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1.
Using the relation between the space of rational functions on , the space ofSU(2)-monopoles on 3, and the classifying space of the braid group, see [10], we show how the index bundle of the family of real Dirac operators coupled toSU(2)-monopoles can be described using permutation representations of Artin's braid groups. We also show how this implies the existence of a pair consisting of a gauge fieldA and a Higgs field on 3 whose corresponding Dirac equation has an arbitrarily large dimensional space of solutions.The first author was supported by a grant from the NSF 相似文献
2.
We investigate the cohomology of nets over Minkowski space and develop exact sequence techniques enabling us to compute many low-dimensional cohomologies. We examine in particular nets derived from smooth solutions of invariant partial differential equations using causal support conditions. Thus the wave equation gives a trivial second cohomology whereas the vector wave equation with Lorentz condition and Maxwell's equations give a second cohomology and × corresponding, respectively, to an electric and an electric and magnetic charge. 相似文献
3.
J. F. Blodwell 《International Journal of Theoretical Physics》1987,26(10):1001-1020
It is argued that the point structure of space and time must be constructed from the primitive extensional character of space and time. A procedure for doing this is laid down and applied to one-dimensional and two-dimensional systems of abstract extensions. Topological and metrical properties of the constructed point systems, which differ nontrivially from the usual and 2 models, are examined. Briefly, constructed points are associated with directions and the Cartesian point is split. In one-dimension each point splits into a point pair compatible with the linear ordering. An application to one-dimensional particle motion is given, with the result that natural topological assumptions force the number of left point, right point transitions to remain locally finite in a continuous motion. In general, Cartesian points are seen to correspond to certain filters on a suitable Boolean algebra. Constructed points correspond to ultrafilters. Thus, point construction gives a natural refinement of the Cartesian systems. 相似文献
4.
Joel Feldman 《Communications in Mathematical Physics》1974,37(2):93-120
The unnormalized doubly cutoff Schwinger functions converge as the ultraviolet cutoff is removed. The limits, the finite volume unnormalized Schwinger functions, are tempered distributions and areC
in the coupling constant. They have asymptotic expansions given by perturbation theory. For sufficiently small they can be normalized and then they are the moments of a measure onI
(IR3).Supported in part by the National Science Foundation under Grant GP 40354X. 相似文献
5.
Brezis Haïm Coron Jean-Michel Lieb Elliott H. 《Communications in Mathematical Physics》1986,107(4):649-705
Two problems concerning maps with point singularities from a domain C 3 toS
2 are solved. The first is to determine the minimum energy of when the location and topological degree of the singularities are prescribed. In the second problem is the unit ball and =g is given on ; we show that the only cases in whichg(x/|x|) minimizes the energy isg=const org(x)=±Rx withR a rotation. Extensions of these problems are also solved, e.g. points are replaced by holes, 3,S
2 is replaced by
N
,S
N–1 or by
N
, P
N–1, the latter being appropriate for the theory of liquid crystals.Work partially supported by U.S. National Science Foundation grant PHY 85-15288-A02 相似文献
6.
Lawrence E. Thomas 《Communications in Mathematical Physics》1980,77(3):211-218
Let 1 and 2 be thermodynamic Gibbs measures on
m
and
n
, respectively. Diffusions are constructed having 1, and 2 as invariant measures. These diffusions are then coupled; inequalities between expectations of certain random variables on the two spaces result.Partially supported by NSF-MCS 74-07313-A03 相似文献
7.
We develop a theory of solutionsn for the Euclidean nonlinear 0(2k+1)-model for arbitraryk and for a regionG2. We consider a subclass of solutions characterized by a condition which is fulfilled, forG=2, by thosen that live on the Riemann sphere S22. We are able to characterize this class completely in terms ofk meromorphic functions, and we give an explicit inductive procedure which allows us to calculate all 0(2k+1) solutions from the trivial 0(1) solutions. 相似文献
8.
M. Ulanovskii 《General Relativity and Gravitation》1999,31(12):1813-1820
We show that to any convex function f:
n
there correspondinfinitely many geodesically complete metricsds2 such that Ric() 0 for anynonspacelike vector . These metrics are constructedas the warped products of the natural metric in and the inner metric of a convexhyperface (the graph of f) in
n + 1. 相似文献
9.
C. Fefferman 《Communications in Mathematical Physics》1985,98(3):289-311
Consider a crystal with nucleii fixed at the lattice points in 3, interacting by Coulomb forces with quantized electrons in . We prove that the pressure tends to a limit as grows infinitely large.Supported by NSF Grant No. MCS80-03072 相似文献
10.
M. E. Osinovsky 《Communications in Mathematical Physics》1973,32(1):39-50
We consider an Einstein spaceV of the Petrov type II or III admitting a group of motionsG of high order. First we calculate the composition law and topological structure ofG. ThenV (or its submanifolds of transitivity) is represented as the homogeneous spaceG/H ofG,H being a subgroup ofG, and the actionG onV and the topology ofV are determined. The topologies of the spacesV are as follows: 4 (spaceT*2), 4 of 3 T1 (spaceT
2), 4 (spaceT*3), 3 (submanifolds of transitivity in spaceT
3).In two cases (spacesT
2 andT
3) we have obtained metrics free of singularities. 相似文献
11.
