اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe ground state energy of a charged particle on a Riemann surface
402
0
0.0
(
0
)
تأليف
J.M. Speight
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
It is shown that the quantum ground state energy of particle of mass m and electric charge e moving on a compact Riemann surface under the influence of a constant magnetic field of strength B is E_0=eB/2m. Remarkably, this formula is completely independent of both the geometry and topology of the Riemann surface. The formula is obtained by reinterpreting the quantum Hamiltonian as the second variation operator of an associated classical variational problem.
قيم البحث
اقرأ أيضاً
It is proved that the moduli space of static solutions of the CP^1 model on spacetime Sigma x R, where Sigma is any compact Riemann surface, is geodesically incomplete with respect to the metric induced by the kinetic energy functional. The geodesic
approximation predicts, therefore, that lumps can collapse and form singularities in finite time in these models.
We initiate the study of (2,0) little string theory of ADE type using its definition in terms of IIB string compactified on an ADE singularity. As one application, we derive a 5d ADE quiver gauge theory that describes the little string compactified o
n a sphere with three full punctures, at low energies. As a second application, we show the partition function of this theory equals the 3-point conformal block of ADE Toda CFT, q-deformed. To establish this, we generalize the A_n triality of cite{AHS} to all ADE Lie algebras; IIB string perspective is crucial for this as well.
In this work we consider the existence and uniqueness of the ground state of the regularized Hamiltonian of the Supermembrane in dimensions $D= 4,,5,,7$ and 11, or equivalently the $SU(N)$ Matrix Model. That is, the 0+1 reduction of the 10-dimensiona
l $SU(N)$ Super Yang-Mills Hamiltonian. This ground state problem is associated with the solutions of the inner and outer Dirichlet problems for this operator, and their subsequent smooth patching (glueing) into a single state. We have discussed properties of the inner problem in a previous work, therefore we now investigate the outer Dirichlet problem for the Hamiltonian operator. We establish existence and uniqueness on unbounded valleys defined in terms of the bosonic potential. These are precisely those regions where the bosonic part of the potential is less than a given value $V_0$, which we set to be arbitrary. The problem is well posed, since these valleys are preserved by the action of the $SU(N)$ constraint. We first show that their Lebesgue measure is finite, subject to restrictions on $D$ in terms of $N$. We then use this analysis to determine a bound on the fermionic potential which yields the coercive property of the energy form. It is from this, that we derive the existence and uniqueness of the solution. As a by-product of our argumentation, we show that the Hamiltonian, restricted to the valleys, has spectrum purely discrete with finite multiplicity. Remarkably, this is in contrast to the case of the unrestricted space, where it is well known that the spectrum comprises a continuous segment. We discuss the relation of our work with the general ground state problem and the question of confinement in models with strong interactions.
Quantum state wave functionals are constructed in exact form for the graviton-like field theory obtained by breaking down the topological symmetry of the string action related with the Euler characteristic of the world-surface; their continuous and d
iscrete symmetries are discussed. The comparison with the so-called Chern-Simons state, which may be inappropriate as quantum state, allows us to conclude that the found wave functionals will give a plausible approximation to the ground state for the considered field theory.
We study the Regge and hard scattering limits of the one-loop amplitude for massless open string states in the type I theory. For hard scattering we find the exact coefficient multiplying the known exponential falloff in terms of the scattering angle
, without relying on a saddle point approximation for the integration over the cross ratio. This bypasses the issues of estimating the contributions from flat directions, as well as those that arise from fluctuations of the gaussian integration about a saddle point. This result allows for a straightforward computation of the small- angle behavior of the hard scattering regime and we find complete agreement with the Regge limit at high momentum transfer, as expected.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
