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1.
We study instanton solutions on noncommutative Euclidean 4-space which are deformations of instanton solutions on commutative Euclidean 4-space. We show that the instanton numbers of these noncommutative instanton solutions coincide with the commutative solutions and conjecture that the instanton number in R4R4 is preserved for general noncommutative deformations. We also study noncommutative deformation of instanton solutions on a T4T4 with twisted boundary conditions.  相似文献   

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For a simply connected, compact, simple Lie group GG, the moduli space of flat GG-bundles over a closed surface ΣΣ is known to be pre-quantizable at integer levels. For non-simply connected GG, however, integrality of the level is not sufficient for pre-quantization, and this paper determines the obstruction–namely a certain cohomology class in H3(G2;Z)H3(G2;Z)–that places further restrictions on the underlying level. The levels that admit a pre-quantization of the moduli space are determined explicitly for all non-simply connected, compact, simple Lie groups GG.  相似文献   

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A curve αα immersed in the three-dimensional sphere S3S3 is said to be a Bertrand curve if there exists another curve ββ and a one-to-one correspondence between αα and ββ such that both curves have common principal normal geodesics at corresponding points. The curves αα and ββ are said to be a pair of Bertrand curves in S3S3. One of our main results is a sort of theorem for Bertrand curves in S3S3 which formally agrees with the classical one: “Bertrand curves in S3S3 correspond to curves for which there exist two constants λ≠0λ0 and μμ such that λκ+μτ=1λκ+μτ=1”, where κκ and ττ stand for the curvature and torsion of the curve; in particular, general helices in the 3-sphere introduced by M. Barros are Bertrand curves. As an easy application of the main theorem, we characterize helices in S3S3 as the only twisted curves in S3S3 having infinite Bertrand conjugate curves. We also find several relationships between Bertrand curves in S3S3 and (1,3)-Bertrand curves in R4R4.  相似文献   

5.
We develop a variational approximation to the entanglement entropy for scalar ?4?4 theory in 1+11+1, 2+12+1, and 3+13+1 dimensions, and then examine the entanglement entropy as a function of the coupling. We find that in 1+11+1 and 2+12+1 dimensions, the entanglement entropy of ?4?4 theory as a function of coupling is monotonically decreasing and convex. While ?4?4 theory with positive bare coupling in 3+13+1 dimensions is thought to lead to a trivial free theory, we analyze a version of ?4?4 with infinitesimal negative bare coupling, an asymptotically free theory known as precarious  ?4?4 theory, and explore the monotonicity and convexity of its entanglement entropy as a function of coupling. Within the variational approximation, the stability of precarious ?4?4 theory is related to the sign of the first and second derivatives of the entanglement entropy with respect to the coupling.  相似文献   

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In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle VkVk to a decreasing family of kk foliations FiFi on a manifold MM. We have shown that there exists a (1,1)(1,1) tensor JJ of VkVk such that Jk≠0Jk0, Jk+1=0Jk+1=0 and we defined by LJ(Vk)LJ(Vk) the Lie Algebra of vector fields XX on VkVk such that, for each vector field YY on VkVk, [X,JY]=J[X,Y][X,JY]=J[X,Y].  相似文献   

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In this paper we show that for a compact minimal hypersurface MM of constant scalar curvature in the unit sphere S6S6 with the shape operator AA satisfying ‖A‖2>5A2>5, there exists an eigenvalue λ>10λ>10 of the Laplace operator of the hypersurface MM such that ‖A‖2=λ−5A2=λ5. This gives the next discrete value of ‖A‖2A2 greater than 0 and 5.  相似文献   

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An exact incompressible quantum liquid is constructed at the filling factor 1/m21/m2 in the square lattice. It supports deconfined fractionally charged excitation. At the filling factor 1/m21/m2, the excitation has fractional charge e/m2e/m2, where ee is the electric charge. This model can be easily generalized to the nn-dimensional square lattice (integer lattice), where the charge of excitations becomes e/mne/mn.  相似文献   

11.
Motivated by the sigma model limit of multicomponent Ginzburg–Landau theory, a version of the Faddeev–Skyrme model is considered in which the scalar field is coupled dynamically to a one-form field called the supercurrent. This coupled model is investigated in the general setting where physical space MM is an oriented Riemannian manifold and the target space NN is a Kähler manifold, and its properties are compared with the usual, uncoupled Faddeev–Skyrme model. In the case N=S2N=S2, it is shown that supercurrent coupling destroys the familiar topological lower energy bound of Vakulenko and Kapitanski when M=R3M=R3, and the less familiar linear bound when MM is a compact 3-manifold. Nonetheless, local energy minimizers may still exist. The first variation formula is derived and used to construct three families of static solutions of the model, all on compact domains. In particular, a coupled version of the unit charge hopfion on a three-sphere of arbitrary radius is found. The second variation formula is derived, and used to analyze the stability of some of these solutions. In particular, it is shown that, in contrast to the uncoupled model, the coupled unit hopfion on the three-sphere of radius RR is unstable   for all RR. This gives an explicit, exact example of supercurrent coupling destabilizing a stable solution of the usual Faddeev–Skyrme model, and casts doubt on the conjecture of Babaev, Faddeev and Niemi that knot solitons should exist in the low energy regime of two-component superconductors.  相似文献   