The group of automorphisms of the Galilei groupG: Aut(G) is calculated. It is shown that Aut(G) has the structure of a semi-direct product byG of the group
m
*
×m where m is the group of reals noted multiplicatively and
m
*
<m is the subgroup of positive reals. 相似文献
12.
H. -J. Borchers 《Communications in Mathematical Physics》1984,96(1):1-13
Let {A,
d
,} be aC*-dynamical system, where
d
is thed-dimensional vector group. LetV be a convex cone in
d
and
its dual cone. We will characterize those representations ofA with the properties (i)
a
,a
d
is weakly inner, (ii) the corresponding unitary representationU(a) is continuous, and (iii) the spectrum ofU(a) is contained in
. 相似文献
13.
A model of deterministic surface growth studied by Krug and Spohn, a model of the annihilating reactionA+Binert studied by Elskens and Frisch, a one-dimensional three-color cyclic cellular automaton studied by Fisch, and a particular automaton that has the number 184 in the classification of Wolfram can be studied via a cellular automaton with stochastic initial data called ballistic annihilation. This automaton is defined by the following rules: At timet=0, one particle is put at each integer point of . To each particle, a velocity is assigned in such a way that it may be either +1 or –1 with probabilities 1/2, independent of the velocities of the other particles. As time goes on, each particle moves along at the velocity assigned to it and annihilates when it collides with another particle. In the present paper we compute the distribution of this automaton for each timet . We then use this result to obtain the hydrodynamic limit for the surface profile from the model of deterministic surface growth mentioned above. We also show the relation of this limit process to the process which we call moving local minimum of Brownian motion. The latter is the processB
x
min
,x , defined byB
x
min
min{B
y
;x–1yx+1} for everyx , whereB
x
,x , is the standard Brownian motion withB
0=0. 相似文献
14.
Reinhard Illner 《Communications in Mathematical Physics》1984,93(3):341-353
The Cauchy problem for the Broadwell model is shown to have a global mild solution for initial data inL
+
1
() with smallL
1-norm, and a local solution for arbitrary initial data inL
+
1
(). For data which are small inL
1(), the asymptotic behaviour of the solutions ast is determined. Moreover, it is shown that a global solution exists for all initial values inL
+
1
() with finite entropy if theH-Theorem holds. 相似文献
15.
G. Date T. R. Govindarajan P. Sankaran R. Shankar 《Communications in Mathematical Physics》1990,132(2):293-313
We compute the homotopy groups
0 and
1 of the classical configuration space of anO(3) invariant field theory on
×, where
is a compact two dimensional manifold for arbitrary genusg and- denotes the time coordinate. We also present the finite dimensional, unitary, irreducible, inequivalent representations of the appropriate fundamental groups and comment on some of their implications. 相似文献
16.
A certain class of unitary representations of Uq((2,)) has the property of being simultanenously a representation of for a particular choice of (q). Faddeev has proposed to unify the quantum groups Uq((2,)) and into some enlarged object for which he has coined the name ``modular double'. We study the R-operator, the co-product and the Haar-measure for the modular double of Uq((2,)) and establish their main properties. In particular it is shown that the Clebsch-Gordan maps constructed in [PT2] diagonalize this R-operator. 相似文献
17.
Nahm's equations and the classification of monopoles 总被引:2,自引:0,他引:2
S. K. Donaldson 《Communications in Mathematical Physics》1984,96(3):387-407
Solutions of Nahm's system of ordinary differential equations are produced by variational methods. This leads to an explicit parametrisation of the solutions to the Bogomolny equation over 3. 相似文献
18.
Erik Balslev 《Communications in Mathematical Physics》1988,114(4):599-612
For potentialsV=V(x)=O(|x|–2–) for |x|,x3 we prove that if theS-matrix of (–, –+V) has an analytic extension
to a regionO in the lower half-plane, then the family of generalized eigenfunctions of –+V has an analytic extension
toO such that
for |Imk|<b. Consequently, the resolvent (–+V–z
2)–1 has an analytic continuation from + to {kOImk|<b} as an operator
from
b
={f=e
–b|x|
g|gL
2(3)} to –b
. Based on this, we define for potentialsW=o(e
–2b|x|) resonances of (–+V, –+V+W) as poles of
and identify these resonances with poles of the analytically continuedS-matrix of (–+V, –+V+W).The author would like to thank the Institute for Advanced Study for its hospitality and the National Science Foundation for financial support under Grant No. DMS-8610730(1) 相似文献
19.
In ordinary quantum mechanics for finite systems, the time evolution induced by Hamiltonians of the form
is studied from the point of view of *-automorphisms of the CCRC*-algebra
(see Ref. [1, 2]). It is proved that those Hamiltonians do not induce *-automorphisms of this algebra in the cases: a)
and b)V L
(,dx) L
1 (,dx), except when the potential is trivial. 相似文献
20.
Claudio Albanese 《Communications in Mathematical Physics》1994,160(1):1-14
Given a pseudodifferential operator (p) satisfying certain growth and smoothness conditions in momentum space, we construct a wavelet basis ofL
2(
d
) in which the corresponding matrix is diagonal dominated with arbitrarily small prefactor. 相似文献