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Other literature type . 1988
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Communications in Mathematical Physics
Article . 1988 . Peer-reviewed
License: Springer TDM
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Topological quantum field theory

Authors: Witten, Edward;

Topological quantum field theory

Abstract

A twisted version of four dimensional supersymmetric gauge theory is formulated. The starting point is the connection between the Floer and Donaldson theories which has led to the conjecture that the ``Morse theory'' interpretation of Floer homology must be an approximation to a relativistic quantum field theory. It is shown that the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally. The Floer theory is generalized to the relativistic case and then the formula for the supersymmetry current and the energy-momentum tensor are obtained. The most important result of the paper is the assertion that the stress tensor is a ``BRST'' commutator \(T_{\alpha \beta}=\{Q,\lambda_{\alpha \beta}\},\) where Q is a linear transformation of the space of all functionals of the field variables, and \(\lambda_{\alpha \beta}^ a \)tensor field characteristic for the model. Finally, the possible physical interpretation of the model is presented. It is pointed out that the model is in a sense a generally covariant quantum theory in which general covariance is unbroken, there are no gravitons, and the only excitations are topological.

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Keywords

Donaldson polynomial invariants, 58F30, 58A10, 58G30, Floer homology, stress tensor, twistor, 57R55, Constructive quantum field theory, Supersymmetric field theories in quantum mechanics, 81E99, Floer theory, Applications of global differential geometry to the sciences, supersymmetric gauge theory

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2K
Top 0.1%
Top 0.01%
Top 0.1%
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