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Considering the constraints from the experimental data on μ→eγμeγ, μ→3eμ3e, μ–eμe conversion, etc., we analyze the lepton flavor violating decays ?(J/Ψ,?(1S))→e+μ+τ)?(J/Ψ,?(1S))e+μ(μ+τ) in the scenarios of the minimal supersymmetric extensions of Standard Model with seesaw mechanism. Numerically, there is parameter space that the LFV processes of J/Ψ(?)→μ+τJ/Ψ(?)μ+τ can reach the upper experimental bounds, meanwhile the theoretical predictions on μ→eγμeγ, μ→3eμ3e, μ–eμe conversion satisfy the present experimental bounds. For searching of new physics, lepton flavor violating processes J/Ψ(?)→μ+τJ/Ψ(?)μ+τ may be more promising and effective channels.  相似文献   

13.
Let MM be a connected complex projective manifold such that c1(T(1,0)M)=0c1(T(1,0)M)=0. If MM admits a holomorphic Cartan geometry, then we show that MM is holomorphically covered by an abelian variety.  相似文献   

14.
We consider a Schrödinger differential expression L=ΔA+qL=ΔA+q on a complete Riemannian manifold (M,g)(M,g) with metric gg, where ΔAΔA is the magnetic Laplacian on MM and q≥0q0 is a locally square integrable function on MM. In the terminology of W.N. Everitt and M. Giertz, the differential expression LL is said to be separated in L2(M)L2(M) if for all u∈L2(M)uL2(M) such that Lu∈L2(M)LuL2(M), we have qu∈L2(M)quL2(M). We give sufficient conditions for LL to be separated in L2(M)L2(M).  相似文献   

15.
A complex symplectic structure on a Lie algebra hh is an integrable complex structure JJ with a closed non-degenerate (2,0)(2,0)-form. It is determined by JJ and the real part ΩΩ of the (2,0)(2,0)-form. Suppose that hh is a semi-direct product g?Vg?V, and both gg and VV are Lagrangian with respect to ΩΩ and totally real with respect to JJ. This note shows that g?Vg?V is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of ΩΩ and JJ are isomorphic.  相似文献   

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Let MM be a connected compact quantizable Kähler manifold equipped with a Hamiltonian action of a connected compact Lie group GG. Let M//G=?−1(0)/G=M0M//G=?1(0)/G=M0 be the symplectic quotient at value 0 of the moment map ??. The space M0M0 may in general not be smooth. It is known that, as vector spaces, there is a natural isomorphism between the quantum Hilbert space over M0M0 and the GG-invariant subspace of the quantum Hilbert space over MM. In this paper, without any regularity assumption on the quotient M0M0, we discuss the relation between the inner products of these two quantum Hilbert spaces under the above natural isomorphism; we establish asymptotic unitarity to leading order in Planck’s constant of a modified map of the above isomorphism under a “metaplectic correction” of the two quantum Hilbert spaces.  相似文献   

18.
We discuss space-time symmetric Hamiltonian operators of the form H=H0+igHH=H0+igH, where H0H0 is Hermitian and gg real. H0H0 is invariant under the unitary operations of a point group GG while HH is invariant under transformation by elements of a subgroup GG of GG. If GG exhibits irreducible representations of dimension greater than unity, then it is possible that HH has complex eigenvalues for sufficiently small nonzero values of gg. In the particular case that HH is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<gc0<g<gc, where gcgc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether HH may exhibit real or complex eigenvalues for g>0g>0. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.  相似文献   

19.
The effects associated to the length of stabilograms, a measure of the time dependence of the center of pressure of an individual standing up, are analyzed. The fractal characteristics of 27 signals with a length of 214214 points, each one corresponding to a different individual, are studied by using the Detrended Fluctuation Analysis technique. The properties of the complete signals are compared to those of various subsignals extracted from them. No differences have been found between the characteristic exponents found for xx and yy signals. The relation between the exponents of the position and velocity signals is accomplished by the 214214 point signals, while subsignals with up to 212212 points do not verify it. Using artificial signals with 214214 points, generated for αα values given, it has been demonstrated that the exponents obtained from these signals take values larger than expected for α<0.3α<0.3, while the exponents of the accumulated series are smaller than expected for 0.7<α0.7<α. For CoP trajectories this indicates that DFA-1 provides feasible exponents for the short ττ-end region of the velocity signal and the large ττ-end region of the accumulated (position) one. It has been found that the characteristic exponents vary along the series. A slightly larger persistence is found in the last part of the signal for large frequencies in the xx direction.  相似文献   

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