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# Topic: Proca equation

###### In the News (Wed 18 Oct 17)

 [No title] For instance, as opposed to the Proca $4$-vector potentials which transform according to the $(1/2,1/2)$ representation of the Lorentz group, in the $j=1$ case the bispinor" functions are constructed via the $(1,0)\oplus (0,1)$ representation what is on an equal footing to the description of Dirac $j=1/2$ particles. Equations are equivalent (within a constant factor) to the Hammer-Tucker equation~\cite{TUCK1}, see also~\cite{DVOE1,VLAS} $$\label{eq:Tucker} (\gamma_{\alpha\beta}p_\alpha p_\beta +p_\alpha p_\alpha +2 m^2) \psi_1 =0 \quad,$$ in the case of the choice $\chi= \vec E +i\vec B$ and $\varphi =\vec E -i\vec B$,\,\,\, $\psi_1 = \mbox{column} (\chi, \quad \varphi)$. \end{eqnarray} The Weinberg bispinor" $(\chi_{\dot\alpha\dot\beta} \quad \varphi^{\alpha\beta})$ corresponds to the equations (\ref{w11}) and (\ref{w21}), meanwhile $(\tilde \chi_{\dot\alpha\dot\beta}\quad \tilde\varphi^{\alpha\beta})$, to the equations (\ref{w1}) and (\ref{w2}). www.ma.utexas.edu /mp_arc/papers/98-106   (7705 words)

 [No title] The Proca field function is obtained in the framework of the Bargmann-Wigner prescription and the interaction is introduced similarly to the $S=1/2$ Dirac oscillator case regarded by Moshinsky and Szczepaniak. The interaction introduced in each of the BW equations in the form proposed by Moshinsky and Szczepaniak results in the oscillatorlike equation with the double degeneracy (in $N$, the principal quantum number) of the spectrum in the low frequency limit ({\it cf.} with Ref.~\cite{Bruce}). The aim of this paper is to consider the $S=1$ Proca oscillator\footnote{I take a liberty to name the equations obtained below as the Proca oscillator since in a free case the equations (\ref{P1}-\ref{P4}) are the well-known Proca equations, Ref.~\cite{Proca}.} with the interaction introduced in the same manner as in ref.~\cite{DV3}. www.ma.utexas.edu /mp_arc/papers/98-73   (1454 words)

 Proca action - Wikipedia, the free encyclopedia In physics, in the area of field theory, the Proca action describes a massive spin-1 field of mass m in Minkowski spacetime. In the dimensionless units commonly employed in theoretical physics, these may both be taken to be one. The Proca action is the gauge-fixed version of the Stückelberg action via the Higgs mechanism. en.wikipedia.org /wiki/Proca_equation   (103 words)

 Biblioteca Virtual Leite Lopes   (Site not responding. Last check: 2007-09-21) Proca's equation incorporates equations (16) and (17) for massive spin 1 fields. It is this equation which allows, as is well known, the construction of a lagrangean for spin 1 fields. Equation (20) is the geometrical transcription of equations (18) and (19) in view of equation (9) and the replacement of www4.prossiga.br /lopes/prodcien/pedagogical/pedagrem3.html   (111 words)

 Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations   (Site not responding. Last check: 2007-09-21) Non-relativistic and ultra-relativistic approximations to the quantum-mechanical Proca-Kemmer-Duffin equation are considered. A conclusion is drawn that this equation can describe a particle with spin 0 in a five-rowed case and with spin 1 in a ten-rowed case only in non-relativistic approximation. In the case of relativistic velocities some states with other spins are added: in a five-rowed case with spin 1 and in a ten-rowed case with spins 0 and 1. www.osti.gov /energycitations/product.biblio.jsp?osti_id=4730108   (162 words)

 Extended Maxwell's Equations: compact formulations in physics Maxwell's equations as a subset of the relativistic quantum unified equation of Maxwell's equations (1a), (2a), (3a) and (4a). in the Maxwell equations (1a) or (1*) and (2a) or (2*) www.wolfram-stanek.de /maxwell_equations.htm   (2516 words)

 Majorana Equation If a particle has a spinor wavefunction ψ which satisfies the Majorana equation, then the quantity m in the equation is called the Majorana mass. 3The representations used in the Dirac equation are (1=2;−3=2) and (1=2; 3=2) and in the Majorana equation... Derivation of the Majorana Equation from Irreducible Poincare' Representations, Nuovo Cimento, 56A, 1113 (1968); www.majoranaequation.info   (377 words)

