Related papers: Topological quantum field theories
I present a selection of conceptual and mathematical problems in the foundations of modern physics as they derive from the title question. Contribution to a panel session, "Springer Forum: Quantum Structures -- Physical, Mathematical and…
These lectures comprise the second half of a quantum field theory course given in 2004. Topics include the path integral, loop expansion, Feynman rules, various regularization methods, renormalization, running couplings and the…
In this expository paper we introduce extended topological quantum field theories and the cobordism hypothesis.
The quantum field theories (QFT) constructed in [1,2] include phenomenology of interest. The constructions approximate: scattering by $1/r$ and Yukawa potentials in non-relativistic approximations; and the first contributing order of the…
A topological quantum field theory is introduced which reproduces the Seiberg-Witten invariants of four-manifolds. Dimensional reduction of this topological field theory leads to a new one in three dimensions. Its partition function yields…
Various aspects of recent works on affine quantum group symmetry of integrable 2d quantum field theory are reviewed and further clarified. A geometrical meaning is given to the quantum double, and other properties of quantum groups.…
A realistic axiomatic formulation of Galilean Quantum Field Theories is presented, from which the most important theorems of the theory can be deduced. In comparison with others formulations, the formal aspect has been improved by the use…
We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On R^d the new theory differs from the original one by the spectrum of operators. Sometimes the local…
These notes grew from a series of lectures given by the authors during the last decade. They will be published in the proceedings of TASI 2021. After a brief introduction to quantum information theory tools, they are organized in four…
This article is a short introduction to the theory of the groups of points of elliptic curves over finite fields. It is concerned with the elementary theory and practice of elliptic curves cryptography, the new generation of public key…
An overview of the accomplishments of constructive quantum field theory is provided.
Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.
Topological properties of the gauge field in a two-dimensional Higgs model are investigated. Results of exploratory numerical simulations are presented.
It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…
These lectures deal with selected aspects of quantum field theory in curved spacetime including the following topics: (1) Quantization of fields on a curved background, particle creation by gravitational fields, particle creation in an…
Mathematical aspects of contemporary classical and quantum gauge theory are sketched.
We discuss topological theories, arising from the general $\mathcal{N}=2$ twisted gauge theories. We initiate a program of their study in the Gromov-Witten paradigm. We re-examine the low-energy effective abelian theory in the presence of…
In this talk, we briefly review the basic concepts of anomalous gauge theories. It has been known for some time how theories with local anomalies can be handled. Recently it has been pointed out that global anomalies, which obstruct the…
The exact solutions to quantum string and gauge field theories are discussed and their formulation in the framework of integrable systems is presented. In particular I consider in detail several examples of appearence of solutions to the…
Modern theories of fundamental interactions describe strong, electromagnetic and weak interactions as quantum field theories with certain kinds of embedded internal symmetries called `gauge symmetries'. This article introduces quantum field…