共查询到20条相似文献,搜索用时 15 毫秒
1.
I. G. Korepanov 《Theoretical and Mathematical Physics》2009,158(1):82-95
Geometric torsions are torsions of acyclic complexes of vector spaces consisting of differentials of geometric quantities
assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a three-dimensional
manifold with a triangulated boundary. These invariants can be naturally combined into a vector, and a change of the boundary
triangulation corresponds to a linear transformation of this vector. Moreover, when two manifolds are glued at their common
boundary, these vectors undergo scalar multiplication, i.e., they satisfy Atiyah’s axioms of a topological quantum field theory.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 1, pp. 98–114, January, 2009. 相似文献
2.
This paper is concerned with topological set theory, and particularly with Skala's and Manakos' systems for which we give a topological characterization of the models. This enables us to answer natural questions about those theories, reviewing previous results and proving new ones. One of these shows that Skala's set theory is in a sense compatible with any ‘normal’ set theory, and another appears on the semantic side as a ‘Cantor theorem’ for the category of Alexandroff spaces. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
We investigate rigidity problems for odd-dimensional compact submanifolds.We show that if Mn(n 5)is an odd-dimensional compact submanifold with parallel mean curvature in Sn+p,and if RicM(n-2-1n)(1+H2)and Hδn,whereδn is an explicit positive constant depending only on n,then M is a totally umbilical sphere.Here H is the mean curvature of M.Moreover,we prove that if Mn(n 5)is an odd-dimensional compact submanifold in the space form Fn+p(c)with c 0,and if RicM(n-2-εn)(c+H2),whereεn is an explicit positive constant depending only on n,then M is homeomorphic to a sphere. 相似文献
4.
Monopoles and vortices are well known magnetically charged soliton solutions of gauge field equations. Extending the idea of Dirac on monopoles, Schwinger pioneered the concept of solitons carrying both electric and magnetic charges, called dyons, which are useful in modeling elementary particles. Mathematically, the existence of dyons presents interesting variational partial differential equation problems, subject to topological constraints. This article is a survey on recent progress in the study of dyons. 相似文献
5.
O. I. Mokhov 《Theoretical and Mathematical Physics》2007,152(2):1183-1190
We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions
of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of
flat torsionless potential submanifolds. We show that all flat torsionless potential submanifolds in pseudo-Euclidean spaces bear natural structures
of Frobenius algebras on their tangent spaces. These Frobenius structures are generated by the corresponding flat first fundamental
form and the set of the second fundamental forms of the submanifolds (in fact, the structural constants are given by the set
of the Weingarten operators of the submanifolds). We prove that each N-dimensional Frobenius manifold can be locally represented
as a flat torsionless potential submanifold in a 2N-dimensional pseudo-Euclidean space. By our construction, this submanifold
is uniquely determined up to motions. Moreover, we consider a nonlinear system that is a natural generalization of the associativity
equations, namely, the system describing all flat torsionless submanifolds in pseudo-Euclidean spaces, and prove that this
system is integrable by the inverse scattering method.
To the memory of my wonderful mother Maya Nikolayevna Mokhova (4 May 1926–12 September 2006)
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 368–376, August, 2007. 相似文献
6.
For any two-colouring of the segments determined by 3n − 3 points in general position in the plane, either the first colour class contains a triangle, or there is a noncrossing
cycle of length n in the second colour class, and this result is tight. We also give a series of more general estimates on off-diagonal geometric
graph Ramsey numbers in the same spirit. Finally we investigate the existence of large noncrossing monochromatic matchings
in multicoloured geometric graphs.
Research partially supported by Hungarian Scientific Research Grants OTKA T043631 and NK67867. 相似文献
7.
LetR be a ring with unit and invariant basis property. In [1], the authors define a functorK(_;R):TOP/LIP
c-LPEP by combining the open cone construction of [7] with a geometric module construction and show this functor is a homology theory. This paper shows that if attention is restricted to objects TOP/LIP
c with a homotopy colimit structure, then the functorK(_;R) is a Quinn homology theory, In particular, for each having a homotopy colimit structure,K(;R) is a homotopy colimit in the category of -spectra. Furthermore, the constituent spectra of this homotopy colimit are obtained naturally from the fibres of .Partially supported by the National Science Foundation under grant number DMS88-03148.Partially supported by the SNF (Denmark) under grant number 11-7792. 相似文献
8.
G. Sartori 《Acta Appl Math》2002,70(1-3):183-207
Functions which are covariant or invariant under the transformations of a reductive linear algebraic group can be advantageously expressed in terms of functions defined in the orbit space of the group, i.e. as functions of a finite set of basic invariant polynomials. This fact and the tools of geometric invariant theory can be exploited in many physical contexts where the study of covariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry and/or supersymmetry breaking in possibly supersymmetric quantum field theories of elementary particles, in the analysis of phase spaces and structural phase transitions in solid state physics (Landau's theory), in covariant bifurcation theory, in crystal field theory and in most areas of solid state theory where use is made of symmetry adapted functions. We shall present some elements of geometric invariant theory and illustrate some of the possible applications in the study of spontaneous symmetry and supersymmetry breaking. 相似文献
9.
