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1.
For a (co)monad T
l
on a category , an object X in , and a functor , there is a (co)simplex in . The aim of this paper is to find criteria for para-(co)cyclicity of Z
*. Our construction is built on a distributive law of T
l
with a second (co)monad T
r
on , a natural transformation , and a morphism in . The (symmetrical) relations i and w need to satisfy are categorical versions of Kaygun’s axioms of a transposition map. Motivation comes from the observation
that a (co)ring T over an algebra R determines a distributive law of two (co)monads and on the category of R-bimodules. The functor Π can be chosen such that is the cyclic R-module tensor product. A natural transformation is given by the flip map and a morphism is constructed whenever T is a (co)module algebra or coring of an R-bialgebroid. The notion of a stable anti-Yetter-Drinfel’d module over certain bialgebroids, the so-called ×
R
-Hopf algebras, is introduced. In the particular example when T is a module coring of a ×
R
-Hopf algebra and X is a stable anti-Yetter-Drinfel’d -module, the para-cyclic object Z
* is shown to project to a cyclic structure on . For a -Galois extension , a stable anti-Yetter-Drinfel’d -module T
S
is constructed, such that the cyclic objects and are isomorphic. This extends a theorem by Jara and Ştefan for Hopf Galois extensions. As an application, we compute Hochschild
and cyclic homologies of a groupoid with coefficients in a stable anti-Yetter-Drinfel’d module, by tracing it back to the
group case. In particular, we obtain explicit expressions for (coinciding relative and ordinary) Hochschild and cyclic homologies
of a groupoid. The latter extends results of Burghelea on cyclic homology of groups. 相似文献
2.
Given a braided vector space
, we show that iterated integrals of operator-valued functions satisfying a certain exchange relation give rise to representations of the quantum shuffle algebra built on
. Using the quantum shuffle construction of the 'upper triangular part'
of a quantum shuffle, this provides a simple proof of the result of Bouwknegt, MacCarthy and Pilch saying that integrals of vertex operators acting on certain Fock modules give rise to representations of
. 相似文献
3.
R.A. Diaz R. Martinez C.E. Sandoval 《The European Physical Journal C - Particles and Fields》2006,46(2):403-405
We find some constraints on the flavor changing vertices of the two Higgs doublet model, from the
measurement. Although bounds from this observable have already been considered, this paper takes into account the role of
a new operator not included previously, as well as the vertices
,
and
. Using the Cheng–Sher parametrization, we find that for a relatively light charged Higgs boson (200–300 GeV), we obtain
, while the parameter
could have values up to about 50. In addition, we use bounds for
and
obtained from
at next to leading order, and study the case where the only vanishing vertex factors are the ones involving quarks from the
first family. We obtain that
is not sensitive to the change of the parameter
, while
. 相似文献
4.
We exhibit a finitely generated group whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping
class group associated to a surface of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus g with n boundary components, for any g ≥ 0 and n > 0. We construct a representation of into the restricted symplectic group of the real Hilbert space generated by the homology classes of non-separating circles on , which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first
universal Chern class in is the pull-back of the Pressley-Segal class on the restricted linear group via the inclusion .
L. F. was partially supported by the ANR Repsurf:ANR-06-BLAN-0311. 相似文献
5.
Marc Wouts 《Communications in Mathematical Physics》2009,289(1):157-204
We study the surface tension and the phenomenon of phase coexistence for the Ising model on with ferromagnetic but random couplings. We prove the convergence in probability (with respect to random couplings) of surface
tension and analyze its large deviations: upper deviations occur at volume order while lower deviations occur at surface order.
We study the asymptotics of surface tension at low temperatures and relate the quenched value τ
q
of surface tension to maximal flows (first passage times if d = 2). For a broad class of distributions of the couplings we show that the inequality –where τ
a
is the surface tension under the averaged Gibbs measure – is strict at low temperatures. We also describe the phenomenon
of phase coexistence in the dilute Ising model and discuss some of the consequences of the media randomness. All of our results
hold as well for the dilute Potts and random cluster models. 相似文献
6.
Liang Kong 《Communications in Mathematical Physics》2008,283(1):25-92
Let V be a vertex operator algebra satisfying certain reductivity and finiteness conditions such that , the category of V-modules, is a modular tensor category. We study open-closed field algebras over V equipped with nondegenerate invariant bilinear forms for both open and closed sectors. We show that they give algebras over
a certain -extension of the so-called Swiss-cheese partial dioperad, and we can obtain Ishibashi states easily in such algebras. The
Cardy condition can be formulated as an additional condition on such open-closed field algebras in terms of the action of
the modular transformation on the space of intertwining operators of V. We then derive a graphical representation of S in the modular tensor category . This result enables us to give a categorical formulation of the Cardy condition and the modular invariance condition for
1-point correlation functions on the torus. Then we incorporate these two conditions and the axioms of the open-closed field
algebra over V equipped with nondegenerate invariant bilinear forms into a tensor-categorical notion called the Cardy -algebra. In the end, we give a categorical construction of the Cardy -algebra in the Cardy case. 相似文献
7.
