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1.
A super extension of the AKNS scheme is presented by proposing a super sl(2, R) valued connection. A class of super integrable equations, containing the super extension of the Lax hierarchy, is found. 相似文献
2.
Metin Gürses 《Letters in Mathematical Physics》1989,17(3):231-238
A soliton geometry is introduced on manifolds with arbitrary dimensions. The usual soliton connection 1-form defined by Crampin et al. is recovered when the soldering form is a 0-form. It is shown that Einstein's vacuum field equations admit a soliton connection and a soldering 1-form. An associated linear equation with a spectral parameter of Einstein's vacuum field equations are found and some properties of this equation are explored. An example of a Bäcklund transformation is also given. 相似文献
3.
Radu Miron 《Reports on Mathematical Physics》2004,54(2):131-147
The Randers spaces RFn were introduced by R. S. Ingarden. They are considered as Finsler spaces Fn = (M, α + β) equipped with the Cartan nonlinear connection. In the present paper we define and study what we call the Ingarden spaces, I Fn, as Finsler spaces I Fn = (M, α + β) equipped with the Lorentz nonlinear connection. The spaces R Fn and I Fn are completely different. For I Fn we discuss: the variational problem, Lorentz nonlinear connection, canonical N-metrical connection and its structure equations, the Cartan 1-form ω, the electromagnetic 2-form tF and the almost symplectic 2-form 0. The formula dω = F+θ is established. It has as a consequence the generalized Maxwell equations. Finally, the almost Hermitian model of I Fn is constructed. 相似文献
4.
《Journal of Nonlinear Mathematical Physics》2013,20(2):227-242
Considering a complex Lagrange space ([24]), in this paper the complex electromagnetic tensor fields are defined as the sum between the differential of the complex Liouville 1-form and the symplectic 2-form of the space relative to the adapted frames of the Chern–Lagrange complex nonlinear connection. In particular, an electrodynamics theory on a complex Finsler space is obtained. We show that our definition of the complex electrodynamics tensors has physical meaning and these tensors generate an adequate field theory which offers the opportunity of coupling with the gravitation. The generalized complex Maxwell equations are written. A gauge field theory of electrodynamics on the holomorphic tangent bundle is put over T′M and the gauge invariance to phase transformations is studied. An extension of the Dirac Lagrangian on T′M coupled with the electrodynamics Lagrangian is studied and it offers the framework for a unified gauge theory of fields. 相似文献
5.
We reformulate the concept of connection on a Hopf–Galois extension B⊆P in order to apply it in computing the Chern–Connes pairing between the cyclic cohomology HC
2
n
(B) and K
0 (B). This reformulation allows us to show that a Hopf–Galois extension admitting a strong connection is projective and left
faithfully flat. It also enables us to conclude that a strong connection is a Cuntz–Quillen-type bimodule connection. To exemplify
the theory, we construct a strong connection (super Dirac monopole) to find out the Chern–Connes pairing for the super line
bundles associated to a super Hopf fibration.
Received: 8 March 2000 / Accepted: 5 January 2001 相似文献
6.
K. Takasaki 《Letters in Mathematical Physics》1989,17(4):351-357
Symmetries of the super Kadomtsev-Petviashvili hierarchy are studied. A key role is played by a D-module structure, which connects the nonlinear system with the geometry of an infinite-dimensional super Grassmannian manifold. Infinitesimal action of a Lie superalgebra on the super Grassmannian manifold, via this connection, gives rise to symmetries of the nonlinear system.Supported in part by the Grant in Aid for Scientific Research, the Ministry of Education. 相似文献
7.
The question of complete integrability of evolution equations associated ton×n first order isospectral operators is investigated using the inverse scattering method. It is shown that forn>2, e.g. for the three-wave interaction, additional (nonlinear) pointwise flows are necessary for the assertion of complete integrability. Their existence is demonstrated by constructing action-angle variables. This construction depends on the analysis of a natural 2-form and symplectic foliation for the groupsGL(n) andSU(n).Research supported by NSF grants DMS-8916968 and DMS 8901607 相似文献
8.
L. K. Norris 《International Journal of Theoretical Physics》1991,30(8):1127-1150
It is shown that the charged symplectic form in Hamiltonian dynamics of classical charged particles in electromagnetic fields defines a generalized affine connection on an affine frame bundle associated with spacetime. Conversely, a generalized affine connection can be used to construct a symplectic 2-form if the associated linear connection is torsion-free and the antisymmetric part of theR
4* translational connection is locally derivable from a potential. Hamiltonian dynamics for classical charged particles in combined gravitational and electromagnetic fields can therefore be reformulated as aP(4)=O(1, 3)R
4* geometric theory with phase space the affine cotangent bundleAT
*
M of spacetime. The sourcefree Maxwell equations are reformulated as a pair of geometrical conditions on the 4* curvature that are exactly analogous to the source-free Einstein equations. 相似文献
9.