In Twistor Conformal Field Theory the Riemann surfaces and holomorphic functions of two-dimensional conformal field theory are replaced by flat twistor spaces (arising from conformally-flat four-manifolds) and elements of the holomorphic first cohomology. The analogue of a Laurent Series is the expansion of a cohomology element in elementary states and we calculate the dimension of the space of these states for twistor spaces of compact hyperbolic manifolds. Our method follows the strategy used in the classical problem of calculating the number of meromorphic functions with prescribed poles on Rieiemann surface. We express the problem globally (in terms of the cohomology of a blown-up twistor space), calculate the holomorphic Euler characteristic of this blown-up space, and then use some vanishing theorems to isolate the first cohomology term. 相似文献
10.
Götz Wiesend 《Mathematische Zeitschrift》2007,256(4):717-729
Let X be a regular arithmetic scheme, i.e. a regular integral separated scheme flat and of finite type over Spec . Generalising classical class field theory for number fields, we define a class group C
X
and show there is a natural surjective map whose kernel is the connected component of 0.
相似文献
11.
We study (n+3)-point correlation functions of exponential fields in the Liouville field theory with n degenerate and three
arbitrary fields and derive an analytic expression for these correlation functions in terms of Coulomb integrals. We consider
the application of these results to the minimal Liouville gravity.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 3, pp. 536–556, March, 2008. 相似文献
12.
Christian Brouder 《Mathematische Nachrichten》2009,282(12):1664-1690
This paper provides a primer in quantum field theory (QFT) based on Hopf algebra and describes new Hopf algebraic constructions inspired by QFT concepts. The following QFT concepts are introduced: chronological products, S ‐matrix, Feynman diagrams, connected diagrams, Green functions, renormalization. The use of Hopf algebra for their definition allows for simple recursive derivations and leads to a correspondence between Feynman diagrams and semi‐standard Young tableaux. Reciprocally, these concepts are used as models to derive Hopf algebraic constructions such as a connected coregular action or a group structure on the linear maps from S (V) to V. In many cases, noncommutative analogues are derived (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
Khodr Shamseddine 《Journal of Mathematical Analysis and Applications》2010,368(1):281-292
Two topologies on the Levi-Civita field R will be studied: the valuation topology induced by the order on the field, and another weaker topology induced by a family of seminorms, which we will call weak topology. We show that each of the two topologies results from a metric on R, that the valuation topology is not a vector topology while the weak topology is, and that R is complete in the valuation topology while it is not in the weak topology. Then the properties of both topologies will be studied in details; in particular, we give simple characterizations of open, closed, and compact sets in both topologies. 相似文献
14.
The authors establish a Cheeger-Müller type theorem for the complex valued analytic torsion introduced by Burghelea and Hailer for fiat vector bundles carrying nondegenerate symmetric bilinear forms. As a consequence, they prove the Burghelea-Haller conjecture in full generality, which gives an analytic interpretation of (the square of) the Turaev torsion. 相似文献
15.
Ludomir Newelski 《Central European Journal of Mathematics》2003,1(3):398-410
Some basic ideas of model theory are presented and a personal outlook on its perspectives is given. 相似文献
16.
We consider the possibility of using the quantum inverse scattering method to study the superconformal field theory and its integrable perturbations. The classical limit of the considered constructions is based on the
(1|2) super-KdV hierarchy. We introduce the quantum counterpart of the monodromy matrix corresponding to the linear problem associated with the L-operator and use the explicit form of the irreducible representations of
q(1|2) to obtain the fusion relations for the transfer matrices (i.e., the traces of the monodromy matrices in different representations).Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 252–264, February, 2005. 相似文献
17.
在扩大模型下,应用单子理论给出了拓扑等度连续和均匀连续的非标准刻画,并应用均匀连续的非标准特征证明了网收敛与均匀连续之间的关系,最后应用拓扑等度连续和均匀连续的非标准特征证明了拓扑等度连续和均匀连续之间的关系. 相似文献
18.
I. Ya. Arefeva P. V. Gorbachev P. B. Medvedev 《Theoretical and Mathematical Physics》2009,158(3):320-332
We find a class of analytic solutions in a modified cubic theory of fermionic strings that includes the GSO(−) sector. This
class contains a solution that involves a tachyon field from the GSO(−) sector and reproduces the correct value of the non-BPS
D-brane tension.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 378–390, March, 2009. 相似文献
19.
A. V. Pokrovskii O. A. Rasskazov 《Proceedings of the American Mathematical Society》2004,132(2):567-577
Dynamical systems in are studied. Let be a bounded open set. We will be interested in those periodic orbits such that at least one of its points lies inside and at least one of its points lies outside ; the orbits with this property are called -broken. Information about the structure of the set of -broken orbits is suggested; results are formulated in terms of topological degree theory.
20.
Correlation Functions and Boundary Conditions in Rational Conformal Field Theory and Three-Dimensional Topology 总被引:3,自引:0,他引:3
Giovanni Felder Jürg Fröhlich Jürgen Fuchs Christoph Schweigert 《Compositio Mathematica》2002,131(2):189-238
We give a general construction of correlation functions in rational conformal field theory on a possibly nonorientable surface with boundary in terms of three-dimensional topological field theory. The construction applies to any modular category in the sense of Turaev. It is proved that these correlation functions obey modular invariance and factorization rules. Structure constants are calculated and expressed in terms of the data of the modular category. 相似文献