A new evaluation of the hadronic vacuum polarization contribution to the muon magnetic moment is presented. We take into account the reanalysis of the low-energy e
+
e
-annihilation cross section into hadrons by the CMD-2 Collaboration. The agreement between e
+
e
-and
spectral functions in the
channel is found to be much improved. Nevertheless, significant discrepancies remain in the center-of-mass energy range between 0.85 and
, so that we refrain from averaging the two data sets. The values found for the lowest-order hadronic vacuum polarization contributions are
where the errors have been separated according to their sources: experimental, missing radiative corrections in e
+
e
-data, and isospin breaking. The corresponding Standard Model predictions for the muon magnetic anomaly read
where the errors account for the hadronic, light-by-light (LBL) scattering and electroweak contributions. The deviations from the measurement at BNL are found to be
(1.9
) and
(0.7
) for the e
+
e
-- and
-based estimates, respectively, where the second error is from the LBL contribution and the third one from the BNL measurement.Received: 7 September 2003, Published online: 30 October 2003 相似文献
8.
We consider the DLA process on a cylinder . It is shown that this process “grows arms”, provided that the base graph G has small enough mixing time. Specifically, if the mixing time of G is at most , the time it takes the cluster to reach the m
th layer of the cylinder is at most of order . In particular we get examples of infinite Cayley graphs of degree 5, for which the DLA cluster on these graphs has arbitrarily
small density.
In addition, we provide an upper bound on the rate at which the “arms” grow. This bound is valid for a large class of base
graphs G, including discrete tori of dimension at least 3.
It is also shown that for any base graph G, the density of the DLA process on a G-cylinder is related to the rate at which the arms of the cluster grow. This implies that for any vertex transitive G, the density of DLA on a G-cylinder is bounded by 2/3. 相似文献
9.
Let S
2 be the 2-dimensional unit sphere and let J
α
denote the nonlinear functional on the Sobolev space H
1(S
2) defined by
$J_\alpha(u) = \frac{\alpha}{16\pi}\int_{S^2}|\nabla u|^2\, d\mu_0 + \frac{1}{4\pi} \int_{S^2} u\, d \mu_0 -{\rm ln} \int_{S^2} e^{u}
\, \frac{d \mu_0}{4\pi},$J_\alpha(u) = \frac{\alpha}{16\pi}\int_{S^2}|\nabla u|^2\, d\mu_0 + \frac{1}{4\pi} \int_{S^2} u\, d \mu_0 -{\rm ln} \int_{S^2} e^{u}
\, \frac{d \mu_0}{4\pi}, 相似文献
10.
Let (M, g) be a pseudo-Riemannian manifold and
the space of densities of degree on M. Denote
the space of differential operators from
to
of order k and S
k
with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map
. This result generalizes that of Duval and Ovsienko. 相似文献
11.
We consider the time-dependent Schrödinger-Hartree equation
12.
We prove bounds on moments of the Smoluchowski coagulation equations with diffusion, in any dimension d ≥ 1. If the collision propensities α(n, m) of mass n and mass m particles grow more slowly than , and the diffusion rate is non-increasing and satisfies for some b
1 and b
2 satisfying 0 ≤ b
2 < b
1 < ∞, then any weak solution satisfies for every and T ∈(0, ∞), (provided that certain moments of the initial data are finite). As a consequence, we infer that these conditions
are sufficient to ensure uniqueness of a weak solution and its conservation of mass.
This work was performed while A.H. held a postdoctoral fellowship in the Department of Mathematics at U.B.C.
This work is supported in part by NSF grant DMS0307021. 相似文献
13.
Carl M. Bender 《Czechoslovak Journal of Physics》2006,56(9):1047-1062
In this paper, two independent methods are used to show that the non-Hermitian
-symmetric wrong-sign quartic Hamiltonian H = (1/2m)p
2 − gx
4 is exactly equivalent to the conventional Hermitian Hamiltonian
. First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated
by using functional-integration methods. As the linear term in the Hermitian Hamiltonian
is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly
is a consequence of the broken parity symmetry of the original non-Hermitian
-symmetric Hamiltonian. The anomaly term in
remains unchanged if an x
2 term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in
are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states. 相似文献
14.
