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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Center of mass (relativistic) ： ウィキペディア英語版 Center of mass (relativistic) In physics, relativistic center of mass refers to the mathematical and physical concepts that define the center of mass of a system of particles in relativistic mechanics and relativistic quantum mechanics. == Introduction == In non-relativistic physics there is a unique and well defined notion of the center of mass vector, a three-dimensional vector (abbreviated: "3-vector"), of an isolated system of massive particles inside the 3-spaces of inertial frames of Galilei spacetime. However, no such a notion exists in special relativity inside the 3-spaces of the inertial frames of Minkowski spacetime. In any rigidly rotating frame (including the special case of a Galilean inertial frame) with coordinates $(t,x)$, the Newton center of mass of ''N'' particles of mass $m\_$ and 3-positions $(t)$ is the 3-vector :$(t)=\}\}\}$ both for free and interacting particles. In a special relativistic inertial frame in Minkowski spacetime with four vector coordinates $x^=(x^0,x)$ a collective variable with all the properties of the Newton center of mass does not exist. The primary properties of the non-relativistic center of mass are :i) together with the total momentum it forms a canonical pair, :ii) it transforms under rotations as a three vector, and :iii) it is a position associated with the spatial mass distribution of the constituents. It is interesting that the following three proposals for a relativistic center of mass appearing in the literature of the last century 〔M.Pauri and G.M.Prosperi, Canonical Realizations of the Poincaré Group. I. General Theory, J.Math.Phys. =, 1503 (1975). M.Pauri, Canonical (Possibly Lagrangian) Realizations of the Poincaré Group with Increasing Mass-Spin Trajectories, talk at the International Colloquium "Group Theoretical Methods in Physica", Cocoyoc, Mexico, 1980, edited by K.B.Wolf (Springer, Berlin, 1980)〕 take on individually these three properties: #The Newton–Wigner–Pryce center of spin or canonical center of mass,〔T.D.Newton and E.P.Wigner, Localized States for Elementary Systems, Rev.Mod.Phys. Vol 21, 400 1969.〕〔R.H.L.Pryce, The Mass-Centre in the Restricted Theory of Relativity and Its Connexion with the Quantum Theory of Elementary Particles , Proc.R.Soc.London, Ser A Vol 195, 62 (1948).〕 (it is the classical counterpart of the Newton–Wigner quantum position operator). It is a 3-vector $\backslash vec,\backslash \}=0$ in phase space. However there is no 4-vector $=(,)$ having it as the space part, so that it does not identify a worldline, but only a pseudo-worldline, depending on the chosen inertial frame. #The Fokker–Pryce center of inertia $\backslash vec\; Y$ ,.〔A.D.Fokker, Relativiteitstheorie (Noordhoff, Groningen, 1929) p.171.〕 It is the space part of a 4-vector $Y^\; =\; (\; Y^0,\; \backslash vec\; Y)$ , so that it identifies a worldline, but it is not canonical, i.e. $\backslash \; \backslash not=\; 0$. #The Møller center of energy $\backslash vec\; R$,〔C. Møller, Sur la dynamique des systemes ayant un moment angulaire interne, Ann.Inst.H.Poincaré vol , 251 (1969); The Theory of Relativity (Oxford: Oxford University Press, 1957)〕 defined as the Newton center of mass with the rest masses $m\_$ of the particles replaced by their relativistic energies. This is not canonical, i.e. $\backslash \backslash \}\backslash not=0$, neither the space part of a 4-vector, i.e. it only identifies a frame-dependent pseudo-worldline. These three collective variables have all the same constant 3-velocity and all of them collapse into the Newton center of mass in the non-relativistic limit. In the 1970s there was a big debate on this problem,〔G.N.Fleming, Covariant Position Operators, Spin and Locality, Phys.Rev. vol 137B, 188 (1965)〕〔A.J.Kalnay, The Localization Problem, in Studies in the Foundations, Methodology and Philosophy of Science, edited by M.Bunge (Springer, Berlin, 1971), vol.4〕〔M.Lorente and P.Roman, {General expressions for the position and spin operators of relativistic systems, J.Math.Phys. vol 15, 70 (1974).〕〔H.Sazdjian, {Position Variables in Classical Relativistic Hamiltonian Mechanics}, Nucl.Phys. vol B161, 469 (1979).〕 without any final conclusion. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Center of mass (relativistic)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.