Related papers: Numerical analyses of a quantum-theoretic eight-di…
We present ongoing investigations of maximally supersymmetric Yang--Mills ($Q = 16$ SYM) theory in three space-time dimensions. At low temperatures and large $N$ this theory is related to black branes in higher-dimensional quantum gravity.…
In the paper, within the background field method, the renormalization and the gauge dependence is studied as for an SU(2) Yang-Mills theory with multiplets of spinor and scalar fields. By extending the quantum action of the BV-formalism…
An explicit canonical transformation is constructed to relate the physical subspace of Yang-Mills theory to the phase space of the ADM variables of general relativity. This maps 3+1 dimensional Yang-Mills theory to local evolution of…
(Withdrawn: This paper turns out incomplete and even misleading. I must apologize to all of the recipients.)
The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is the first step towards this goal. This…
This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe…
It is shown that a $d$-dimensional classical SU(N) Yang-Mills theory can be formulated in a $d+2$-dimensional space, with the extra two dimensions forming a surface with non-commutative geometry.
We report on our non-perturbative investigations of supersymmetric Yang-Mills quantum mechanics with 4 supercharges. We employ two independent numerical methods. First of them is the cut Fock space method whose numerical implementation was…
This paper has been withdrawn because it is superseded by quant-ph/9905084 "Bayesian analysis of Bell inequalities.
We study the transformation law of quantum fields in super Yang-Mills theory quantized in the Wess-Zumino gauge. It can be derived from a local version of generalized Slavnov-Taylor identities for general Green functions. Under suitable…
Classical three dimensional Yang-Mills is seen to be related to the topological Chern-Simons term through a nonlinear but fully local and covariant gauge field redefinition. A classical recursive cohomological argument is provided.
Electromagnetism can be generalized to Yang-Mills theory by replacing the group U(1)$ by a nonabelian Lie group. This raises the question of whether one can similarly generalize 2-form electromagnetism to a kind of "higher-dimensional…
We examine an extension of the ideas of quantum cosmology and, in particular, the proposal of Hartle and Hawking for the boundary conditions of the Universe, to models which incorporate Yang-Mills fields. Inhomogeneous perturbations about a…
Recently Anishetty, Majumdar and Sharatchandra have proposed a way of characterizing topologically non-trivial configurations for 2+1 dimensional Yang-Mills theory in a local and manifestly gauge invariant manner. In this paper paper we…
The geometric description of Yang-Mills theories and their configuration space M is reviewed. The presence of singularities in M is explained and some of their properties are described. The singularity structure is analyzed in detail for…
A rough overview is given over the most essential structures underlying all working quantum theoretical models as well as axiomatic and algebraic quantum field theory .
We review two works arXiv:2006.04987 and arXiv:2201.03487 which study the stochastic quantisation equations of Yang-Mills on two and three dimensional Euclidean space with finite volume. The main result of these works is that one can…
We investigate domain-wall/quantum field theory correspondences in various dimensions. We give particular emphasis to the special case of the quantum mechanics of 0--branes.
We study a class of noncommutative geometries that give rise to dimensionally reduced Yang-Mills theories. The emerging geometries describe sets of copies of an even dimensional manifold. Similarities to the D-branes in string theory are…
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner…