Related papers: Intermediate Field Representation for Positive Mat…
Skew-representable matroids form a fundamental class in matroid theory, bridging combinatorics and linear algebra. They play an important role in areas such as coding theory, optimization, and combinatorial geometry, where linear structure…
A scheme suggested in the literature to determine the symmetry-imposed shape of linear response tensors is revised and extended to allow for the treatment of more complex situations. The extended scheme is applied to discuss the shape of…
In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a $1/p^2$ propagator and quartic interactions and on the comparison…
This thesis investigates the interactions of partially massless (PM) fields in 4-dimensional (anti)de Sitter spaces, along with conformal higher spin fields and their coupling to matter in arbitrary dimensions. The first part of the thesis…
We investigate simulation-based bandpower covariance matrices commonly used in cosmological parameter inferences such as the estimation of the tensor-to-scalar ratio $r$. We find that upper limits on $r$ can be biased low by tens of…
While conformal transformations in metric scalar-tensor theories recover General Relativity, this feature is notably absent in standard non-metricity-based theories. We demonstrate that by introducing the boundary term C, a non-metricity…
We develop the spectral representation of propagator for $n$ mixing fermion fields in the case of $\mathsf{P}$-parity violation. The approach based on the eigenvalue problem for inverse matrix propagator makes possible to build the system…
The tensorial principal component analysis is a generalization of ordinary principal component analysis, focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative…
We consider a special class of quantum non-dynamical $R$-matrices in the fundamental representation of ${\rm GL}_N$ with spectral parameter given by trigonometric solutions of the associative Yang-Baxter equation. In the simplest case $N=2$…
We propose that maximal depth, partially massless, higher spin excitations can mediate charged matter interactions in a de Sitter universe. The proposal is motivated by similarities between these theories and their traditional Maxwell…
In the presence of a thermal medium or an external electro-magnetic field, neutrinos can interact with photon, mediated by the corresponding charged leptons (real or virtual). The effect of a medium or an electromagnetic field is two-fold -…
We give the complete list of all first-order consistent interaction vertices for a set of exterior form gauge fields of form degree >1, described in the free limit by the standard Maxwell-like action. A special attention is paid to the…
The paper introduces the isotopic Foldy-Wouthuysen representation. This representation was used to derive equations for massive interacting fermion fields. When the interaction Hamiltonian commutes with the matrix, these equations possess…
We establish basic information about border rank algorithms for the matrix multiplication tensor and other tensors with symmetry. We prove that border rank algorithms for tensors with symmetry (such as matrix multiplication and the…
A coordinate-space representation for a charged scalar particle propagator in a constant magnetic field was obtained as a series over the Landau levels. Using the recently developed modified Fock-Schwinger method, an intermediate expression…
Many observables in quantum field theory can be expressed in terms of trans-series, in which one adds to the perturbative series a typically infinite sum of exponentially small corrections, due to instantons or to renormalons. Even after…
We discuss a general mean field plus random phase approximation (RPA) for describing composite systems at zero and finite temperature. We analyze in particular its implementation in finite systems invariant under translations, where for…
We study the 2D massive fields in the presence of moving mirrors. We do that for standing mirror and mirror moving with constant velocity. We calculate the modes and commutation relations of the field operator with the corresponding…
We prove that $\Theta$-positive representations of fundamental groups of surfaces (possibly cusped or of infinite type) satisfy a collar lemma, and their associated cross-ratios are positive. As a consequence we deduce that…
The effective approach is applied to the analysis of inflationary magnetogenesis. Rather than assuming a particular underlying description, all the generally covariant terms potentially appearing with four space-time derivatives in the…