Related papers: Noncommutative Induced Gauge Theories on Moyal Spa…
In the space-of-histories approach to gauge fields and their quantization, the Maxwell, Yang--Mills and gravitational field are well known to share the property of being type-I theories, i.e. Lie brackets of the vector fields which leave…
The field equations in modified gravity theories possess an important decoupling property with respect to certain classes of nonholonomic frames. This allows us to construct generic off--diagonal solutions depending on all spacetime…
The renormalization-group improved effective potential for an arbitrary renormalizable massless gauge theory in curved spacetime is found,thus generalizing Coleman-Weinberg's approach corresponding to flat space.Some explicit examples are…
These notes provide an introduction to the noncommutative matrix geometry which arises within matrix models of Yang-Mills type. Starting from basic examples of compact fuzzy spaces, a general notion of embedded noncommutative spaces…
The Poisson gauge algebra is a semi-classical limit of complete non-commutative gauge algebra. In the present work we formulate the Poisson gauge theory which is a dynamical field theoretical model having the Poisson gauge algebra as a…
We generalize to noncommutative cylinder the solution generation technique, originally suggested for gauge theories on noncommutative plane. For this purpose we construct partial isometry operators and complete set of orthogonal projectors…
A long-standing conjecture on the structure of renormalized, gauge invariant, integrated operators of arbitrary dimension in Yang-Mills theory is established. The general solution of the consistency condition for anomalies with sources…
We consider four-dimensional non-Abelian gauge theory living on a complex projective space $\mathbb{CP}^2$ as a way of gaining insights into (3+1)-dimensional QCD. In particular, we use a complex parametrization of gauge fields on which…
A gauge-invariant field is found which describes physical configurations, i.e. gauge orbits, of non-Abelian gauge theories. This is accomplished with non-Abelian generalizations of the Poincare'-Hodge formula for one-forms. In a particular…
The simplest non commutative renormalizable field theory, the $\phi_4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe up to three loops, as shown by H. Grosse and R. Wulkenhaar, M. Disertori and V.…
The U(1) gauge theory on a space with Lie type noncommutativity is constructed. The construction is based on the group of translation in Fourier space, which in contrast to space itself is commutative. In analogy with lattice gauge theory,…
We consider the supersymmetric field theories on the noncommutative $R^4$ using the superspace formalism on the commutative space. The terms depending on the parameter of the noncommutativity $\Theta$ are regarded as the interactions. In…
Seiberg-Witten maps and a recently proposed construction of noncommutative Yang-Mills theories (with matter fields) for arbitrary gauge groups are reformulated so that their existence to all orders is manifest. The ambiguities of the…
Products defined in the context of noncommutative gauge theory allow for an interpolation between exact results on tachyon potentials at zero and large background B-fields. Techniques for computations of effective actions are transposed…
It is shown that non-commutative spaces, which are quotients of associative algebras by ideals generated by non-linear relations of a particular type, admit extremely simple formulae for deformed or star products. Explicit construction of…
A four dimensional gauge theory with nonpolynomial but local interactions of 1-form and 2-form gauge potentials is constructed. The model is a nontrivial deformation of a free gauge theory with nonpolynomial dependence on the deformation…
We consider the construction of gauge theories of gravity that are invariant under local conformal transformations. We first clarify the geometric nature of global conformal transformations, in both their infinitesimal and finite forms, and…
Starting from relativistic quantum field theories, describing interacting nucleons and pions coupled to the dynamical electromagnetic field, the pion degrees of freedom are eliminated by means of functional integration. Apart from taking…
Motivated by the recent construction of a translation-invariant renormalizable non-commutative model for a scalar field (see arXiv:0802.0791 [math-ph]), we introduce models for non-commutative U(1) gauge fields along the same lines. More…
Old folklore says that there is no non-trivial renormalization group fixed point with $U(1)$ gauge symmetry in four dimensions, but it can be circumvented by the existence of magnetic monopoles. We propose to construct (potentially…