The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with
bounded dimension growth. Consequently, is totally disconnected.
Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group
of A is an extension of a simple topological group by the discrete group . 相似文献
15.
G. Duplančić P. Minkowski J. Trampetić 《The European Physical Journal C - Particles and Fields》2004,35(2):189-193
We calculate the absorption probability of photons radiated from the surface of the Sun by a left-handed neutrino with definite mass and a typical momentum for which we choose |p1| = 0.2 MeV, producing a heavier right-handed antineutrino. Considering the two transitions
and
we obtain the two oscillation lengths L12 = 4960.8 m, L23 = 198.4 m, the two absorption probabilities P12abs. = 2.5 x 10-67, P23abs. = 1.2 x 10-58 and the two absorption ranges
au,
au, using a neutrino mass differences of
meV,
meV and associated transition dipole moments. We collect all necessary theoretical ingredients, i.e. neutrino mass and mixing scheme, induced electromagnetic transition dipole moments, quadratic charged lepton mass asymmetries and their interdependence.Received: 4 November 2003, Revised: 23 March 2004, Published online: 5 May 2004 相似文献
16.
Asao Arai 《Letters in Mathematical Physics》2006,77(3):283-290
A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral
of a family of self-adjoint operators
acting in the Hilbert space
, where
is the Hilbert space of the quantum radiation field. The fiber operator
is called the Hamiltonian of the Dirac polaron with total momentum
. The main result of this paper is concerned with the non-relativistic (scaling) limit of
. It is proven that the non-relativistic limit of
yields a self-adjoint extension of a Hamiltonian of a polaron with spin 1/2 in non-relativistic quantum electrodynamics. 相似文献
17.
Yakov Sinai 《Journal of statistical physics》2005,121(5-6):779-803
In this paper we study the Fourier transform of the
-Navier-Stokes System without external forcing on the whole space R
3. The properties of solutions depend very much on the space in which the system is considered. In this paper we deal with
the space
of functions
where
and c (k) is bounded,
. We construct the power series which converges for small t and gives solutions of the system for bounded intervals of time. These solutions can be estimated at infinity (in k-space) by
. 相似文献
18.
Li-Yun Hu Shi-You Liu Kai-Min Zheng Fang Jia Hong-Yi Fan 《International Journal of Theoretical Physics》2014,53(2):380-389
We find new operator formulas for converting Q?P and P?Q ordering to Weyl ordering, where Q and P are the coordinate and momentum operator. In this way we reveal the essence of operators’ Weyl ordering scheme, e.g., Weyl ordered operator polynomial ${_{:}^{:}}\;Q^{m}P^{n}\;{_{:}^{:}}$ , $$\begin{aligned} {_{:}^{:}}\;Q^{m}P^{n}\;{_{:}^{:}} =&\sum_{l=0}^{\min (m,n)} \biggl( \frac{-i\hbar }{2} \biggr) ^{l}l!\binom{m}{l}\binom{n}{l}Q^{m-l}P^{n-l} \\ =& \biggl( \frac{\hbar }{2} \biggr) ^{ ( m+n ) /2}i^{n}H_{m,n} \biggl( \frac{\sqrt{2}Q}{\sqrt{\hbar }},\frac{-i\sqrt{2}P}{\sqrt{\hbar }} \biggr) \bigg|_{Q_{\mathrm{before}}P} \end{aligned}$$ where ${}_{:}^{:}$ ${}_{:}^{:}$ denotes the Weyl ordering symbol, and H m,n is the two-variable Hermite polynomial. This helps us to know the Weyl ordering more intuitively. 相似文献
19.
We derive explicit formulas for the multipoint series of
in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of
. We also obtain explicit formulas for the Hodge integrals
, in the cases i=0 and 1. 相似文献
20.
T. Padmanabhan 《General Relativity and Gravitation》2006,38(11):1547-1552
Principle of equivalence, general covariance and the demand that the variation of the action functional should be well defined,
lead to a generic Lagrangian for semiclassical gravity of the form
with
. The expansion of
in terms of the derivatives of the metric tensor determines the structure of the theory uniquely. The zeroth order term gives
the Einstein–Hilbert action and the first order correction is given by the Gauss–Bonnet action. Remarkably, any such Lagrangian
can be decomposed into a surface and bulk terms which are related holographically. The equations of motion can be obtained
purely from a surface term in the gravity sector and hence gravity does not respond to the changes in the bulk vacuum energy
density.
Third award in the 2006 Essay Competition of the Gravity Research Foundation. 相似文献
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