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1.
Let F be a differentiable manifold endowed with an almost K?hler structure (J,ω), α a J-holomorphic action of a compact Lie group on F, and K a closed normal subgroup of which leaves ω invariant. The purpose of this article is to introduce gauge theoretical invariants for such triples (F,α,K). The invariants are associated with moduli spaces of solutions of a certain vortex type equation on a Riemann surface Σ. Our main results concern the special case of the triple
where αcan denotes the canonical action of on . We give a complex geometric interpretation of the corresponding moduli spaces of solutions in terms of gauge theoretical quot spaces, and compute the invariants explicitly in the case r=1. Proving a comparison theorem for virtual fundamental classes, we show that the full Seiberg–Witten invariants of ruled surfaces, as defined in [OT2], can be identified with certain gauge theoretical Gromov–Witten invariants of the triple (Hom(ℂ,ℂ< r 0),αcan, U(1)). We find the following formula for the full Seiberg–Witten invariant of a ruled surface over a Riemann surface of genus g:
where [F] denotes the class of a fibre. The computation of the invariants in the general case r >1 should lead to a generalized Vafa-Intriligator formula for “twisted”Gromov–Witten invariants associated with sections in Grassmann bundles. Received: 22 February 2001 / Accepted: 16 January 2002  相似文献   

2.
S. N. Kaul  Anita Semwal 《Pramana》2003,61(6):1129-1144
Isothermal remanent magnetization decay,M r(t), and ‘in-field’ growth of zero-field-cooled magnetization,M ZFC(t), with time have been measured over four decades in time at temperatures ranging from 0.25T c to 1.25T c (whereT c is the Curie temperature, determined previously for the same sample from static critical phenomena measurements) for a nearly ordered intermetallic compound Ni3Al, which is an experimental realization of a three-dimensional (d = 3) ferromagnet with weak quenched random-exchange disorder. None of the functional forms ofM r(t) predicted by the existing phenomenological models of relaxation dynamics in spin systems with quenched randomness, but only the expressions and closely reproduce such data in the present case. The most striking features of magnetic relaxation in the system in question are as follows: Aging effects are absent in bothM r t andM ZFC(t) at all temperatures in the temperature range covered in the present experiments. A cross-over in equilibrium dynamics from the one, characteristic of a pured = 3 ferromagnet with complete atomic ordering and prevalent at temperatures away from Tc, to that, typical of ad = 3 random-exchange ferromagnet, occurs asT → Tc. The relaxation times τ1(T)(τ1 (T)) and τ2(T)(τ2 (T)) exhibit logarithmic divergence at critical temperatures and ; and both increase with the external magnetic field strength,H, such that at any given field value, . The exponent characterizing the logarithmic divergence in τ 1 (T) and τ 2 T possesses a field-independent value of ≃16 for both relaxation times. Of all the available theoretical models, the droplet fluctuation model alone provides a qualitative explanation for some aspects of the present magnetic relaxation data  相似文献   

3.
We examine the effects of mixing induced non-diagonal light-heavy neutrino weak neutral currents on the amplitude for the process (with a=e, μ or τ). By imposing constraint that the amplitude should not exceed the perturbative unitarity limit at high energy , we obtain bounds on light-heavy neutrino mixing parameter sin2 where is the mixing angle. In the case of one heavy neutrino (mass mξ) or mass degenerate heavy neutrinos, for Λ=1 TeV, no bound is obtained for mξ<0.50 TeV. However, sin2 ≤3.8 × 10−6 for mξ=5 TeV and sin ≤6.0 × 10−8 for mξ=10 TeV. For Λ=∞, no constraint is obtained for mξ<0.99 TeV and sin2 ≤3.8 × 10−2 (for mξ=5 TeV) and sin2 ≤9.6 × 10−3 (for mξ=10 TeV).  相似文献   

4.
S. Rajasekar 《Pramana》2004,62(1):1-12
Integrability of a linearly damped two-coupled non-linear oscillators equation is investigated by employing the Painlevé analysis. The following two integrable cases are identified: (i)d = 0, α =β, δ_1 and δ_2 are arbitrary, (ii) d^2= 25α/6, α =β, δ_1 and δ_2 are arbitrary. Exact analytical solution is constructed for the integrable choices.  相似文献   

