Exact Conservation Laws of the Gradient Expanded Kadanoff–Baym Equations
✍ Scribed by J. Knoll; Yu.B. Ivanov; D.N. Voskresensky
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 158 KB
- Volume
- 293
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
It is shown that the Kadanoff-Baym equations at consistent first-order gradient approximation reveal exact rather than approximate conservation laws related to global symmetries of the system. The conserved currents and energy-momentum tensor coincide with corresponding Noether quantities in the local approximation. These exact conservations are valid, provided a derivable approximation is used to describe the system, and possible memory effects in the collision term are also consistently evaluated up to first-order gradients. C 2001 Academic Press
1. Introduction
Nonequilibrium Green function techniques, developed by Schwinger, Kadanoff, Baym, and Keldysh [1-4], provide the appropriate concepts to study the space-time evolution of many-particle quantum systems. This formalism finds now applications in various fields, such as quantum chromodynamics [5,6], nuclear physics, in particular heavy ion collisions [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], astrophysics [11,24,25], cosmology [26], spin systems [27], lasers [28], physics of plasma [29,30], physics of liquid 3 He [31], critical phenomena, quenched random systems and disordered systems [32], normal metals and superconductors [24,33,34], semiconductors [35], and tunneling and secondary emission [36].
For actual calculations certain approximation steps are necessary. In many cases perturbative approaches are insufficient, like for systems with strong couplings as treated in nuclear physics. In such cases, one must resum certain subseries of diagrams in order to obtain a reasonable approximation scheme. In contrast to perturbation theory, for such resummations one frequently encounters the fact that the scheme may no longer be conserving, although for each diagram considered the conservation laws are implemented at each vertex. Thus, the resulting equations of motion may no longer comply