Related papers: BBGKY Hierarchy in Scalar QFT
For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework…
We discuss the relations between (topological) quantum field theories in 4 dimensions and the theory of 2-knots (embedded 2-spheres in a 4-manifold). The so-called BF theories allow the construction of quantum operators whose trace can be…
We develop the basic formalism of complex $q$-analysis to study the solutions of second order $q$-difference equations which reduce, in the $q\rightarrow 1$ limit, to the ordinary Laplace equation in Euclidean and Minkowski space. After…
The standard way to do computations in Quantum Field Theory (QFT) often results in the requirement of dramatic cancellations between contributions induced by a "heavy" sector into the physical observables of the "light" (or low energy)…
We introduce a new class of gauge field theories in any complex dimension, based on algebra-valued (p,q)-forms on complex n-manifolds. These theories are holomorphic analogs of the well-known Chern-Simons and BF topological theories defined…
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
This is a further explanation of a new and simple renormalization approach recently proposed by the author (hep-th/9708104, Ref. [1], that is somewhat sketchy) for any ordinary QFT (whether renormalizable or not) in any spacetime dimension.…
The transfer operator due to Bogomolny provides a convenient method for obtaining a semiclassical approximation to the energy eigenvalues of a quantum system, no matter what the nature of the analogous classical system. In this paper, the…
New equations governing the scale transformation behaviors of a QFT with underlying structures are derived. These equations, with their several equivalent versions, can yield some new and significant insights and results that are difficult…
The construction of heavy quark effective field theory (HqEFT) is extended to arbitrary order in both expansion parameters $\alpha_s$ and $1/m_q$. Matching conditions are discussed for the general case, and it is verified that this approach…
We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending 't~Hooft's one-loop result. The method can also be used for theories with…
In the paper by Bazeia D. et al., EPL, 119 (2017) 61002, the authors demonstrate the equivalence between the second-order differential equation of motion and a family of first-order differential equations of Bogomolnyi type for the cases of…
A systematic analysis is made of the relations between the symmetries of a classical field and the symmetries of the one-particle quantum system that results from quantizing that field in regimes where interactions are weak. The results are…
We discuss motivation and goals of renormalization analyses of group field theory models of simplicial 4d quantum gravity, and review briefly the status of this research area. We present some new computations of perturbative GFT (spin foam)…
Topological defects and operators give a far-reaching generalization of symmetries of quantum fields. An auxiliary topological field theory in one dimension higher than the QFT of interest, known as the SymTFT, provides a natural way for…
A finite formulation of quantum field theory based on a system of differential equations reminiscent of the Callan-Symanzik equations is discussed. This system of equations was previously formulated in the bare language. We rederive it in a…
We begin with personal notes describing the atmosphere of "Bogoliubov renormalization group" birth. Then we expose the history of RG discovery in the QFT and of the RG method devising in the mid-fifties. The third part is devoted to…
In this article, we propose a q-analogue of the Drinfeld-Sokolov hierarchy of type A. We also discuss its relationship with the q-Painleve VI equation and the q-hypergeometric function.
In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one…
The quantum correlations of scalar fields are examined as a power series in derivatives. Recursive algebraic equations are derived and determine the amplitudes; all loop integrations are performed. This recursion contains the same…