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Search Results: 1 - 10 of 7707 matches for " Momentum Space "
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A Photonic Model of the Big Bang  [PDF]
J. G. Lartigue
Journal of Modern Physics (JMP) , 2018, DOI: 10.4236/jmp.2018.914157
Abstract: There are two main theories about the origin of the Universe that show similitude with the Genesis writings, though in different verses: the Big Bang1 and the eternal Universe2 (an eventual quantum fluctuation). However, it is possible to partially include the quantum theory in the Big Bang thanks to the nature of photons, to obtain a simple model. It is assumed as the origin of the Universe (space, time, matter and physical laws). A subsequent enormous expansion has been explained by a supposed brief Inflation period, followed up today by a constant adiabatic expansion acceleration. This paper assumes that the Universe is the total Space which contains the Physical Universe covered by an external, empty Space, both expanding at a constant Hubble acceleration ΓH [1]. A Big Bang design is intended by a deduction of the energy and number of primeval photons, from the present CMB value; they would have reacted whether to generate the Physical Universe or to decay till the CMB level. It follows an approach to the Universe expansion work, based on the Hubble field (VH) as well as on Thermo-dynamics. They are calculated: the time and angular momentum required for the Physical Universe to reach the maximum internal velocity c as well as, simultaneously, a c tangential velocity. The Universe luminosity at different periods and the adequate expressions of parameters (Ω, q, k) are revised. It is proposed a modification in the equation of the H(t) parameter and the Ho value. The operator of convective derivative is applied to obtain an equation of continuity for the photonic energy; an adiabatic Jacobian gives similar results. This essay differs from others based on black box radiation, since the Universe has no walls and the photons energy decays continuously.
Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space I: Newtonian Mechanics  [PDF]
Akihiro Ogura
World Journal of Mechanics (WJM) , 2018, DOI: 10.4236/wjm.2018.89025
Abstract: We present the usefulness of the diagrammatic approach for analyzing two dimensional elastic collision in momentum space. In the mechanics course, we have two major purposes of studying the collision problems. One is that we have to obtain velocities of the two particles after the collision from initial velocities by using conservation laws of momentum and energy. The other is that we have to study two ways of looking collisions, i.e. laboratory system and center-of-mass system. For those two major purposes, we propose the diagrammatic technique. We draw two circles. One is for the center-of-mass system and the other is for the laboratory system. Drawing these two circles accomplish two major purposes. This diagrammatic technique can help us understand the collision problems quantitatively and qualitatively.
Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space II: Special Relativity  [PDF]
Akihiro Ogura
World Journal of Mechanics (WJM) , 2018, DOI: 10.4236/wjm.2018.89026
Abstract: The diagrammatic approach to the collision problems in Newtonian mechanics is useful. We show in this article that the same technique can be applied to the case of the special relativity. The two circles play an important role in Newtonian mechanics, while in the special relativity, we need one circle and one ellipse. The circle shows the collision in the center-of-mass system. And the ellipse shows the collision in the laboratory system. These two figures give all information on two dimensional elastic collisions in the special relativity.
The Propagation Delay Effect of the Expansion and Inflation of the Universe  [PDF]
Philipp Kornreich
Journal of Applied Mathematics and Physics (JAMP) , 2018, DOI: 10.4236/jamp.2018.610173
Abstract: The effect of the propagation delay of gravitational interactions results in a singularity of the normalized acceleration of the radius of a sphere representing the Universe. Stephen Hawking in his Inflation Model also discusses a delay type interaction. This term can be used to model the inflationary rapid expansion of the early Universe. Since the Universe is thought to occupy all of space-time, one cannot define a boundary or radius of the Universe. Therefore, the properties of a sphere in the Universe are analyzed. It is assumed that the Universe will behave similarly to this sphere. This analysis is performed by including the effect of the propagation delay of gravitational interactions in Einstein’s equation.
Look at Neutrino Oscillations in Space-Like Continuum  [PDF]
Xiaobai Ai
Journal of Modern Physics (JMP) , 2018, DOI: 10.4236/jmp.2018.97087
Abstract: Based on the special theory of relativity in space-like continuum, the pre-sent author points that if there exist tachyons in nature, they should be neutral point-like particles with lepton appearance, which are very much like our early understanding about neutrinos before. The author also points that an alternative explanation for neutrino oscillations may be the conversion between mass-less neutrinos with different flavors expressed in different “lowest limited momentum” during their flight journey, which originates from that the argument in the squared sine function of the probability of neutrino oscillation may be less than zero, which is mathematical foresight and may not be ignored.
Non-commutative Fock-- Darwin system and its magnetism properties

Yu Xiao-Min,Li Kang,

中国物理 B , 2009,
Riemannian Space-Time, de Donder Conditions and Gravitational Field in Flat Space-Time  [PDF]
Gordon Liu
International Journal of Astronomy and Astrophysics (IJAA) , 2013, DOI: 10.4236/ijaa.2013.31002

Let the coordinate system xi of flat space-time to absorb a second rank tensor field Φij of the flat space-time deforming into a Riemannian space-time, namely, the tensor field Φuv is regarded as a metric tensor with respect to the coordinate system xu. After done this, xu is not the coordinate system of flat space-time anymore, but is the coordinate system of the new Riemannian space-time. The inverse operation also can be done. According to these notions, the concepts of the absorption operation and the desorption operation are proposed. These notions are actually compatible with Einstein’s equivalence principle. By using these concepts, the relationships of the Riemannian space-time, the de Donder conditions and the gravitational field in flat space-time are analyzed and elaborated. The essential significance of the de Donder conditions (the harmonic conditions or gauge) is to desorb the tensor field of gravitation from the Riemannian space-time to the Minkowski space-time with the Cartesian coordinates. Einstein equations with de Donder conditions can be solved in flat space-time. Base on Fock’s works, the equations of gravitational field in flat space-time are

Energy momentum complex
Nashed, Gamal G.L.;
Brazilian Journal of Physics , 2010, DOI: 10.1590/S0103-97332010000300010
Abstract: we show that the definition of the energy- momentum complex given by m?ller using weitzenb?ck space- time in the calculations of gravitational energy gives results which are different from those obtained from other definitions given in the framework of general relativity.
Elastic Collisions in Minkowski Momentum Space with Lorentz Transformations  [PDF]
Akihiro Ogura
World Journal of Mechanics (WJM) , 2019, DOI: 10.4236/wjm.2019.912018
Abstract: We reexamined the elastic collision problems in the special relativity for both one and two dimensions from a different point of view. In order to obtain the final states in the laboratory system of the collision problems, almost all textbooks in the special relativity calculated the simultaneous equations. In contrast to this, we make a detour through the center-of-mass system. The two frames of references are connected by the Lorentz transformation with the velocity of the center-of-mass. This route for obtaining the final states is easy for students to understand the collision problems. For one dimensional case, we also give an example for illustrating the states of the particles in the Minkowski momentum space, which shows the whole story of the collision.
Relaxation of Energy and Momentum in an Carrier-Phonon System  [PDF]
A. Rossani
Journal of Modern Physics (JMP) , 2012, DOI: 10.4236/jmp.2012.38103
Abstract: If electrons (e) and holes (h) in metals or semiconductors are heated to the temperatures Te and Th greater than the lattice temperature Tp, the electron-phonon interaction causes energy relaxation. In the non-uniform case a momentum relaxation occurs as well. In view of such an application, a new model, based on an asymptotic procedure for solving the generalized kinetic equations of carriers and phonons is proposed, which gives naturally the displaced Maxwellian at the leading order. After that, balance equations for the electron number, hole number, energy densities, and momentum densities are constructed, which constitute now a system of five equations for the electron chemical potential, the temperatures and the drift velocities. In the drift-diffusion approximation the constitutive laws are derived and the Onsager relations recovered.
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