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The Batalin-Vilkovisky formalism in quantum field theory was originally invented to address the difficult problem of finding diagrammatic descriptions of oscillating integrals with degenerate critical points. But since then, BV algebras…

In this paper, we develop a nonequilibrium theory for transient electron transport dynamics in nanostructures based on the Feynman-Vernon influence functional approach. We extend our previous work on the exact master equation describing the…

For the massless N=1supersymmetric electrodynamics, regularized by higher derivatives, the Feynman diagrams, which define the divergent part of the two-point Green function and can not be found from Schwinger-Dyson equations and Ward…

Quantum graphity is a background independent model for emergent locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly…

The present paper provides a method for finding partial differential equations satisfied by the Feynman integrals for diagrams of various types, using the Griffiths theorem on the reduction of poles of rational differential forms. As an…

The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A…

In calculating Feynman diagrams at finite temperature, it is sometimes convenient to isolate subdiagrams which do not depend explicitly on the temperature. We show that, in the imaginary time formalism, such a separation can be achieved…

We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.

A factorisation property of Feynman diagrams in the context the Effective Field Theory approach to the compact binary problem has been recently employed to efficiently determine the static sector of the potential at fifth post-Newtonian…

We propose a new procedure by using the recursive Green's functions which remove all the repetition terms from the time-independent perturbation series for finite-level quantum systems. These Green's functions are introduced as a…

After a brief presentation of Feynman diagrams, we criticizise the idea that Feynman diagrams can be considered to be pictures or depictions of actual physical processes. We then show that the best interpretation of the role they play in…

There has been rapid development of systems that yield strong interactions between freely propagating photons in one dimension via controlled coupling to quantum emitters. This raises interesting possibilities such as quantum information…

We prove a deletion-contraction formula for motivic Feynman rules given by the classes of the affine graph hypersurface complement in the Grothendieck ring of varieties. We derive explicit recursions and generating series for these motivic…

We show that momentum space Feynman diagrams involving internal massless fields can be cast as conformal integrals. This leads to a classification of all Feynman diagrams into conformal families, labelled by conformal integrals. Computing…

For certain types of quantum graphs we show that the random-matrix form factor can be recovered to at least third order in the scaled time $\tau$ from periodic-orbit theory. We consider the contributions from pairs of periodic orbits…

The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…

We present a systematic description of the mathematical techniques for studying multiloop Feynman diagrams which constitutes a full-fledged and inherently more powerful alternative to the BPHZ theory. The new techniques emerged as a…

The differential equations satisfied by the wavefunction coefficients of conformally coupled scalars in a power-law cosmology can be recast into an iterative differential system of basis functions. These functions can be encoded within…

The mathematical formalism necessary for the diagramatic evaluation of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The evaluation of…

The symmetry factor of Feynman diagrams for real and complex scalar fields is presented. Being analysis of Wick expansion for Green functions, the mentioned factor is derived in a general form. The symmetry factor can be separated into two…