Notes on non-commutative Chern–Simons quantum mechanics

The European Physical Journal C - We investigate the classical and quantum aspects of non-commutative topological (Chern–Simons) mechanics. We introduce the magnetic field by the minimal...     

Chern–Simons theory and BCS superconductivity

We study the relationship between the holomorphic unitary connection of Chern–Simons theory with temporal Wilson lines and the Richardson's exact solution of the reduced BCS Hamiltonian. We derive the integrals of motion of the BCS model, their eigenvalues and eigenvectors as a limiting case of the Chern–Simons theory.     

Equivalence between supersymmetric self-dual and Maxwell–Chern–Simons models coupled to a matter spinor superfield

We study the duality of the supersymmetric self-dual and Maxwell–Chern–Simons theories coupled to a fermionic matter superfield, using a master action. This approach evades the difficulties inherent to the quartic couplings that appear when matter is represented by a scalar superfield. The price is that the spinorial matter superfield represents a unusual supersymmetric multiplet, whose main physical properties we also discuss.     

On Chern–Simons and WZW Partition Functions

Direct analysis of the path integral reduces partition functions in Chern-Simons theory on a three-manifold M with group G to partition functions in a WZW model of maps from a Riemann surface ‡ to G. In particular, Chern-Simons theory on S³, S¹ 2 ‡, B³ and the solid torus correspond, respectively, to the WZW model of maps from S² to G, the G/G model for ‡, and Witten's gauged WZW path integral Ansatz for Chern-Simons states using maps from S² and from the torus to G. The reduction hinges on the characterization of {\cal A / G}_{n}$, the space of connections modulo those gauge transformations which are the identity at a point n, as itself a principal fiber bundle with affine-linear fiber.     

Nucleon–nucleon scattering in the light of supersymmetric quantum mechanics

By exploiting supersymmetry-inspired factorization method together with a judiciously chosen deuteron ground-state wave function, approximate higher partial wave nucleon–nucleon potentials are generated. In this context, a minor modification is also introduced to the generated potentials. The n–p scattering phase shifts are computed and analysed via the phase function method.     

Remarks on Chern–Simons Invariants

The perturbative Chern–Simons theory is studied in a finite-dimensional version or assuming that the propagator satisfies certain properties (as is the case, e.g., with the propagator defined by Axelrod and Singer). It turns out that the effective BV action is a function on cohomology (with shifted degrees) that solves the quantum master equation and is defined modulo certain canonical transformations that can be characterized completely. Out of it one obtains invariants.     

Chern–Simons Gravities (CSG) and Gravitational Chern–Simons (GCS) Densities in All Dimensions

Physics of Atomic Nuclei - Chern–Simons gravities and gravitational Chern–Simons densities are constructed using the non-Abelian Yang–Mills Chern–Simons densities. As such,...     

Decoupling and reduction in Chern–Simons modified gravity

We show that for four-dimensional spacetimes with a non-null hypersurface orthogonal Killing vector and for a Chern–Simons (CS) background (non-dynamical) scalar field, which is constant along the Killing vector, the source-free equations of CS modified gravity decouple into their Einstein and Cotton constituents. Thus, the model supports only general relativity solutions. We also show that, when the cosmological constant vanishes and the gradient of the CS scalar field is parallel to the non-null hypersurface orthogonal Killing vector of constant length, CS modified gravity reduces to topologically massive gravity in three dimensions. Meanwhile, with the cosmological constant such a reduction requires an appropriate source term for CS modified gravity.     

Maxwell–Chern–Simons场的Casimir效应

利用约束理论对AbelMaxwell-Chem-Simons场进行路径积分量子化. 并利用复变函数论中Plana求和公式,计算(2+1)维空间中两个平行导线型边界的Casimir效应. 不引任何截断参数,而得出有限的解析表达式.     

Higher Spins from Nambu–Chern–Simons Theory

We propose a new theory of higher spin gravity in three spacetime dimensions. This is defined by what we will call a Nambu–Chern–Simons (NCS) action; this is to a Nambu 3-algebra as an ordinary Chern–Simons (CS) action is to a Lie (2-)algebra. The novelty is that the gauge group of this theory is simple; this stands in contrast to previously understood interacting 3D higher spin theories in the frame-like formalism. We also consider the N = 8 supersymmetric NCS-matter model (BLG theory), where the NCS action originated: Its fully supersymmetric M2 brane configurations are interpreted as Hopf fibrations, the homotopy type of the (infinite) gauge group is calculated and its instantons are classified.     

Resolution of Chern–Simons–Higgs Vortex Equations

It is well known that the presence of multiple constraints of non-Abelian relativisitic Chern–Simons–Higgs vortex equations makes it difficult to develop an existence theory when the underlying Cartan matrix K of the equations is that of a general simple Lie algebra and the strongest result in the literature so far is when the Cartan subalgebra is of dimension 2. In this paper we overcome this difficulty by implicitly resolving the multiple constraints using a degree-theorem argument, utilizing a key positivity property of the inverse of the Cartan matrix deduced in an earlier work of Lusztig and Tits, which enables a process that converts the equality constraints to inequality constraints in the variational formalism. Thus this work establishes a general existence theorem that settles a long-standing open problem in the field regarding the general solvability of the equations.     

Chern–Simons–Rozansky–Witten topological field theory

We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern–Simons and Rozansky–Witten theory and can be regarded as a topologically-twisted version of the N=4$N=4$d=3$d=3$ supersymmetric gauge theory recently discovered by Gaiotto and Witten. The model depends on a gauge group G and a hyper-Kähler manifold X with a tri-holomorphic action of G. In the case when X is an affine space, we show that the model is equivalent to Chern–Simons theory whose gauge group is a supergroup. This explains the role of Lie superalgebras in the construction of Gaiotto and Witten. For general X, our model appears to be new. We describe some of its properties, focusing on the case when G is simple and X is the cotangent bundle of the flag variety of G. In particular, we show that Wilson loops are labeled by objects of a certain category which is a quantum deformation of the equivariant derived category of coherent sheaves on X.     

Chern–Simons theory in the temporal gauge and knot invariants through the universal quantum R-matrix

In temporal gauge A₀=0$A_0=0$ the 3d Chern–Simons theory acquires quadratic action and an ultralocal propagator. This directly implies a 2d R-matrix representation for the correlators of Wilson lines (knot invariants), where only the crossing points of the contours projection on the xy plane contribute. Though the theory is quadratic, P-exponents remain non-trivial operators and R  -factors are easier to guess then derive. We show that the topological invariants arise if additional flag structure R³⊃R²⊃R¹${\mathbb{R}}^3\supset {\mathbb{R}}^2\supset {\mathbb{R}}^1$ (xy plane and a y line in it) is introduced, R is the universal quantum R  -matrix and turning points contribute the “enhancement” factors qρ$q^{\rho }$.     

Chern–Simons particles with nonstandard gravitational interaction

The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity is extended to include Abelian or non-Abelian charges coupled to Chern–Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern–Simons particles coupled, in a reparameterization invariant way, to a translational Chern–Simons action. The quantum 2-body problem is described by a nonstandard Schr?dinger equation with a noninteger angular momentum depending on energy as well as particle charges. Some numerical results describing the modification of the energy levels by these charges in the confined regime are presented. The modification involves a shift as well as splitting of the levels. Received: 16 March 2001 / Published online: 13 June 2001