 Predmety - Predmety   (Site not responding. Last check: 2007-09-21) Weyl equation and its invariance properties: proper Lorentz transformations, P, C, CP. Dirac equation for particle in external spherically symetric field. Solution of radial equations in the case of Coulomb potential. www.mff.cuni.cz /vnitro/is/sis/predmety/kod.php?kod=jsf068   (216 words)

 Biblioteca Virtual Leite Lopes   (Site not responding. Last check: 2007-09-21) In this way we obtained the wave equations for free spin 1/2 fields, spin 1 fields including Proca's equation, spin 3/2 fields and Einstein equation for weak gravitational fields. In this note, I would like to show that the geometrical equation associated to Dirac's equation leads in a natural way to the Feynman-Wheeler interpretation of anti-particles as fermions with negative energy particles propagating backward in time. The condition for the existence of solutions of equations (2) is that the determinant of their coefficients vanish which gives. www4.prossiga.br /Lopes/prodcien/PedagogicalII/Pedagogical.html   (290 words)

 correct Energy Mass equation - Page 3 As anyone who has grappled with QED quantization, the difficulties of quantizing a massless spin 1 field are tougher than for a massive spin1 system, all due to the requirements of gauge invariance. The equation is that which is derived by requiromg c=const. The Proca lagrangian is another example, as are the lagrangians of QED and QCD. www.physicsforums.com /showthread.php?p=1040721#post1040721   (988 words)

 Publications In this paper the aging of the Universe is investigated in the frame of quantum hyperbolic heat transport equation. In this paper the quantum hyperbolic equation formulated in [M. Kozlowski, J. Marciak-Kozlowska, From Quarks to Bulk Matter, Hadronic Press, 2001] is applied to the study of the propagation of the initial thermal state of the Universe. > 1.125 eV the QHT is the Klein-Gordon equation. info.fuw.edu.pl /~mirkoz/publ.html   (6687 words)

 The Tom Bearden Website The Lehnert equations are a subset of the O(3) Yang-Mills field equations. Both O(3) and Lehnert equations are superior to the Maxwell-Heaviside equations in being able to describe phenomena not amenable to the latter. Extended forms of Maxwell's equations as well as EM fields, based on a nonzero divergence of the electric field and a nonzero electric conductivity in vacuo. www.cheniere.org /correspondence/072301.htm   (5184 words)

 Quantum mechanics of charged massive spin-1 particle in curved spacetime with torsion: quasiclassical analysis of the ...   (Site not responding. Last check: 2007-09-21) The authors present the trajectory-coherent approximation for the Proca equation in the Riemann-Cartan space with an external electromagnetic field. The problem of the TCS construction is reduced to solving the Pauli-type linear evolution equation for the polarization vector. The pseudovector of the spin as the quantum mechanical average of the suitable spin operator in the TCS is defined and the covariant generalization for the well known Bargmann-Michel-Telegchi spinning equation in the case of background torsion fields from the Proca equation is obtained. stacks.iop.org /0264-9381/9/533   (304 words)

 [42.05] Sinusoidal Potential and Cosmology An alternative is being explored by several scientists: changing Einstein’s field equations. With the exception of cosmologists, astronomers generally have been content to test the older alternative, MOdified Newtonian Dynamics (Milgrom 1984) that challenges Newton but leaves relativistic gravity as an issue for the future. At AAS 200, I showed that a similar equation for electricity, the Proca equation, \nabla www.aas.org /publications/baas/v36n2/aas204/661.htm   (175 words)

 Rarita Schwinger Equation The massless Rarita-Schwinger equation has a gauge symmetry, under the gauge transformation of... We construct solutions to the Rarita-Schwinger spin-3/2 equation describing the gravitino in the field of these cosmic strings and show that... Generalized Rarita-Schwinger Equations (I. Lovas and K. Sailer) The wave function must satisfy the Dirac-equation and it must be www.rarita-schwingerequation.info   (315 words)