5.
We construct approximate solutions to the time–dependent Schr?dinger?equation
for small values of ħ. If V satisfies appropriate analyticity and growth hypotheses and , these solutions agree with exact solutions up to errors whose norms are bounded by
for some C and γ>0. Under more restrictive hypotheses, we prove that for sufficiently small T , implies the norms of the errors are bounded by
for some C , γ>0, and σ > 0. Received: 7 January 1999 / Accepted: 30 April 1999  相似文献   

6.
Let stand for the integral operators with the sine kernels acting on L 2[0,α]. Dyson conjectured that the asymptotics of the Fredholm determinants of are given by
as α→∞. In this paper we are going to give a proof of these two asymptotic formulas.  相似文献   

7.
In this short note, we study the local times of the fractional Ornstein–Uhlenbeck process X H with Hurst index 1/2<H<1 solving the Langevin equation with fractional noise
where ν > 0 and B H is a fractional Brownian motion with Hurst index 1/2<H<1. We give Tanaka formula for the process and some properties of local times. Mathematics Subject Classifications (2000): 60G15, 60J55, 60H05. *The Project-sponsored by SRF for ROCS, SEM.  相似文献   

8.
Explicit evaluation of the following parameters has been carried out in the extraU (1) superstring inspired model: (i) As Mz2 varies from 555 GeV to 620 GeV and (m t) CDF = 175.6 ± 5.7 GeV (Table 1): (a) SNew varies from -0.100 ± 0.089 to -0.130 ± 0.090, (b) TNew varies from -0.098 ± 0.097 to -0.129 ± 0.098, (c) UNew varies from -0.229 ± 0.177 to -0.253 ± 0.206, (d) Τz varies from 2.487 ± 0.027 to 2.486 ± 0.027, (e) ALR varies from 0.0125 ± 0.0003 to 0.0126 ± 0.0003, (f) A FB b remains constant at 0.0080 ± 0.0007. Almost identical values are obtained for (m t)D0 = 169 GeV (see table 2). (ii) Triple gauge boson vertices (TGV) contributions: AsMz 2 varies from 555 GeV to 620 GeV and (m t) CDF = 175.6 ±5.7 GeV. (a)√s = 500 GeV, asymptotic case: varies from -0.301 to -0.179; varies from -0.622 to -0.379; varies from +0.0061 to 0.0056; varies from -3.691 to -2.186. varies from +0.270 to +0.118; varies from +0.552 to 0.238; varies from +0.0004 to +0.0002; remains constant at -0.110. (b)√s = 700 GeV, asymptotic case: varies from -0.297 to -0.176; varies from -0.609 to -0.370; varies from -0.0082 to -0.0078; varies from -3.680 to -2.171.√s = 700 GeV, nonasymptotic case: varies from -0.173 to -0.299; varies from-0.343 to -0.591; varies from -0.005 to -0.011; remains constant at -0.110. The pattern of form factors values for√s = 1000, 1200 GeV is almost identical to that of√s= 700 GeV. Further the values of the form factors for (m t)D0 (=169 GeV) follow identical pattern as that of (m t) CDF form factors values (see tables 5, 6, 9, 10). We conclude that the values of all the form factors with the exception of these of , are comparable or larger than theS, T values and therefore the TGV contributions are important while deciding the use of extraU (1) model for doing physics beyond standard model.  相似文献   

9.
The prong-number distributions in collisions at relatively low laboratory momenta (≾7 GeV/c) exhibit the same type of scaling which has been observed in pp and π-N collisions at momenta ≿ 50 GeV/c.  相似文献   

10.
Probir Roy 《Pramana》2007,69(5):895-901
An event-shape analysis of the dileptons in the process e + e → ℓ+ , studied in ILC or CLIC, can clearly discriminate between a supersymmetric or a large extra dimensional (ADD) production mechanism.   相似文献   

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