMS ENERGY MENGGUNAKAN SOFTWARE ETAP 12.6.0

ABSTRACT The research aims to determine the size of the OCR Motor Pump, Grading Time OCR Motor Pump, coordination Motor Pump OCR and auxiliary OCR on PLTU SMS Energy in the Bolok industrial area.  Research started by collecting electricity data PLTU SMS Energy in the form of secondary data. These data are used to create single line diagrams, simulations and analysis using ETAP 12.6.0. The results of the research get an  OCR Setting with the following short-circuiting value parameters.  Setting relay Bus 1 FCP with Ip = 3 A and TMS = 0.1 s, setting relay Auxiliary bus I with IP = 2 A and TMS = 0.21 s, setting relay bus OutGoing 1 with IP = 0.6666 A and TMS = 0.30 s and setting relay bus G1 with IP = 1 A and TMS = 0.45 S. TMS OCR on Pump motor is plotted faster due to the most downstream OCR location with smaller short-circuited tension. From the coordinating curve of Grading Time obtained that has been in accordance with IEEE Standard 242-namely  0.2 – 0.4 seconds.  Keywords: Over Current Relay, OCR Coordination, Grading time, OCR setting, ETAP 12.6.0   ABSTRAK Penelitian ini bertujuan untuk mengetahui besaran settingan OCR Motor Pump, Grading Time OCR Motor Pump, koordinasi OCR Motor Pump dan OCR auxiliary pada PLTU SMS Energi di kawasan industri Bolok.  Penelitian diawali dengan mengumpulkan data kelistrikan PLTU SMS Energy berupa data sekunder. Data-data tersebut digunakan  untuk membuat single line diagram, simulasi dan analisis menggunakan  ETAP 12.6.0. Hasil Penelitian mendapatkan Settingan OCR dengan parameter nilai arus hubung singkat sebagai berikut. Setting Rele Bus 1 FCP dengan Ip = 3 A dan TMS = 0,1 s,  Setting Rele Bus Auxiliary I dengan Ip = 2 A dan TMS = 0,21 s, Setting Rele Bus OutGoing 1 dengan Ip = 0,6666 A dan TMS = 0,30 s dan Setting Rele Bus G1 dengan Ip = 1 A dan TMS = 0,45 s. TMS OCR pada motor Pump disetting lebih cepat karena letak OCR paling hilir dengan ganguan hubung singkat lebih kecil. Dari koordinasi kurva didapatkan Grading Time yang sudah sesuai dengan standar IEEE 242-yakni 0.2 – 0.4 detik.  Kata Kunci: Over Current Relay, Koordinasi OCR, Grading time, Settingan OCR, ETAP 12.6.

"Square Root" of the Proca Equation: Spin-3/2 Field Equation

New equations describing particles with spin 3/2 are derived. The non-local equation with the unique mass can be considered as "square root" of the Proca equation in the same sense as the Dirac equation is related to the Klein-Gordon-Fock equation. The local equation describes spin 3/2 particles with three mass states. The equations considered involve fields with spin-3/2 and spin-1/2, i.e. multi-spin 1/2, 3/2. The projection operators extracting states with definite energy, spin, and spin projections are obtained. All independent solutions of the local equation are expressed through projection matrices. The first order relativistic wave equation in the 20-dimensional matrix form, the relativistically invariant bilinear form and the corresponding Lagrangian are given. Two parameters characterizing non-minimal electromagnetic interactions of fermions are introduced, and the quantum-mechanical Hamiltonian is found. It is proved that there is only causal propagation of waves in the approach considered.Comment: 17 pages, corrections in Eqs. (50), (51

Angular and energy dependence of (e,e′)(e,e^{\prime}) cross sections for orbital 1+^+ excitations

The main features of the $(e,e^{\prime})$ cross sections of low-lying orbital excitations with $K^{\pi} = 1^+$ in heavy deformed nuclei are studied in RPA on the example of $^{156}$Gd. The dependence of the DWBA E2 and M1 cross sections on the scattering angle $0^{\circ} < \theta < 180 ^{\circ}$ and incident electron energy $E_i < 210$ MeV is analyzed in PWBA. The cross section is larger for M1 than for E2 transitions at any angle if $E_i < 30$ MeV. The longitudinal (Coulomb) C2 excitation dominates the E2 response for $5^{\circ} < \theta < 170 ^{\circ}$. Only transverse M1 and E2 excitations compete for $\theta > 175 ^{\circ}$ and the former one is dominant for $q < 1.2$ fm$^{-1}$. The M1 response is almost purely orbital up to $q = 1.4$ fm$^{-1}$ even in backward scattering. Qualitative PWBA estimates based on the $q$-dependence of the form factors alone are not able to predict some important features of the $(e,e^{\prime})$ cross sections stemming from the strong magnetic and orbital character of the studied 1$^+$ excitations. The expectation for M1 over E2 dominance in backward scattering should not be extended to higher momentum transfers and incident energies.Comment: Latex, 28 pages, 12 postscript figures included using uufile

Field theory of massive and massless vector particles in the Duffin - Kemmer - Petiau formalism

Field theory of massive and massless vector particles is considered in the first-order formalism. The Hamiltonian form of equations is obtained after the exclusion of non-dynamical components. We obtain the canonical and symmetrical Belinfante energy-momentum tensors and their nonzero traces. We note that the dilatation symmetry is broken in the massive case but in the massless case the modified dilatation current is conserved. The canonical quantization is performed and the propagator of the massive fields is found in the Duffin - Kemmer - Petiau formalism.Comment: 20 pages, typos corrected, a reference added, journal version, accepted in Int.J.Mod.Phys.

Note on Dirac--K\"ahler massless fields

We obtain the canonical and symmetrical Belinfante energy-momentum tensors of Dirac--K\"{a}hler's fields. It is shown that the traces of the energy-momentum tensors are not equal to zero. We find the canonical and Belinfante dilatation currents which are not conserved, but a new conserved dilatation current is obtained. It is pointed out that the conformal symmetry is broken. The canonical quantization is performed and the propagator of the massless fields in the first-order formalism is found.Comment: 16 pages, minor corrections in the text, published versio

On superluminal fermions within the second derivative equation

We postulate the second-order derivative equation with four parameters for spin-1/2 fermions possessing two mass states. For some choice of parameters fermions propagate with the superluminal speed. Thus, the novel tachyonic equation is suggested. The relativistic 20-component first-order wave equation is formulated and projection operators extracting states with definite energy and spin projections are obtained. The Lagrangian formulation of the first-order equation is presented and the electric current and energy-momentum tensor are found. The minimal and non-minimal electromagnetic interactions of fermions are considered and Schr\"{o}dinger's form of the equation and the quantum-mechanical Hamiltonian are obtained. The canonical quantization of the field in the first-order formalism is performed and we find the vacuum expectation of chronological pairing of operators.Comment: 21 pages, minor corrections, journal version, accepted in IJMP