Chern–Simons theory,Stokes’ theorem,and the Duflo map

We consider a novel derivation of the expectation values of holonomies in Chern–Simons theory, based on Stokes’ Theorem and the functional properties of the Chern–Simons action. It involves replacing the connection by certain functional derivatives under the path integral. It turns out that ordering choices have to be made in the process, and we demonstrate that, quite surprisingly, the Duflo isomorphism gives the right ordering, at least in the simple cases that we consider. In this way, we determine the expectation values of unknotted, but possibly linked, holonomy loops for SU(2) and SU(3), and sketch how the method may be applied to more complicated cases. Our manipulations of the path integral are formal but well motivated by a rigorous calculus of integration on spaces of generalized connections which has been developed in the context of loop quantum gravity.     

Statistical mechanics of an ideal gas of non-Abelian anyons

We study the thermodynamical properties of an ideal gas of non-Abelian Chern–Simons particles and we compute the second virial coefficient, considering the effect of general soft-core boundary conditions for the two-body wavefunction at zero distance. The behaviour of the second virial coefficient is studied as a function of the Chern–Simons coupling, the isospin quantum number and the hard-core parameters. Expressions for the main thermodynamical quantities at the lower order of the virial expansion are also obtained: we find that at this order the relation between the internal energy and the pressure is the same found (exactly) for 2D Bose and Fermi ideal gases. A discussion of the comparison of obtained findings with available results in literature for systems of hard-core non-Abelian Chern–Simons particles is also supplied.     

Second-Order Five-Dimensional Chern–Simons Gravity

Continuing our previous discussion of the canonical covariant formalism (Zandron, O. S. (in press). International Journal of Theoretical Physics), the second-order canonical fünfbein formalism of the topological five-dimensional Chern–Simons gravity is constructed. Since this gravity model naturally contains a Gauss–Bonnet term quadratic in curvature, the second-order formalism requires the implementation of the Ostrogradski transformation in order to introduce canonical momenta. This is due to the presence of second time-derivatives of the fünfbein field. By performing the space–time decomposition of the manifold M ⁵, the set of first-class constraints that determines all the Hamiltonian gauge symmetries can be found. The total Hamiltonian as generator of time evolution is constructed, and the apparent gauge degrees of freedom are unambiguously removed, leaving only the physical ones.     

Global wellposedness for a one-dimensional Chern–Simons–Dirac system in Lp

The global wellposedness in L^p(?) for the Chern–Simons–Dirac equation in the 1+1 space and time dimension is discussed. We consider two types of quadratic nonlinearity: the null case and the non-null case. We show the time global wellposedness for the Chern–Simon–Dirac equation in the framework of L^p(?), where 1≤p≤∞ for the null case. For the scaling critical case, p = 1, mass concentration phenomena of the solutions may occur in considering the time global solvability. We invoke the Delgado–Candy estimate which plays a crucial role in preventing concentration phenomena of the global solution. Our method is related to the original work of Candy (2011), who showed the time global wellposedness for the single Dirac equation with cubic nonlinearity in the critical space L²(?).     

二维模糊球上的量子霍尔流体

在回顾了Haldane对量子Hall效应在二维球面S2上的描述后,本文构造了二维模糊球S2上的非对易代数及其Hilbert空间的Moyal结构.通过构造模糊球上不可压缩量子霍尔流体的非对易Chern-Simons理论,求解具有准粒子源的Gaussian约束,找出模糊球上的Calogero矩阵及最低Landau能级Laughlin波函数的完全集,此Laughlin波函数由旋量坐标推广的Jack多项式表示.     

Vortex Solutions of the Liouville Equation

The most general vortex solution of the Liouville equation (which arises in nonrelativistic Chern–Simons theory) is associated with rational functions, f(z)=P(z) Qz), where P(z) and Q(z) are both polynomials, deg P相似文献   

The Integral Form of D = 3 Chern‐Simons Theories Probing Singularities

We consider D=3 supersymmetric Chern Simons gauge theories both from the point of view of their formal structure and of their applications to the AdS₄/CFT₃ correspondence. From the structural view‐point, we use the new formalism of integral forms in superspace that utilizes the rheonomic Lagrangians and the Picture Changing Operators, as an algorithmic tool providing the connection between different approaches to supersymmetric theories. We provide here the generalization to an arbitrary Kähler manifold with arbitrary gauge group and arbitrary superpotential of the rheonomic lagrangian of D=3 matter coupled gauge theories constructed years ago. From the point of view of the AdS₄/CFT₃ correspondence and more generally of M2‐branes we emphasize the role of the Kähler quotient data in determining the field content and the interactions of the Cherns Simons gauge theory when the transverse space to the brane is a non‐compact Kähler quotient K ₄ of some flat variety with respect to a suitable group. The crepant resolutions of singularities fall in this category. In the present paper we anticipate the general scheme how the geometrical data are to be utilized in the construction of the D=3 Chern‐Simons Theory supposedly dual to the corresponding M2‐brane solution.     

Chern–Simons forms on associated bundles,and boundary terms

Let E be a principle bundle over a compact manifold M with compact structural group G. For any G-invariant polynomial P, the transgressive forms defined by Chern and Simons in (Ann. Math. 99:48–69, 1974) are shown to extend to forms on associated bundles B with fiber a quotient F = G/H of the group. These forms satisfy a heterotic formula relating the characteristic form to a fiber-curvature characteristic form. For certain natural bundles B, , giving a true transgressive form on the associated bundle, which leads to the standard obstruction properties of characteristic classes as well as natural expressions for boundary terms. These forms also yield new secondary characteristic classes giving refined information about the associated bundles B.