We investigate the concept of projective equivalence of connections in supergeometry. To this aim, we propose a definition for (super) geodesics on a supermanifold in which, as in the classical case, they are the projections of the integral curves of a vector field on the tangent bundle: the geodesic vector field associated with the connection. Our (super) geodesics possess the same properties as in the classical case: there exists a unique (super) geodesic satisfying a given initial condition and when the connection is metric, our supergeodesics coincide with the trajectories of a free particle with unit mass. Moreover, using our definition, we are able to establish Weyl’s characterization of projective equivalence in the super context: two torsion-free (super) connections define the same geodesics (up to reparametrizations) if and only if their difference tensor can be expressed by means of a (smooth, even, super) 1-form. 相似文献
10.
A connection between the Einstein and Yang-Mills equations 总被引:1,自引:0,他引:1
It is our purpose here to show an unusual relationship between the Einstein equations and the Yang-Mills equations. We give a correspondence between solutions of the self-dual Einstein vacuum equations and the self-dual Yang-Mills equations with a special choice of gauge group. The extension of the argument to the full Yang-Mills equations yields Einstein's unifield equations. We try to incorporate the full Einstein vacuum equations, but the approach is incomplete. We first consider Yang-Mills theory for an arbitrary Lie-algebra with the condition that the connection 1-form and curvature are constant on Minkowski space. This leads to a set of algebraic equations on the connection components. We then specialize the Lie-algebra to be the (infinite dimensional) Lie-algebra of a group of diffeomorphisms of some manifold. The algebraic equations then become differential equations for four vector fields on the manifold on which the diffeomorphisms act. In the self-dual case, if we choose the connection components from the Lie-algebra of the volume preserving 4-dimensional diffeomorphism group, the resulting equations are the same as those obtained by Ashtekar, Jacobsen and Smolin, in their remarkable simplification of the self-dual Einstein vacuum equations. (An alternative derivation of the same equations begins with the self-dual Yang-Mills connection now depending only on the time, then choosing the Lie algebra as that of the volume preserving 3-dimensional diffeomorphisms.) When the reduced full Yang-Mills equations are used in the same context, we get Einstein's equations for his unified theory based on absolute parallelism. To incorporate the full Einsteinvacuum equations we use as the Lie group the semi-direct product of the diffeomorphism group of a 4-dimensional manifold with the group of frame rotations of anSO(1, 3) bundle over the 4-manifold. This last approach, however, yields equations more general than the vacuum equations.Andrew Mellon Postdoctoral fellow and Fulbright ScholarSupported in part by NSF grant no. PHY 80023 相似文献
11.
K. Takasaki 《Letters in Mathematical Physics》1990,19(3):229-236
A new super Toda lattice hierarchy is proposed and formulated in the language of differential algebra. AD-module structure is shown to exist behind this nonlinear system and to play the same role as a similarD-module for the super KP hierarchy. From the structure of thisD-module, one can indeed see a direct connection with a set of affine coordinates on an infinite-dimensional super Grassmannian manifold. These affine coordinates are the basic ingredients of an intrinsic construction of functions as well as symmetries. 相似文献
12.
We propose a super Lax type equation based on a certain class of Lie superalgebra as a supersymmetric extension of generalized (modified) KdV hierarchy. We are able to construct an infinite set of conservation laws and the consistent time evolution generators for generalized modified super KdV equations. Thefirst few of the conserved currents, the (modified) super KdV equation and the super Miura transformation are worked out explicitly in the case of twisted affine Lie superalgebraOSp(2/2)(2).Partially supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture (#01540246 and #01790203).RIFP will be known as Yukawa Institute for Theoretical Physics from June 8, 1990 相似文献
13.
In the modern literature, the oscillations of flow parameters have been investigated insufficiently; their connection with
the fundamental solution of the Navier-Stokes equations has not been shown. Some types of vortical structures in a 2D steady
incompressible flow were analyzed in [2]. Below, a nonlinear system of the Navier-Stokes equations was used for calculation
of unsteady gas flow in the vicinity of a cylindrical vortex. The problem is set within the domain z ≥ 0 and the flow is shown to be oscillatory; the oscillations of pressure, density, and temperature were investigated. The
distinctive feature of this computation method is that no finite-difference schemes are used. The method can be used on the
condition that the gas is considered as a perfect one (c
p
/c
v
= γ = const). 相似文献
14.
