اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNoncommutative Quantum Mechanics Viewed from Feynman Formalism
159
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Dyson published in 1990 a proof due to Feynman of the Maxwell equations. This proof is based on the assumption of simple commutation relations between position and velocity. We first study a nonrelativistic particle using Feynman formalism. We show that Poincar{e}s magnetic angular momentum and Dirac magnetic monopole are the direct consequences of the structure of the sO(3) Lie algebra in Feynman formalism. Then we show how to extend this formalism to the dual momentum space with the aim of introducing Noncommutative Quantum Mechanics which was recently the subject of a wide range of works from particle physics to condensed matter physics.
قيم البحث
اقرأ أيضاً
We study the effect of noncommutativity of space on the physics of a quantum interferometer located in a rotating disk in a gauge field background. To this end, we develop a path-integral approach which allows defining an effective action from which
relevant physical quantities can be computed as in the usual commutative case. For the specific case of a constant magnetic field, we are able to compute, exactly, the noncommutative Lagrangian and the associated shift on the interference pattern for any value of $theta$.
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called entangled sta
te representations. Furthermore, we derive unitary transformations between the new representations and the ordinary one used in noncommutative quantum mechanics (NCQM) and obtain eigenfunctions of some basic operators in these representations. To show the potential applications of the entangled state representations, a two-dimensional harmonic oscillator on the noncommutative plane with both coordinate-coordinate and momentum-momentum couplings is exactly solved.
A general three-dimensional noncommutative quantum mechanical system mixing spatial and spin degrees of freedom is proposed. The analogous of the harmonic oscillator in this description contains a magnetic dipole interaction and the ground state is e
xplicitly computed and we show that it is infinitely degenerated and implying a spontaneous symmetry breaking. The model can be straightforwardly extended to many particles and the main above properties are retained. Possible applications to the Bose-Einstein condensation with dipole-dipole interactions are briefly discussed.
We reformulate Super Quantum Mechanics in the context of integral forms. This framework allows to interpolate between different actions for the same theory, connected by different choices of Picture Changing Operators (PCO). In this way we retrieve c
omponent and superspace actions, and prove their equivalence. The PCO are closed integral forms, and can be interpreted as super Poincare duals of bosonic submanifolds embedded into a supermanifold.. We use them to construct Lagrangians that are top integral forms, and therefore can be integrated on the whole supermanifold. The $D=1, ~N=1$ and the $D=1,~ N=2$ cases are studied, in a flat and in a curved supermanifold. In this formalism we also consider coupling with gauge fields, Hilbert space of quantum states and observables.
We consider the noncommutative space-times with Lie-algebraic noncommutativity (e.g. $kappa$-deformed Minkowski space). In the framework with classical fields we extend the $star$-product in order to represent the noncommutative translations in terms
of commutative ones. We show the translational invariance of noncommutative bilinear action with local product of noncommutative fields. The quadratic noncommutativity is also briefly discussed.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
