Related papers: On the Enumerative Structures in Quantum Field The…
Since the quantum field theory treats a system of particles, there must be a distribution which is associated with the system of particles. It means that a meaningful quantity is adjoined in the system of particles. It seems that these…
We revisit the damped string equation on a compact interval with a variety of boundary conditions and derive an infinite sequence of trace formulas associated with it, employing methods familiar from supersymmetric quantum mechanics. We…
In quantum field theory, characteristics of resonances are related to self-energy diagrams, which are ultra-violet divergent and require renormalization. We demonstrate the proper way to define the resonance coupling $g_M$ such that the…
A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of…
We employ the recent results on the generalization of the $c$-theorem to 2+1-d to derive non-perturbative results for strongly interacting quantum field theories, including QED-3 and the critical theory corresponding to certain quantum…
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed.…
To set up a self-consistent quantum field theory of degenerate systems, the unperturbed state should be described by a density matrix instead of a pure state. This increases the combinatorial complexity of the many-body equations. Hopf…
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…
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…
An arbitrary renormalizable quantum field theory is considered as finite if its dimensionless couplings conspire to yield, at every order of its perturbative expansion, no ultraviolet-divergent renormalizations of the physical parameters of…
This paper investigates the relationships between closed and mixed string amplitudes at the tree level in string theory. Through the analytic continuation of complex variables, we establish a factorization of closed string amplitudes into…
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…
I review the formalism, Feynman rules, and combinatorics that constrain a field to propagate ``classically", strictly in tree diagrams, either by itself, or interacting with other, purely quantum fields. The perturbation theory is…
The large-$N$ quantum field theories provide a window into the regime of strongly-coupled physics. Our principal object of study in this thesis is the large-$N$ family of melonic QFTs, which contain the Sachdev-Ye-Kitaev-like models, tensor…
Methods of summation of power series relevant to applications in quantum theory are reviewed, with particular attention to expansions in powers of the coupling constant and in inverse powers of an energy variable. Alternatives to the Borel…
In view of various field-theoretic reasons, in the present work, we study the question of if the usual dimensional regularization can be extended to quantum field theories with an ultraviolet cutoff (Poincare-breaking scale) in a way…
The solution of some equations involving functional derivatives is given as a series indexed by planar binary trees. The terms of the series are given by an explicit recursive formula. Some algebraic properties of these series are…
We study symmetries of quantum field theories involving topologically distinct sectors of the field space. To exhibit these symmetries we define special gauge invariant observables, which we call the $qq$-characters. In the context of the…
We propose a quantum field theory (QFT) method to approach the classification of indefinite sector of Kac-Moody algebras. In this approach, Vinberg relations are interpreted as the discrete version of the QFT_{2} equation of motion of a…
Practically measurable quantities resulting from quantum field theory are not described by hermitian operators, contradicting one of the cornerstone axioms of orthodox quantum theory. This could be a sign that some of the axioms of orthodox…