共查询到20条相似文献,搜索用时 9 毫秒
1.
Norio Suzuki 《Communications in Mathematical Physics》1987,113(1):155-172
Witten's gauge fields are interpreted as motions on an infinite-dimensional Grassmann manifold. Unlike the case of self-dual Yang-Mills equations in Takasaki's work, the initial data must satisfy a system of differential equations since Witten's equations comprise a pair of spectral parameters. Solutions corresponding to (anti-) self-dual Yang-Mills fields are characterized in the space of initial data and in application, some Yang-Mills fields which are not self-dual, anti-self-dual nor abelian can be constructed. 相似文献
2.
J. A. de Wet 《Foundations of Physics》1987,17(10):993-1018
Products of particlelike representations of the homogeneous Lorentz group are used to construct the degrees of spin angular momentum of a composite system of protons and neutrons. If a canonical labeling system is adopted for each state, a shell structure emerges. Furthermore the use of the Dirac ring ensures that the spin is characterized by half-angles in accord with the neutron-rotation experiment. It is possible to construct a Clebsch-Gordan decomposition to reduce a state of complex angular momentum into simpler states which can be identified with and particles, multipole operators, etc. Finally, ground-state energy levels are calculated for all the even-even nuclei by using a differentiable manifold that is spin-graded and gauge-invariant by construction. It is shown that this manifold is Grassmann. 相似文献
3.
Nagatomo's universal Grassmann manifold scheme is extended to a double form, which is used to find the exact solutions of the stationary axisymmetric vacuum gravitational field equations. Some new results are given. 相似文献
4.
K. Nagatomo 《Communications in Mathematical Physics》1989,122(3):439-453
We find a linearization of the Ernst equation by means of universal Grassmann manifold (UGM) techniques. All local analytic solutions defined at the origin are obtained by solving an initial value problem for a linear differential equation on a UGM. We give an explicit formula which represents solutions of the Ernst equation. By using this formula, we generate several special solutions. 相似文献
5.
Piotr Godlewski 《Reports on Mathematical Physics》2003,52(1):81-88
We investigate a model of self-interacting field of linear frames on the product manifold M × G, where G is a semisimple Lie group acting freely and transitively on a manifold M. We find two families of solutions of the Euler-Lagrange equations for the field of frames. 相似文献
6.
As an alternative to the conventional deformed harmonic oscillator basis expansion, a method is developed in which the coupled integro-differential Hartree-Fock equations are solved directly in coordinate space for a simple effective interaction. The single particle wave functions are obtained on a finite mesh by minimizing a discretized energy functional and solving the resulting finite difference equations using the Lanczos algorithm. Expressions to correct the total energy to second order in the mesh spacing are derived, and the accuracy of the method is demonstrated by numerical comparison with spherical results. Applications and advantages of this new technique are briefly discussed. 相似文献
7.
We present results for the gluon and ghost propagators in SU (N) Yang-Mills theory on a four-torus at zero and non-zero temperatures from a truncated set of Dyson-Schwinger equations. When compared to continuum solutions at zero temperature sizeable modifications due to the finite volume of the manifold, especially in the infrared, are found. Effects due to non-vanishing temperatures T, on the other hand, are minute for T < 250 MeV. 相似文献
8.
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggest the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum–atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. 相似文献
9.
Metin Gürses 《Letters in Mathematical Physics》1986,11(1):59-65
The Painlevé property of the vacuum Einstein field equations is investigated. It is observed that the field equations possess this property when spacetime admits commuting, nonnull two Killing vector fields. 相似文献
10.
The Generalized Ginzburg-Landau equations, introduced by one of us (H.H.), are considered in a simplified version to clarify their relation to the center manifold theorem. 相似文献
11.
The Generalized Ginzburg-Landau equations, introduced by one of us (H.H.), are considered in a simplified version to clarify their relation to the center manifold theorem. 相似文献
12.
Generalizing the work of Einstein and Mayer, it is assumed that at each point of space-time there exists a vector-spinor space with Nv vector dimensions and Ns spinor dimensions, where Nv=2k and Ns=2
k, k3. This space is decomposed into a tangent space with4 vector and4 spinor dimensions and an internal space with Nv–4 vector and Ns–4 spinor dimension. A variational principle leads to field equations for geometric quantities which can be identified with physical fields such as the electromagnetic field, Yang-Mills gauge fields, and wave functions of bosons and fermions. 相似文献
13.
In this note, we prove that the CR manifold induced from the canonical parabolic geometry of a quaternionic contact (qc) manifold via a Fefferman-type construction is equivalent to the CR twistor space of the qc manifold defined by O. Biquard. 相似文献
14.
15.
《Physics letters. A》1997,229(3):173-182
The singularity confinement method is applied to the systematic derivation of the bilinear equations for discrete soliton equations. Using the bilinear forms, the N-soliton and algebraic solutions of the discrete potential mKdV equation are constructed. 相似文献
16.
A. Nabutovsky 《Communications in Mathematical Physics》1996,181(2):303-330
In this paper we study the spaceT
M of triangulations of an arbitrary compact manifoldM of dimension greater than or equal to four. This space can be endowed with the metric defined as the minimal number of bistellar operations required to transform one of two considered triangulations into the other. Recently, this space became and object of study in Quantum Gravity because it can be regarded as a toy discrete model of the space of Riemannian structures onM.Our main result can be informally explained as follows: LetM be either any compact manifold of dimension greater than four or any compact four-dimensional manifold from a certain class described in the paper. We prove that for a certain constantC>1 depending only on the dimension ofM and for all sufficiently largeN the subsetT
M(N) ofT
M formed by all triangulations ofM with N simplices can be represented as the union of at least [C
N] disjoint non-empty subsets such that any two of these subsets are very far from each other in the metric ofT
M. As a corollary, we show that for any functional from a very wide class of functionals onT
M the number of its deep local minima inT
M(N) grows at least exponentially withN, whenN.This work was partially supported by the New York University Research Challenge Fund Grant, by Grant ARO-DAAL-03-92-G-0143 and by NSERC Grant OGP0155879. 相似文献
17.
U. Meyer 《Communications in Mathematical Physics》1996,174(3):457-475
We give a systematic account of a component approach to the algebra of forms onq-Minkowski space, introducing the corresponding exterior derivative, Hodge star operator, coderivative, Laplace-Beltrami operator and Lie-derivative. Using this (braided) differential geometry, we then give a detailed exposition of theq-d'Alembert andq-Maxwell equation and discuss some of their non-trivial properties, such as for instance, plane wave solutions. For theq-Maxwell field, we also give aq-spinor analysis of theq-field strength tensor. 相似文献
18.
Recently, the discrete fractional calculus (DFC) is receiving attention due to its potential applications in the mathematical modelling of real-world phenomena with memory effects. In the present paper, the chaotic behaviour of fractional difference equations for the tent map, Gauss map and 2x(mod 1) map are studied numerically. We analyse the chaotic behaviour of these fractional difference equations and compare them with their integer counterparts. It is observed that fractional difference equations for the Gauss and tent maps are more stable compared to their integer-order version. 相似文献
19.
《Physics letters. A》1987,121(1):15-18
A two space dimensional Burgers hierarchy is constructed and analyzed in terms of an invariant, Nijenhuis mixed tensor field on the phase manifold. The analysis extends to Burgers equations in higher dimension as well. 相似文献