Related papers: Generating Functionals for Quantum Field Theories …
In these lectures we consider some topics of Quantum Field Theory in Curved Space. In the first one particle creation in curved space is studied from a mathematical point of view, especially, particle production at a given time using the so…
We calculate connected correlators in Gaussian orthogonal, unitary and symplectic random matrix ensembles by the replica method in the 1/N-expansion. We obtain averaged one-point Green's functions up to the next-to-leading order O(1/N) and…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
In this paper we continue the study of codes over imaginary quadratic fields and their weight enumerators and theta functions. We present new examples of non-equivalent codes over rings of characteristic $p=2$ and $p=5$ which have the same…
In the paper we begin a description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and are the q-generalization of the colored particles which appear in many…
Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs…
Algorithms for computing rational generating functions of solutions of one-dimensional difference equations are well-known and easy to implement. We propose an algorithm for computing rational generating functions of solutions of…
Gaussian fields $(g_x)$ on $\mathbb{Z}_q^d$ are constructed from a class of reversible long range random walks $(X_t)_{t\in \mathbb{N}}$ on $\mathbb{Z}_q^d$ in arXiv:2510.22554. The construction is from taking the covariance function of…
In quantum field theory (QFT), the vacuum expectation value of a normal product of creation and annihilation operators is always zero. This simple property paves the way to the classical treatment of perturbative QFT. This is no longer the…
This article will review quantum particle creation in expanding universes. The emphasis will be on the basic physical principles and on selected applications to cosmological models. The needed formalism of quantum field theory in curved…
The solution of QCD equations for generating functions of multiplicity distributions reveals new peculiar features of cumulant moments oscillating as functions of their rank. This prediction is supported by experimental data on $e^{+}e^{-},…
We construct a $k$-fold $q$-series as a generating function of $k$-regular partitions for each positive integer $k$. The $k=1$ case is one of Euler's $q$-series identities pertaining to the partitions into distinct parts. The construction…
We present a pedagogical, hands-on tutorial on \emph{replica tensor-network} techniques for random quantum circuits. At its core, the method recasts circuit-averaged observables acting on multiple copies of the system as the contraction of…
I define central functions c(g) and c'(g) in quantum field theory, useful to study the flow of the numbers of vector, spinor and scalar degrees of freedom from the UV limit to the IR limit and basic ingredients for a description of quantum…
An infinite range spin glass like model for granular systems is introduced and studied through the replica mean field formalism. Equilibrium, density dependent properties under vibration and gravity are obtained.
Many phenomena and fundamental predictions, ranging from Hawking radiation to the early evolution of the Universe rely on the interplay between quantum mechanics and gravity or more generally, quantum mechanics in curved spacetimes.…
By treating generators of the reflection equation algebra corresponding to a Hecke symmetry as quantum analogs of vector fields, we exhibit the corresponding Leibniz rule via the so-called quantum doubles. The role of the function algebra…
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…
We provide a generating functional for the gravitational field, associated to the relaxation of the primary constraints as extended to the quantum sector. This requirement of the theory, relies on the assumption that a suitable time…