共查询到20条相似文献,搜索用时 31 毫秒
1.
It was argued in [Y. Maeda, A. Sako, Noncommutative deformation of instantons, J. Geom. Phys. 58 (2008) 1784] that the noncommutative deformation of instantons on a 4-torus T4 should alter the instanton numbers for arbitrary noncommutativity parameter θ. We show that this is not the case for the U(N2) theory discussed there. And we discuss the instanton numbers in general gauge theories on the noncommutative T4. 相似文献
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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 M is an oriented Riemannian manifold and the target space N is a Kähler manifold, and its properties are compared with the usual, uncoupled Faddeev–Skyrme model. In the case N=S2, it is shown that supercurrent coupling destroys the familiar topological lower energy bound of Vakulenko and Kapitanski when M=R3, and the less familiar linear bound when M 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 R is unstable for all R. 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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We develop a variational approximation to the entanglement entropy for scalar ?4 theory in 1+1, 2+1, and 3+1 dimensions, and then examine the entanglement entropy as a function of the coupling. We find that in 1+1 and 2+1 dimensions, the entanglement entropy of ?4 theory as a function of coupling is monotonically decreasing and convex. While ?4 theory with positive bare coupling in 3+1 dimensions is thought to lead to a trivial free theory, we analyze a version of ?4 with infinitesimal negative bare coupling, an asymptotically free theory known as precarious ?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 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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A curve α immersed in the three-dimensional sphere S3 is said to be a Bertrand curve if there exists another curve β and a one-to-one correspondence between α and β such that both curves have common principal normal geodesics at corresponding points. The curves α and β are said to be a pair of Bertrand curves in S3. One of our main results is a sort of theorem for Bertrand curves in S3 which formally agrees with the classical one: “Bertrand curves in S3 correspond to curves for which there exist two constants λ≠0 and μ such that λκ+μτ=1”, where κ and τ 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 S3 as the only twisted curves in S3 having infinite Bertrand conjugate curves. We also find several relationships between Bertrand curves in S3 and (1,3)-Bertrand curves in R4. 相似文献
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Considering the constraints from the experimental data on μ→eγ, μ→3e, μ–e conversion, etc., we analyze the lepton flavor violating decays ?(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+τ− can reach the upper experimental bounds, meanwhile the theoretical predictions on μ→eγ, μ→3e, μ–e conversion satisfy the present experimental bounds. For searching of new physics, lepton flavor violating processes J/Ψ(?)→μ+τ− may be more promising and effective channels. 相似文献
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For a simply connected, compact, simple Lie group G, the moduli space of flat G-bundles over a closed surface Σ is known to be pre-quantizable at integer levels. For non-simply connected G, 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)–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 G. 相似文献
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We consider a complete nonnegative biminimal submanifold M (that is, a complete biminimal submanifold with λ≥0) in a Euclidean space EN. Assume that the immersion is proper , that is, the preimage of every compact set in EN is also compact in M. Then, we prove that M is minimal. From this result, we give an affirmative partial answer to Chen’s conjecture. For the case of λ<0, we construct examples of biminimal submanifolds and curves. 相似文献
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M. Teresa Blázquez Marta Anguiano Fernando Arias de Saavedra Antonio M. Lallena Pedro Carpena 《Physica A》2012
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 214 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 x and y signals. The relation between the exponents of the position and velocity signals is accomplished by the 214 point signals, while subsignals with up to 212 points do not verify it. Using artificial signals with 214 points, generated for α values given, it has been demonstrated that the exponents obtained from these signals take values larger than expected for α<0.3, while the exponents of the accumulated series are smaller than expected for 0.7<α. For CoP trajectories this indicates that DFA-1 provides feasible exponents for the short τ-end region of the velocity signal and the large τ-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 x direction. 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 Vk to a decreasing family of k foliations Fi on a manifold M. We have shown that there exists a (1,1) tensor J of Vk such that Jk≠0, Jk+1=0 and we defined by LJ(Vk) the Lie Algebra of vector fields X on Vk such that, for each vector field Y on Vk, [X,JY]=J[X,Y]. 相似文献
