Related papers: SL_q(3) Fields
The paper contains the construction of a topological quantum field theory in which gluings along surfaces with boundary are allowed. The construction is made by using quantum deformations of sl(2,C). In the construction there appears a sign…
We start with the observation that the quantum group SL_q(2), described in terms of its algebra of functions has a quantum subgroup, which is just a usual Cartan group. Based on this observation we develop a general method of constructing…
Field-theoretic models for fields taking values in quantum groups are investigated. First we consider $SU_q(2)$ $\sigma$ model ($q$ real) expressed in terms of basic notions of noncommutative differential geometry. We discuss the case in…
Motivated by the question of exploring the "theory space" of quantum field theories, we review the concept of "decomposing" and "gluing" quantum field theories. We explain this in the context of three-dimensional $\mathcal{N}=2$…
There are suggestive experimental indications that the leptons, neutrinos, and quarks are composite and that their structure is described by the quantum group SLq(2). Since the hypothetical preons must be very heavy relative to the masses…
The representation theory of the quantum group su$_q(2)$ is used to introduce $q$-analogues of the Wigner rotation matrices, spherical functions, and Legendre polynomials. The method amounts to an extension of variable separation from…
We have examined the deformation of a generic non-Abelian gauge theory obtained by replacing its Lie group by the corresponding quantum group. This deformed gauge theory has more degrees of freedom than the theory from which it is derived.…
The q-deformation of the Lie algebras underlying the standard field theories leads to a pair of dual algebras. We describe a simple choice of possible field theories based on these derived algebras. One of these approximates the standard…
We give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.
The vector fields of the quantum Lie algebra are described for the quantum groups $GL_q(N), SL_q(N)$ and $SO_q(N)$ as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their…
When the symmetry of a physical theory describing a finite system is deformed by replacing its Lie group by the corresponding quantum group, the operators and state function will lie in a new algebra describing new degrees of freedom. If…
A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a…
Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the…
A general method is presented which allows one to determine from the local gauge invariant observables of a quantum field theory the underlying particle and symmetry structures appearing at the lower (ultraviolet) end of the…
Starting from the quantum group SL_q(2,C), we construct operator invariants of 3-cobordisms with spin structure, satisfying the requirements of a topological quantum field theory and refining the Reshetikhin--Turaev and Turaev--Viro models.…
We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we…
Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field…
Phenomenological evidence suggests the existence of non-trivial background fields in the QCD vacuum. On the other hand SU(3) gauge theory possessses three different classes of both non-generic and non-trivial strata that may be used as…
Using methods of effective field theory, we show that after resummation of Sudakov logarithms the spectral densities of interacting quark and gluon fields in ordinary quantum field theories such as QCD are virtually indistinguishable from…
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…