Related papers: Notes on Tensor Models and Tensor Field Theories
Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the $20^{\text{th}}$ century, they have since then spread to…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…
We study the dynamics of the scalar tensor cosmological model in the presence of tachyon field. In an alternative approach, in two exponential and power law form of the scalar field functions in the model, field equations are solved by…
In this note we wish to complement some recent work in the cosmological literature concerning the Weyl conformal curvature tensor and its parts. In particular, we shall give a clear-cut definition of the Newtonian limits of electric and…
Tensor network methods have been a key ingredient of advances in condensed matter physics and have recently sparked interest in the machine learning community for their ability to compactly represent very high-dimensional objects. Tensor…
A conceptual summary is given of a deterministic unified field and particle theory (the metron model) developed in more mathematical detail in a four-part paper published in Physics Essays (1996/97). The model is developed from Einsteins…
Recently, several discussions on the possible observability of 4-vector fields have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 fundamental field. We re-examine the theory of…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…
These lecture notes are intended as an introduction to several notions of tensor rank and their connections to the asymptotic complexity of matrix multiplication. The latter is studied with the exponent of matrix multiplication, which will…
We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean…
We present the superfield generalization of free higher spin equations in tensorial superspaces and analyze tensorial supergravities with GL(n) and SL(n) holonomy as a possible framework for the construction of a non-linear higher spin…
We prove the existence of a 1/N expansion to all orders in beta matrix models with a confining, off-critical potential corresponding to an equilibrium measure with a connected support. Thus, the coefficients of the expansion can be obtained…
Tensor models admit the large $N$ limit, dominated by the graphs called melons. The melons are characterized by the Gurau number $\varpi=0$ and the amplitude of the Feynman graphs are proportional to $N^{-\varpi}$. Other leading order…
Newtonian limit of Extended Theories of Gravity (in particular, higher--order and scalar--tensor theories) is theoretically discussed taking into account recent observational and experimental results.
Tensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They are not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus of…
Abstract. The purpose of this paper is twofold. We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work arXiv:1910.08492, to study the propagation of randomness under…
We study new consistent scalar-tensor theories of gravity recently introduced by Langlois and Noui with potentially interesting cosmological applications. We derive the conditions for the existence of a primary constraint that prevents the…
We suggest an extension of the gauge principle which includes tensor gauge fields. In this extension of the Yang-Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The…
We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…