Topological field theory

The scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible manifolds. This yields globally well-defined scalar and vector topological BRST operators. These operators generate a subalgebra of maximally supersymmetric Yang-Mills theory, which is small enough to be closed off-shell with a finite set of auxiliary fields and large enough to determine the Yang-Mills supersymmetric theory. Poincar\'e supersymmetry is reached in the limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs is thus removed by the requirement of scalar and vector topological symmetry, which also determines the complete supersymmetry transformations in a twisted way. Provided additional Killing vectors exist on the manifold, an equivariant extension of our geometrical framework is provided, and the resulting "equivariant topological field theory" corresponds to the twist of super Yang-Mills theory on Omega backgrounds.

This volume contains the complete collection of published and
unpublished work on German grammar by Tilman N. Höhle. It consists of
two parts. The first part is Topologische Felder, a book-length manuscript that was written in 1983 but was never finished nor published. It is a careful examination of the topological properties of German sentences, including a discussion of typological assumptions. The second part assembles all other published and unpublished papers by Höhle on German grammar.

All of these papers were highly influential in German linguistics, in
theoretical linguistics in general, and in a specific variant of
theoretical linguistics, Head-Driven Phrase Structure Grammar. Topics
covered are clause structure, constituent order, coordination, (verum)
focus, word structure, the relationship between relative pronouns and
verbs in V2, extraction, and the foundations of a theory of phonology
in constraint-based grammar.

In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of large deviations theory to time-averaged quantities which describe such stochastic maps, in particular time-averaged currents and density functionals. We derive the large deviations principle for these quantities, as well as

This paper pro­vides an overview of the most im­por­tant gram­mat­i­cal prop­er­ties of Ger­man. A large part of the paper is con­cerend with the basic clause types of Ger­man. I start with the Topo­log­i­cal Fields Model, which is very use­ful as a de­scrip­tive tool, but – as will be shown – not suf­fi­cient for a thor­ough ac­count of Ger­man clausal struc­ture. I there­fore ex­plain ad­di­tion­al the­o­ret­i­cal as­sump­tions that were made in order to as­sign struc­ture to the ob­serv­able lin­ear se­quences. After a sketch of an anal­y­sis of the basic sen­tence pat­terns in the Sec­tions 2–5, I give an ac­count of pas­sive, case as­sign­ment, and sub­ject-​verb agree­ment in Sec­tion 6.

Various approaches to high energy forward scattering in quantum gravity are compared using the eikonal approximation. The massless limit of the eikonal is shown to be equivalent to other approximations for the same process, specifically the semiclassical calculation due to G. 't Hooft and the topological field theory due to H. and E. Verlinde. This comparison clarifies these previous results, as it is seen that the amplitude arises purely from a linearised gravitational interaction. The interpretation of poles in the scattering amplitude is also clarified.

The 2-dimensional BF theory is both a gauge theory and a topological Poisson $\sigma$-model corresponding to a linear Poisson bracket. In \cite{To1}, Torossian discovered a connection which governs correlation functions of the BF theory with sources for the $B$-field. This connection is flat, and it is a close relative of the KZ connection in the WZW model. In this paper, we show that flatness of the Torossian connection follows from (properly regularized) quantum equations of motion of the BF theory.

Yang-Mills theory in the first order formalism appears as the deformation of a topological field theory, the pure BF theory. We discuss this formulation at the quantum level, giving the Feynman rules of the BF-YM theory, the structure of the renormalization and checking its uv-behaviour in the computation of the beta-function which agrees with the expected result.

Yang-Mills theory in the first order formalism appears as the deformation of a topological field theory, the pure BF theory. In this approach new non local observables are inherited from the topological theory and the operators entering the t'Hooft algebra find an explicit realization. A calculation of the {\it vev}'s of these operators is performed in the Abelian Projection gauge.

We show that [Tre05] can be generalised to provide uniform ways of extending certain model complete theories of field expansions in characteristic 0 to model complete theories of differential field expansions with several commuting derivatives. Key to our method is a new notion of large sets we present here which generalises the notion of large fields to subsets of the field. Then, given n ∈ N and a class M of fields expanded to some fixed language whose definable sets reduce to a combination of affine varieties and large sets, we show that there exists a theory U N (which we call a uniform companion) such that given a model complete theory T whose models are in M then T ∪ U N is a model-complete theory of differential fields in N commuting derivatives. Similarly to [Tre05], U N also preserves quantifier elimination, model companionship, model completions, and completeness (upon adding certain constants to the language). We apply our results to classes of fields with finite number of orderings and valuations that satisfy local-global principles in the sense of [Pop96] as well as valued fields enriched with a subfield of the residue field. Note that in all expansions considered here, the additional structure is independent from the derivatives.

Based on a weak action of a finite group J on a finite group G, we present a geometric construction of J-equivariant Dijkgraaf-Witten theory as an extended topological field theory. The construction yields an explicitly accessible class of equivariant modular tensor categories. For the action of a group J on a group G, the category is described as the representation

We establish a connection between topological field theories, Nicolai maps, BRST quantization and Langevin equations. In particular we show that there is a one-to-one correspondence between global unbroken supersymmetric theories which admit a Nicolai map and theories which arise as the BRST quantization of the square of the Langevin equation, setting the random field to zero. As such they are topological in nature. As an example we consider the topological quantum field theory of Witten in the Labastida-Pernici form and show that it is the first example of a theory admitting a complete Nicolai map in four dimensions. We also consider the topological sigma models of Witten and show that they too arise from the BRST quantization of the square of the Langevin equation.

The problem of creation of Unitary Field theory, or the Theory of Everything, which the Einstein was so eager to solve by means of physics, remained unsolved since it is solvable only by means of the Word: because the Word, according to Bible — is the God and «the God has»: Universe, His Child. This particular solution is given by the linguistic work about the Existing, offered by me to you and based on the Pressing method, the founder of which is Dionysus (Bacchus) — the ancient's god of the Word, Moon and Wine. // Познать Мир, Божий Храм - есть познать Слово нам. Слово - это Луна.

We exhibit the bi-Hamiltonian structure of the equations of associativity (Witten-Dijkgraaf-Verlinde-Verlinde-Dubrovin equations) in 2-d topological field theory, which reduce to a single equation of Monge-Ampère type $ f_{ttt}=f_{xxt}^{\;\;\;\;\;2} - f_{xxx}f_{xtt} \, ,$ in the case of three primary fields. The first Hamiltonian structure of this equation is based on its representation as a 3-component system of hydrodynamic type and the second Hamiltonian structure follows from its formulation in terms of a variational principle with a degenerate Lagrangian.