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1.
We show that the composition of not only two SO(3,1) boosts, but also that of two SO(n,1) boosts for anyn 2, is basically an SO(2,1) problem and hence can be analysed completely using SL(2,R) matrices. By computing the expression for the Thomas/Wigner angle directly using SL(2,R) matrices we show that this approach results in considerable economy of algebra. 相似文献
2.
The understanding of mesoscopic transport has now attained an ultimate simplicity. Indeed, orthodox quantum kinetics would seem to say little about mesoscopics that has not been revealed — nearly effortlessly — by more popular means. Such is far from the case, however. The fact that kinetic theory remains very much in charge is best appreciated through the physics of a quantum point contact. While discretization of its conductance is viewed as the exclusive result of coherent, single-electron-wave transmission, this does not begin to address the paramount feature of all metallic conduction: dissipation. A perfect quantum point contact still has finite resistance, so its ballistic carriers must dissipate the energy gained from the applied field. How do they manage that? The key is in standard many-body quantum theory, and its conservation principles. 相似文献
3.
We present a new approach to Hamilton’s theory of turns for the groups SO(3) and SU(2) which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection.
We show that the entire construction can be based on binary rotations rather than mirror reflections. 相似文献
4.
Reznikov et al. [Phys. Rev. Lett. 75, 3340 (1995)]] have presented definitive observations of nonequilibrium noise in a quantum point contact. Especially puzzling is the "anomalous" peak structure of the excess noise measured at constant current; to date it remains unexplained. We show that their experiment directly reveals the deep link between conservation principles in the electron gas and its low-dimensional, mesoscopic behavior. The keys to that connection are gauge invariance and the compressibility sum rule. These are central not only to the experiment of Reznikov et al., but to the very nature of all mesoscopic transport. 相似文献
5.
We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular
groupSU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real linear vector space, are developed
in anSU(3) covariant manner. Thef andd symbols ofSU(3) lead to two ways of ‘multiplying’ two vectors to produce a third, and several useful geometric and algebraic identities
are derived. The axis-angle parametrization ofSU(3) is developed as a generalization of that forSU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined. 相似文献
6.
7.
In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble
of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions,
not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of
expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides
a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new
class of discrete diagonal representations.
Work supported in part by the Energy Research and Development Administration, Contract No. E(40-I)3992. 相似文献
8.
N Mukunda 《Annals of Physics》1976,99(2):408-433
A general analysis of symmetries and constraints for singular Lagrangian systems is given. It is shown that symmetry transformations can be expressed as canonical transformations in phase space, even for such systems. The relation of symmetries to generators, constraints, commutators, and Dirac brackets is clarified. 相似文献
9.
Hamilton’s theory of turns for the group SU(2) is exploited to develop a new geometrical representation for polarization optics.
While pure polarization states are represented by points on the Poincaré sphere, linear intensity preserving optical systems
are represented by great circle arcs on another sphere. Composition of systems, and their action on polarization states, are
both reduced to geometrical operations. Several synthesis problems, especially in relation to the Pancharatnam-Berry-Aharonov-Anandan
geometrical phase, are clarified with the new representation. The general relation between the geometrical phase, and the
solid angle on the Poincaré sphere, is established. 相似文献
10.