An exotic class of nonlinear p-form non-Abelian gauge theories is studied, arising from the most general allowed covariant deformation of linear Abelian gauge theory for a set of massless 1-form fields and 2-form fields in four dimensions. These theories combine a Chapline–Manton type coupling of the 1-forms and 2-forms, along with a Yang–Mills coupling of the 1-forms, a Freedman–Townsend coupling of the 2-forms, and an extended Freedman–Townsend type coupling between the 1-forms and 2-forms. It is shown that the resulting theories have a geometrically interesting dual formulation that is equivalent to an exotic Yang–Mills dilaton theory involving a nonlinear sigma field. In particular, the nonlinear sigma field couples to the Yang–Mills 1-form field through a generalized Chern class 4-form term. 相似文献
15.
A Poincaré affine frame bundle
(M) and its associated bundleÊ are established. Using the connection theory of fiber bundles, nonlinear connections on the bundleÊ are introduced as nonlinear gauge fields. An action and two sets of gauge field equations are presented. 相似文献
16.
Vladislav S. Olkhovsky 《Central European Journal of Physics》2011,9(1):13-44
The analytic structure of the non-relativistic unitary and non-unitary S-matrix is investigated for the cases of the unknown interactions with the unknown motion equations inside a sphere of radius
a, surrounded by the centrifugal and rapidly decreasing (exponentially or by the Yukawian law or by the more rapidly decreasing)
potentials. The one-channel case and special examples of many-channel cases are considered. Some kinds of symmetry conditions
are imposed. The Schroedinger equation for r > a for the particle motion and the condition of the completeness of the correspondent wave functions are assumed. The connection
of the obtained results with the usual (temporal) causality is examined. Finally a scientific program is presented as a clear
continuation and extension of the obtained results. 相似文献
17.
The osp(N, 2) extension of the AKNS scheme is reconsidered. It leads to a general class of integrable nonlinear evolution equations for 2+N(N–1)/2 commuting and 2N anticommuting fields. by reduction, various osp(N, 2) versions of the Korteweg-de Vries equation can be obtained. One of these is shown to be bi-Hamiltonian and its second Hamiltonian structure corresponds to the classical limit of the so(N) superconformal algebra. The nonlinear Schrödinger and modified Korteweg-de Vries reductions are also briefly discussed.Work supported by NSerc and FCAR. 相似文献
18.
Alberto S. Cattaneo P. Cotta-Ramusino M. Rinaldi 《Communications in Mathematical Physics》1999,204(3):493-524
We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel transports and holonomies are computed and their expressions in local coordinates are
exhibited. When the 2-form B is given by the curvature of A, then the so-called non-abelian Stokes formula follows.
For a generic 2-form B, we distinguish the cases when the parallel transport depends on the whole path of paths and when it depends only on the
spanned surface. In particular we discuss generalizations of the non-abelian Stokes formula. We study also the invariance
properties of the (trace of the) holonomy under suitable transformation groups acting on the pairs (A,B).
In this way we are able to define observables for both topological and non-topological quantum field theories of the BF type. In the non-topological case, the surface terms may be relevant for the understanding of the quark-confinement problem.
In the topological case the (perturbative) four-dimensional quantum BF-theory is expected to yield invariants of imbedded (or immersed) surfaces in a 4-manifold M.
Received: 28 March 1998 / Accepted: 12 September 1998 相似文献
19.
P. C. Stavrinos A. P. Kouretsis M. Stathakopoulos 《General Relativity and Gravitation》2008,40(7):1403-1425
A generalized FRW model of space-time is studied, taking into consideration the anisotropic structure of fields which are
depended on the position and the direction (velocity). The Raychaudhouri and Friedman-like equations are investigated assuming
the Finslerian character of space-time. A long range vector field of cosmological origin is considered in relation to a physical
geometry where the Cartan connection has a fundamental role. The Friedman equations are produced including extra anisotropic
terms. The variation of anisotropy z
t
is expressed in terms of the Cartan torsion tensor of the Finslerian manifold. A physical generalization of the Hubble and
other cosmological parameters arises as a direct consequence of the equations of motion. 相似文献
20.
A connection between nonlinear autonomous systems of ordinary differential equations, first integrals, Bose operators and Lie algebras is described. An extension to nonlinear partial differential equations is given. 相似文献