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1.
We apply cluster expansion methods to to theN=2 Wess-Zumino models in finite volume, in two space-time dimensions. We show that in the region of convergence of the cluster expansion, a vanishing theorem holds for the supercharge of the theory; that is, the dimension of the kernel of the Hamiltonian is equal to the index of the supercharge.Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 90-07206Supported in part by National Science Foundation Mathematical Sciences Postodoctoral Research Fellowship DmS 88-07291 相似文献
2.
We construct a convergent cluster expansion for the two-dimensionalN=2 Wess-Zumino model, in a region of parameter space where there are multiple phase. As a result of this expansion, we are able to construct the infinite volume field theory and demonstrate exponential decay of correlations. We are also able to investigate the different phases of the model, develop the phase diagram, and show that the free energy of each phase vanishes.Supported in part by National Science Foundation grants DMS 90-08827, PHY/DMS 88-16214 and DMS 88-58073Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291 相似文献
3.
Let G be a compact Lie group, and let LG denote the corresponding loop group. Let (X,) be a weakly symplectic Banach manifold. Consider a Hamiltonian action of LG on (X,), and assume that the moment map :XL
* is proper. We consider the function ||2:X, and use a version of Morse theory to show that the inclusion map j:-1(0)X induces a surjection j
*:H
G
*(X)H
G
*(-1(0)), in analogy with Kirwans surjectivity theorem in the finite-dimensional case. We also prove a version of this surjectivity theorem for quasi-Hamiltonian G-spaces. 相似文献
4.
Jonathan Weitsman 《Letters in Mathematical Physics》2011,95(3):275-296
We show that the Yang–Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent,
term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction terms. When
a further momentum cutoff is imposed, this Fermionic theory has a convergent perturbation expansion. To zeroth order in this
perturbation expansion, the correlation function E(x,y) of generic components of pairs of connections is given by an explicit, finite-dimensional integral formula, which we conjecture
will behave as
E(x,y) ~ |x - y|-2 - 2 dG, E(x,y) \sim |x - y|^{-2 - 2 d_G}, 相似文献
5.
Arthur Jaffe Andrzej Lesniewski Jonathan Weitsman 《Communications in Mathematical Physics》1988,114(1):147-165
We construct a family of supersymmetric, two-dimensional quantum field models. We establish the existence of the HamiltonianH and the superchargeQ as self-adjoint operators. We establish the ultraviolet finiteness of the model, independent of perturbation theory. We develop functional integral representations of the heat kernel which are useful for proving estimates in these models. In a companion paper [1] we establish an index theorem forQ, an infinite dimensional Dirac operator on loop space. This paper and, another related one [2], provide the technical justification for our claim thatQ is Fredholm, and for our computation of its index by a homotopy onto quantum mechanics.Supported in part by the National Science Foundation under Grant DMS/PHY 86-45122Hertz Foundation Graduate Fellow 相似文献
6.
We show how the moduli space of flatSU(2) connections on a two-manifold can be quantized in the real polarization of [15], using the methods of [6]. The dimension of the quantization, given by the number of integral fibres of the polarization, matches the Verlinde formula, which is known to give the dimension of the quantization of this space in a Kähler polarization.Supported in part by MSRI under NSF Grant 85-05550Supported in part by an NSF Graduate fellowship, and by a grant-in-aid from the J. Seward Johnson Charitable TrustSupported in part by NSF Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291. Address as of January 1, 1993: Department of Mathematics, Columbia University, New York, NY 10027, USA 相似文献
7.
8.
This research was carried out while Professor Weitsman was visiting the University of York. He wishes to thank the SERC for
its support and the Department of Mathematics of the University of York for its hospitality. Research supported in part by
the N.S.F. 相似文献
9.
10.
We show that the cohomology of the moduli space of flatSU(2) connections on a two-manifold may be computed using a perfectMorse function. 相似文献
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