Related papers: Gauged q-Fields
We write a gravity theory with Yang-Mills type action using the biconformal gauging of the conformal group. We show that the resulting biconformal Yang-Mills gravity theories describe 4-dim, scale-invariant general relativity in the case of…
The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation. The operators for area and volume defined in the q-deformation of the theory are partly diagonalized. The…
Two-dimensional SU(N) Yang-Mills theory is endowed with a non-trivial vacuum structure (k-sectors). The presence of k-sectors modifies the energy spectrum of the theory and its instanton content, the (Euclidean) space-time being…
We find certain functional identities for the Gauss q-power function of a sum of q-commuting variables. Then we use these identities to obtain two-parameter twists of the quantum affine algebra U_q (\hat{sl}_2) and of the Yangian Y(sl_2).…
A scheme of q-deformation of nonlinear maps is introduced. As a specific example, a q-deformation procedure related to the Tsallis q-exponential function is applied to the logistic map. Compared to the canonical logistic map, the resulting…
There is an interesting dichotomy between a space-time metric considered as external field in a flat background and the same considered as an intrinsic part of the geometry of space-time. We shall describe and compare two other external…
We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string…
Generalized numbers, arithmetic operators and derivative operators, grouped in four classes based on symmetry features, are introduced. Their building element is the pair of $q$-logarithm/$q$-exponential inverse functions. Some of the…
Quantum integrable spin chains are known to possess a large family of long-range deformations generated by the local, boost and bilocal operators. Although these deformations are well-understood on the level of the pairwise commuting…
A q-deformed two-dimensional phase space is studied as a model for a noncommutative phase space. A lattice structure arises that can be interpreted as a spontaneous breaking of a continuous symmetry. The eigenfunctions of a Hamiltonian that…
We give in this paper a partial classification of the consistent quadratic gauge actions that can be written in terms of s-form fields. This provides a starting point to study the uniqueness of the Yang-Mills action as a deformation of…
The quantization of Yang-Mills field theories requires the introduction of a gauge fixing which leads to a violation of the Local Gauss Law described by the so-called Gauss operator. We discuss the local quantizations of Yang-Mills theories…
In a recent article, Dieks has proposed a way to implement the modal interpretation of (nonrelativistic) quantum theory in relativistic quantum field theory. We show that his proposal fails to yield a well-defined prescription for which…
A noncommutative gauge theory is developed using a covariant star-product between differential forms defined on a symplectic manifold, considered as the space-time. It is proven that the field strength two-form is gauge covariant and…
We address the construction and interpretation of diffeomorphism-invariant observables in a low-energy effective theory of quantum gravity. The observables we consider are constructed as integrals over the space of coordinates, in analogy…
In this talk we consider the mass-deformed Yang-Mills theory in the covariant gauge which is obtained by just adding a gluon mass term to the Yang-Mills theory with the covariant gauge fixing term and the associated Faddeev-Popov ghost…
In this thesis we study different aspects of noncommutativity in quantum mechanics, field theory and gravity. We give particular emphasis on the underlying symmetries of these theories. Deformations of usual symmetries like the external…
Pseudoaffine theories are characterized by formal replacement of the level to the fractional number: $k\to\frac{k}{q}$, where $q$ is integer strange to $k(g+k)$ ($g$ - dual Coxeter number). An example of "forbidden" $q$ is considered…
We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…