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In this paper we show that for a compact minimal hypersurface M of constant scalar curvature in the unit sphere S6 with the shape operator A satisfying ‖A‖2>5, there exists an eigenvalue λ>10 of the Laplace operator of the hypersurface M such that ‖A‖2=λ−5. This gives the next discrete value of ‖A‖2 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/m2 in the square lattice. It supports deconfined fractionally charged excitation. At the filling factor 1/m2, the excitation has fractional charge e/m2, where e is the electric charge. This model can be easily generalized to the n-dimensional square lattice (integer lattice), where the charge of excitations becomes e/mn. 相似文献
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We propose methods towards a systematic determination of d -dimensional curved spaces where Euclidean field theories with rigid supersymmetry can be defined. The analysis is carried out from a group theory as well as from a supergravity point of view. In particular, by using appropriate gauged supergravities in various dimensions we show that supersymmetry can be defined in conformally flat spaces, such as non-compact hyperboloids Hn+1 and compact spheres Sn or – by turning on appropriate Wilson lines corresponding to R-symmetry vector fields – on S1×Sn, with n<6. By group theory arguments we show that Euclidean field theories with rigid supersymmetry cannot be consistently defined on round spheres Sd if d>5 (despite the existence of Killing spinors). We also show that distorted spheres and certain orbifolds are also allowed by the group theory classification. 相似文献
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We consider an interacting scalar quantum field theory on noncommutative Euclidean space. We implement a family of noncommutative deformations, which – in contrast to the well known Moyal–Weyl deformation – lead to a theory with modified kinetic term, while all local potentials are unaffected by the deformation. We show that our models, in particular, include propagators with anisotropic scaling z=2 in the ultraviolet (UV). For a Φ4-theory on our noncommutative space we obtain an improved UV behaviour at the one-loop level and the absence of UV/IR-mixing and of the Landau pole. 相似文献
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Let M be a connected compact quantizable Kähler manifold equipped with a Hamiltonian action of a connected compact Lie group G. Let M//G=?−1(0)/G=M0 be the symplectic quotient at value 0 of the moment map ?. The space M0 may in general not be smooth. It is known that, as vector spaces, there is a natural isomorphism between the quantum Hilbert space over M0 and the G-invariant subspace of the quantum Hilbert space over M. In this paper, without any regularity assumption on the quotient M0, 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
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This article gives a study of the higher-dimensional Penrose transform between conformally invariant massless fields on space–time and cohomology classes on twistor space, where twistor space is defined to be the space of projective pure spinors of the conformal group. We focus on the six-dimensional case in which twistor space is the 6-quadric Q in CP7 with a view to applications to the self-dual (0,2)-theory. We show how spinor-helicity momentum eigenstates have canonically defined distributional representatives on twistor space (a story that we extend to arbitrary dimension). These yield an elementary proof of the surjectivity of the Penrose transform. We give a direct construction of the twistor transform between the two different representations of massless fields on twistor space (H2 and H3) in which the H3s arise as obstructions to extending the H2s off Q into CP7. 相似文献
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A complex symplectic structure on a Lie algebra h is an integrable complex structure J with a closed non-degenerate (2,0)-form. It is determined by J and the real part Ω of the (2,0)-form. Suppose that h is a semi-direct product g?V, and both g and V are Lagrangian with respect to Ω and totally real with respect to J. This note shows that g?V is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω and J are isomorphic. 相似文献
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We consider a Schrödinger differential expression L=ΔA+q on a complete Riemannian manifold (M,g) with metric g, where ΔA is the magnetic Laplacian on M and q≥0 is a locally square integrable function on M. In the terminology of W.N. Everitt and M. Giertz, the differential expression L is said to be separated in L2(M) if for all u∈L2(M) such that Lu∈L2(M), we have qu∈L2(M). We give sufficient conditions for L to be separated in L2(M). 相似文献