 PT mikroseminar "ad maiorem DI gloriam" This seems to be an affront to the physical nature of the system which should be independent of the mathematical mode of description. We propose a mathematical solution based upon the algebraic properties of the Schroedinger Equation. The instability of the equidistant-grid version of the Weideman's - Weigert's discretization method of solving Schroedinger equation disqualifies its use for the numerical evaluation of the exceptional points. gemma.ujf.cas.cz /~znojil/conf/microsem.html   (298 words)

 [No title] AIAS paper, "Runaway Solutions of the Lehnert Equations: The Possibility of Extracting Energy from the Vacuum", Optik, submitted, ref 99-222. AIAS paper "On the Representation of the Maxwell Heaviside Equations in terms of the Barut field four vector", Optik, submitted, ref. 99-210. 30) M. Evans et al., AIAS paper, "Operator Derivation of the Gauge Invariant Proca Equation, Lehnert Equation, and Elimination of the Lorenz Condition.", Found. quantumfuture.net /quantum_future/aias.txt   (1636 words)

 Dr. Evans Blog » June 05, 2004 - Wave Equation for the Lamb Shift June 05, 2004 - Wave Equation for the Lamb Shift The Proca equation of quantum mechanics is recovered as a limit of the Evans Lemma of the free electromagnetic field, and photon mass is recovered as a least www.atomicprecision.com /blog/?p=1244   (409 words)

 [No title]   (Site not responding. Last check: 2007-09-21) 2) In 1929 Lanczos used quaternionic methods to derive and generalize Dirac's equation (anticipation of "isospin" doublets and of Proca's equation). Lanczos's generalization implied the existence of spin 1/2 particle doublets, a corner stone of today's "standard model" of elementary particles. The Lanczos Collection features 52 commentaries on specific papers by Lanczos, many of which containing extraordinary achievements in physics and mathematics that were not fully appreciated at the time they were published. www.clifford.org /anonftp/pub/books/lanczos.txt   (593 words)

 AIAS Papers and References   (Site not responding. Last check: 2007-09-21) [PDF] Derivation of the Dirac Equation from the Evans Wave Equation [PDF] Derivation of the Evans Wave Equation from the Maurer Cartan Structure Relations of Differential Geometry [PDF] Derivation of the Evans Wave Equation from the Lagrangian and Action: Origin of the Planck Constant in General www.aias.us /pub.html   (1218 words)

 Solutions of higher-spin wave equations in external electromagnetic plane-wave fields   (Site not responding. Last check: 2007-09-21) Solutions of higher-spin wave equations in external electromagnetic plane-wave fields The Proca equation for a vector particle with an arbitrary magnetic dipole and electric quadrupole moment and the Rarita-Schwinger equation in the presence of an external electromagnetic plane-wave field are reduced by systems of ordinary differential equations which can be solved in special cases. The propagation behaviour of the solutions is investigated and found to exhibit in general the inconsistencies predicted by Velo and Zwanziger (1971). stacks.iop.org /0305-4470/9/149   (247 words)

 The Enigmatic Photon: The Field B3:1402005164:Evans, Myron W.; Vigier, Jean-Pierre:eCampus.com Equations of the Quantum Field Theory of Light Covariance of the Proca Equation in Free Space Derivation of B(3) from the Relativistic Hamilton-Jacobi Equation of e In Aμ www.ecampus.com /bk_detail.asp?isbn=1402005164   (314 words)

 Physics 513   (Site not responding. Last check: 2007-09-21) `classical' electrodynamics -- magnetic charge -- Proca's equation and photon mass -- vacuum polarization effects discrete charge distributions and delta-functions -- surface boundary conditions -- Poisson and Laplace equations magnetic diffusion - Maxwell's equations - retarded solutions for fields - Poynting's theorem - Dirac monopoles www.aoc.nrao.edu /~jweather/phys513/syllabus.html   (59 words)

 Spin 2 graviton Text - Physics Forums Library h^ab = h^ba, and write the most general linear second order equation for the symmetric, massless field h^ab in presence of the conserved source T^ab, then we write the equation in term of the tensor; THE ABOVE EQUATION IS EXACTLY THE LINEAR FORM OF EINSTEIN'S EQUTION WITH If you read post#2 carefully, you find it, more or less, is the Pauli-feirz method for constructing "relativistically invariant wave equation for massive and massless spin-2 field". www.physicsforums.com /archive/index.php/t-91769.html   (1084 words)

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