Related papers: Intermediate Field Representation for Positive Mat…
In this paper we give explicit first order Lagrangian formulation for mixed symmetry tensor fields \Phi_{[\mu\nu],\alpha}, T_{[\mu\nu\alpha],\beta} and R_{[\mu\nu],[\alpha\beta]}. We show that such Lagrangians could be written in a very…
Antisymmetric tensor fields interacting with quarks and leptons have been proposed as a possible solution to the gauge hierarchy problem. We compute the one-loop beta function for a quartic self-interaction of the chiral antisymmetric…
It is proved that for each prime field $GF(p)$, there is an integer $f(p)$ such that a 4-connected matroid has at most $f(p)$ inequivalent representations over $GF(p)$. We also prove a stronger theorem that obtains the same conclusion for…
The paper proves the intermediate value theorem for polynomials and power series over a valued field with divisible valuation group and infinite residue field. Some further results on the behaviour of the valuation are obtained using…
"Resummed-Range Effective Field Theory'' is a consistent nonrelativistic effective field theory of contact interactions with large scattering length $a$ and an effective range $r_0$ large in magnitude but negative. Its leading order is…
The Loop Vertex Expansion (LVE) is a constructive technique using canonical combinatorial tools. It works well for quantum field theories without renormalization, which is the case of the field theory studied in this paper. Tensorial Group…
Fourth-order tensor-valued functions appear in numerous fields of study. The formulation of practical models for these complex functions often requires their representation in terms of tensors of order two. In this paper, we develop an…
Cubic couplings between a complex scalar field and a tower of symmetric tensor gauge fields of all ranks are investigated. A symmetric conserved current, bilinear in the scalar field and containing r derivatives, is provided for any rank…
In this work we study the interaction strength among a neutral scalar boson and two massless vector bosons in presence of an external magnetic field. Based on global symmetries, we build the general tensor structure amplitude…
Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus here is the class of physically symmetric and positive…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
A free field representation for the type $I$ vertex operators and the corner transfer matrices of the eight-vertex model is proposed. The construction uses the vertex-face correspondence, which makes it possible to express correlation…
We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants…
We propose a discrete-space representation of a one-dimensional zero-range odd-parity pseudopotential. The proposed representation is validated by applying it to the analytically solvable case of two fermions in a harmonic trap and…
We define new norms for symmetric tensors over ordered normed spaces; these norms are defined by considering linear combinations of tensor products or powers of positive elements only. Relations between the different norms are studied. The…
In a previous paper, field theory in curved space was considered, and a formula that expresses the first order variation of correlation functions with respect to the external metric was postulated. The formula is given as an integral of the…
Theories containing infinite number of higher spin fields require a particular definition of summation over spins consistent with their underlying symmetries. We consider a model of massless scalars interacting (via bilinear conserved…
We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on…
A representation field for a non-maximal order $\Ha$ in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders containing a copy of $\Ha$. Not every…
It is well-known that a symmetric matrix with its entries $\pm1$ is not positive definite. But this is not ture for symmetric tensors (hyper-matrix). In this paper, we mainly dicuss the positive (semi-)definiteness criterion of a class of…