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1.
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
2.
We discuss space-time symmetric Hamiltonian operators of the form H=H0+igH′, where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H′ is invariant under transformation by elements of a subgroup G′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<gc, where gc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g>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
3.
T. Rożek D. Grzonka H.-H. Adam A. Budzanowski R. Czyżykiewicz M. Janusz L. Jarczyk B. Kamys A. Khoukaz K. Kilian P. Klaja P. Kowina P. Moskal W. Oelert C. Piskor-Ignatowicz J. Przerwa J. Ritman T. Sefzick M. Siemaszko J. Smyrski A. Täschner P. Winter M. Wolke P. Wüstner Z. Zhang W. Zipper 《Physics letters. [Part B]》2006
4.
We study rigid string solutions rotating in AdS5×S5 background. For particular values of the parameters of the solutions we find multispin solutions corresponding to giant magnons and single spike strings. We present an analysis of the dispersion relations in the case of three spin solutions distributed only in S5 and the case of one spin in AdS5 and two spins in S5. The possible relation of these string solutions to gauge theory operators and spin chains are briefly discussed. 相似文献
5.
Let M be a connected complex projective manifold such that c1(T(1,0)M)=0. If M admits a holomorphic Cartan geometry, then we show that M is holomorphically covered by an abelian variety. 相似文献
6.
The deviation δQW of the weak charge from its standard model prediction due to the mixing of the W boson with the charged bilepton Y as well as of the Z boson with the neutral Z′ and the real part of the non-Hermitian neutral bilepton X in the economical 3–3–1 model is established. Additional contributions to the usual δQW expression in the extra U(1) models and the left–right models are obtained. Our calculations are quite different from previous analyzes in this kind of the 3–3–1 models and give the limit on mass of the Z′ boson, the Z–Z′ and W–Y mixing angles with the more appropriate values: MZ′>564 GeV, −0.018<sinφ<0 and |sinθ|<0.043. 相似文献
7.
The question of whether BPS invariants are protected in maximally supersymmetric Yang–Mills theories is investigated from the point of view of algebraic renormalisation theory. The protected invariants are those whose cohomology type differs from that of the action. It is confirmed that one-half BPS invariants (F4) are indeed protected while the double-trace one-quarter BPS invariant (d2F4) is not protected at two loops in D=7, but is protected at three loops in D=6 in agreement with recent calculations. Non-BPS invariants, i.e. full superspace integrals, are also shown to be unprotected. 相似文献
8.
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
9.
10.
Using quantum field theory and bosonization, we determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U at half-filling, for small values of the interactions. We show that it is essential to take into account formally irrelevant terms of order X . They generate relevant terms proportional to X2 in the flow of the renormalization group (RG). These terms are calculated using operator product expansions. The model shows three phases separated by a charge transition at U=Uc and a spin transition at U=Us>Uc. For U<Uc singlet superconducting correlations dominate, while for U>Us, the system is in the spin-density wave phase as in the usual Hubbard model. For intermediate values Uc<U<Us, the system is in a spontaneously dimerized bond-ordered wave phase, which is absent in the ordinary Hubbard model with X=0. We obtain that the charge transition remains at Uc=0 for X≠0. Solving the RG equations for the spin sector, we provide an analytical expression for Us(X). The results, with only one adjustable parameter, are in excellent agreement with numerical ones for X<t/2 where t is the hopping. 相似文献
11.
The large-n expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic d-dimensional systems at m -axial Lifshitz points. We derive the leading non-trivial 1/n correction for the perpendicular correlation-length exponent νL2 and hence several related thermal exponents to order O(1/n). The results are consistent with known large-n expansions for d -dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension d?=4+m/2 for generic m∈[0,d]. Analytical results are given for the special case d=4, m=1. For uniaxial Lifshitz points in three dimensions, 1/n coefficients are calculated numerically. The estimates of critical exponents at d=3, m=1 and n=3 are discussed. 相似文献
12.
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
13.
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
14.
We employ chaotic (?2 and ?4) inflation to illustrate the important role radiative corrections can play during the inflationary phase. Yukawa interactions of ? , in particular, lead to corrections of the form −κ?4ln(?/μ), where κ>0 and μ is a renormalization scale. For instance, ?4 chaotic inflation with radiative corrections looks compatible with the most recent WMAP (5 year) analysis, in sharp contrast to the tree level case. We obtain the 95% confidence limits 2.4×10−14?κ?5.7×10−14, 0.931?ns?0.958 and 0.038?r?0.205, where ns and r respectively denote the scalar spectral index and scalar to tensor ratio. The limits for ?2 inflation are κ?7.7×10−15, 0.929?ns?0.966 and 0.023?r?0.135. The next round of precision experiments should provide a more stringent test of realistic chaotic ?2 and ?4 inflation. 相似文献
15.
The field theory renormalization group is used for analyzing the fractional Langevin equation with the order of the temporal derivative 0<α<1, fractional Laplacian of the order σ, and Gaussian noise correlator. The case of non-linearity φm with odd m≥3 is considered. It is proved that the model is multiplicatively renormalizable. Propagators were found in the momentum and coordinate representation, expressed in terms of Fox’s H functions. 相似文献
16.
We analyze the radiative pion decay π+→e+νeγ within nonlocal chiral quark models that include wave function renormalization. In this framework we calculate the vector and axial-vector form factors FV and FA at q2=0 — where q2 is the e+νe squared invariant mass — and the slope a of FV(q2) at q2→0. The calculations are carried out considering different nonlocal form factors, in particular those taken from lattice QCD evaluations, showing a reasonable agreement with the corresponding experimental data. The comparison of our results with those obtained in the (local) NJL model and the relation of FV and a with the form factor in π0→γ?γ decays are discussed. 相似文献
17.
A family of spherically symmetric solutions with horizon in the model with m -component anisotropic fluid is presented. The metrics are defined on a manifold that contains a product of n−1 Ricci-flat “internal” spaces. The equation of state for any s -th component is defined by a vector Us belonging to Rn+1. The solutions are governed by moduli functions Hs obeying non-linear differential equations with certain boundary conditions imposed. A simulation of black brane solutions in the model with antisymmetric forms is considered. An example of solution imitating M2–M5 configuration (in D=11 supergravity) corresponding to Lie algebra A2 is presented. 相似文献
18.
In addition to the narrow spin-one resonances ρT, ωT and aT occurring in low-scale technicolor, there will be relatively narrow scalars in the mass range 200 to 600–700 GeV. We study the lightest isoscalar state, σT. In several important respects it is like a heavy Higgs boson with a small vev. It may be discoverable with high luminosity at the LHC where it is produced via weak boson fusion and likely has substantial W+W− and Z0Z0 decay modes. 相似文献
19.