共查询到20条相似文献,搜索用时 0 毫秒
1.
B. Durhuus 《Journal of Geometry and Physics》1993,11(1-4):155-180
First, we describe a rather general scheme for constructing three-dimensional euclidean topological quantum field theories, whose basic building blocks are provided by the representation theory of a certain class of (bi-)algebras. Secondly, we discuss in some detail examples, where the algebra is either the function algebra of a finite group, the group algebra of a finite group or a deformation of the enveloping algebra of a classical simple Lie group. 相似文献
2.
《Physics letters. [Part B]》1988,212(2):187-190
We present an action which generates the supersymmetric self-dual equations corresponding to euclidean super Yang-Mills theory in four dimensions. By adding additional constraint fields with new local symmetries, the classical equations of this system are the usual super self-dual equations when a gauge is chosen for the constraint fields. This construction is a supersymmetric generalization of the Labastida-Pernici action which corresponds to a gauge unfixed version of Witten's topological quantum field theory. We discuss some topological prospects for this model, and the role of supersymmetric instantons in Donaldson theory. 相似文献
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Letters in Mathematical Physics - Motivated by gauge theory, we develop a general framework for chain complex-valued algebraic quantum field theories. Building upon our recent operadic approach to... 相似文献
4.
John C. Baez 《Letters in Mathematical Physics》1996,38(2):129-143
Starting from a Lie group G whose Lie algebra is equipped with an invariant nondegenerate symmetric bilinear form, we show that four-dimensional BF theory with cosmological term gives rise to a TQFT satisfying a generalization of Atiyah's axioms to manifolds equipped with principal G-bundle. The case G=GL(4,) is especially interesting because every 4-manifold is then naturally equipped with a principal G-bundle, namely its frame bundle. In this case, the partition function of a compact oriented 4-manifold is the exponential of its signature, and the resulting TQFT is isomorphic to that constructed by Crane and Yetter using a state sum model, or by Broda using a surgery presentation of four-manifolds. 相似文献
5.
Shahn Majid 《Letters in Mathematical Physics》1991,22(2):83-90
We show that every topological quantum field theory (understood as a functor) has an associated quasi-quantum group of internal symmetries. 相似文献
6.
A. Yu. Khrennikov 《Russian Physics Journal》1992,35(11):1036-1039
A p-adic generalization of the frequency theory of probability is developed. Within the framework of this theory frequency meaning is imparted to probabilities belonging to the field of p-adic numbers. The Bargmann-Fock representation is constructed for the p-adic field theory. A frequency interpretation of quantum states in the Bargmann-Fock representation is proposed. The p-adic generalization is essentially an introduction of new quantum states which are meaningless from the point of view of the standard theory of probability based on Kolmogorov's axiomatics.Moscow Institute of Electronic Engineering. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 51–55, November, 1992. 相似文献
7.
《Physics letters. [Part B]》1988,214(1):91-97
We show how Witten's topological Yang-Mills and gravitational quantum field theories may be obtained by a straightforward BRST gauge fixing procedure. We investigate some aspects of the renormalization of the topological Yang-Mills theory. It is found that the beta function for the Yang-Mills coupling constant is not zero. 相似文献
8.
The combinatorial state sum of Turaev and Viro for a compact 3-manifold in terms of quantum 6j-symbols is generalized by introducing observables in the form of coloured graphs. They satisfy braiding relations and allow for surgeries and a discussion of cobordism theory. Application of these techniques give the dimension and an explicit basis for the vector space of the topological quantum field theory associated to any Riemann surface with arbitrary coloured punctures.Dedicated to H. Araki and E. Lieb on the occasion of their 60th birthdaysSupported by DFG, SFB 288 Differentialgeometrie und Quantenphysik 相似文献
9.
Louis Funar 《Communications in Mathematical Physics》1995,171(2):405-458
We describe the relation between three dimensional topological quantum field theory and two dimensional conformal field theory. Some Applications to quantum knot invariants leading to the equivalence of Chern-Simons-Witten and Kohno's approaches are outlined. 相似文献
10.
M. Temple-Raston 《Letters in Mathematical Physics》1991,23(2):91-97
We examine a class of topological field theories defined by Lagrangians that under certain conditions can be written as the sum of two characteristic numbers or winding numbers. Therefore, the action or the energy is a topological invariant and stable under perturbations. The sufficient conditions required for stability take the form of first-order field equations, analogous to the self-duality and Bogomol'nyi equations in Yang-Mills(-Higgs) theory. Solutions to the first-order equations automatically satisfy the full field equations. We show the existence of nontrivial, nonsingular, minimum energy spherically symmetric dyon solutions and that they are stable. We also discuss evidence for a dual field theory to Yang-Mills-Higgs in topological field theory. The existence of dual field theories and electric monopoles is predicted by Montonen and Olive. 相似文献
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《Journal of Geometry and Physics》1995,16(1):39-70
The generalisation of the topological quantum field theory construction of Turaev and Viro to arbitrary dimension is presented, and it is shown that q-deformed spin-networks, or the recoupling theory of the quantum group Uqsl(2) provide a realisation of the initial data for the construction of 2-, 3- and 4-dimensional TQFTs. 相似文献
14.
In this paper we prove the existence and uniqueness of a topological quantum field theory that incorporates, for all Riemann surfaces, the corresponding spaces of theta functions and the actions of the Heisenberg groups and modular groups on them. 相似文献
15.
M. Temple-Raston 《International Journal of Theoretical Physics》1997,36(4):871-881
A tensor product generalization ofB ∧F theories is proposed that has a Bogomol'nyi structure. Nonsingular, stable, finite-energy particle-like solutions to the
Bogomol'nyi equations are studied. Unlike Yang-Mills(-Higgs) theory, the Bogomol'nyi structure does not appear as a perfect
square in the Lagrangian. Consequently, the Bogomol'nyi energy can be obtained in more than one way. The added flexibility
permits electric monopole solutions. 相似文献
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17.
J. Rayski 《International Journal of Theoretical Physics》1977,16(10):729-740
Mathematically regular and more precise versions of quantum field theories are discussed. A new class of representations called minimal wave-packet representations is introduced. Several possibilities of constructing nonconventional, bounded interaction operators (nonpolynomial, nonlinear, explicitly or implicitly nonlocal) corresponding to the traditional
4 or
3 interactions are reviewed. The problem of macrocausality is discussed. A procedure of renormalization of regular theories is indicated. 相似文献
18.
《Nuclear Physics B》1999,549(3):579-612
We investigate the thermodynamic Bethe ansatz (TBA) equations for a system of particles which dynamically interacts via the scattering matrix of affine Toda field theory and whose statistical interaction is of a general Haldane type. Up to the first leading order, we provide general approximated analytical expressions for the solutions of these equations from which we derive general formulae for the ultraviolet scaling functions for theories in which the underlying Lie algebra is simply laced. For several explicit models we compare the quality of the approximated analytical solutions against the numerical solutions. We address the question of existence and uniqueness of the solutions of the TBA equations, derive precise error estimates and determine the rate of convergence for the applied numerical procedure. A general expression for the Fourier transformed kernels of the TBA equations allows one to derive the related Y-systems and a reformulation of the equations into a universal form. 相似文献
19.
Topologically non-trivial effects appearing in the discussion of duality transformations in higher genus manifolds are discussed in a simple example. Their relation with the properties of Topological Field Theories is established. 相似文献