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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 Causal fermion system ： ウィキペディア英語版 Causal fermion system The theory of causal fermion systems is an approach to describe fundamental physics. It gives quantum mechanics, general relativity and quantum field theory as limiting cases〔F. Finster, ''The Principle of the Fermionic Projector'', hep-th/0001048, hep-th/0202059, hep- th/0210121, AMS/IP Studies in Advanced Mathematics, vol. 35, American Mathematical Society, Providence, RI, 2006.〕〔F. Finster, ''A formulation of quantum field theory realizing a sea of interacting Dirac particles'', arXiv:0911.2102 (), Lett. Math. Phys. 97 (2011), no. 2, 165–183.〕〔F. Finster, ''An action principle for an interacting fermion system and its analysis in the continuum limit'', arXiv:0908.1542 () (2009).〕〔F. Finster, ''The continuum limit of a fermion system involving neutrinos: Weak and gravitational interactions'', arXiv:1211.3351 () (2012).〕〔F. Finster, ''Perturbative quantum field theory in the framework of the fermionic projector'', arXiv:1310.4121 (), J. Math. Phys. 55 (2014), no. 4, 042301.〕 and is therefore a candidate for a unified physical theory. Instead of introducing physical objects on a preexisting space-time manifold, the general concept is to derive space-time as well as all the objects therein as secondary objects from the structures of an underlying causal fermion system. This concept also makes it possible to generalize notions of differential geometry to the non-smooth setting.〔〔 In particular, one can describe situations when space-time no longer has a manifold structure on the microscopic scale (like a space-time lattice or other discrete or continuous structures on the Planck scale). As a result, the theory of causal fermion systems is a proposal for quantum geometry and an approach to quantum gravity. Causal fermion systems were introduced by Felix Finster and collaborators. == Motivation and physical concept == The physical starting point is the fact that the Dirac equation in Minkowski space has solutions of negative energy which are usually associated to the Dirac sea. Taking the concept seriously that the states of the Dirac sea form an integral part of the physical system, one finds that many structures (like the causal and metric structures as well as the bosonic fields) can be recovered from the wave functions of the sea states. This leads to the idea that the wave functions of all occupied states (including the sea states) should be regarded as the basic physical objects, and that all structures in space-time arise as a result of the collective interaction of the sea states with each other and with the additional particles and "holes" in the sea. Implementing this picture mathematically leads to the framework of causal fermion systems. More precisely, the correspondence between the above physical situation and the mathematical framework is obtained as follows. All occupied states span a Hilbert space of wave functions in Minkowski space $\backslash hat$. The observable information on the distribution of the wave functions in space-time is encoded in the ''local correlation operators'' $F(x),\; x\; \backslash in\; \backslash hat,$ which in an orthonormal basis $(\backslash psi\_i)$ have the matrix representation :$\backslash big(\; F(x)\; \backslash big)^i\_j\; =\; -\; \backslash overline\; \backslash psi\_j(x)$ (where $\backslash overline$ is the adjoint spinor). In order to make the wave functions into the basic physical objects, one considers the set $\backslash$ as a set of linear operators on an ''abstract'' Hilbert space. The structures of Minkowski space are all disregarded, except for the volume measure $d^4x$, which is transformed to a corresponding measure on the linear operators (the ''"universal measure"''). The resulting structures, namely a Hilbert space together with a measure on the linear operators thereon, are the basic ingredients of a causal fermion system. The above construction can also be carried out in more general space-times. Moreover, taking the abstract definition as the starting point, causal fermion systems allow for the description of generalized "quantum space-times." The physical picture is that one causal fermion system describes a space-time together with all structures and objects therein (like the causal and the metric structures, wave functions and quantum fields). In order to single out the physically admissible causal fermion systems, one must formulate physical equations. In analogy to the Lagrangian formulation of classical field theory, the physical equations for causal fermion systems are formulated via a variational principle, the so-called ''causal action principle''. Since one works with different basic objects, the causal action principle has a novel mathematical structure where one minimizes a positive action under variations of the universal measure. The connection to conventional physical equations is obtained in a certain limiting case (the continuum limit) in which the interaction can be described effectively by gauge fields coupled to particles and antiparticles, whereas the Dirac sea is no longer apparent. 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「Causal fermion system」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.