Related papers: Mixed Models: Combining Incompatible Scalar Models…
N=2 supersymmetric field theories in two dimensions have been extensively studied in the last few years. Many of their properties can be determined along the whole renormalization group flow, like their coupling dependence and soliton…
Certain power-counting non-renormalizable theories, including the most general self-interacting scalar fields in four and three dimensions and fermions in two dimensions, have a simplified renormalization structure. For example, in…
Constructing renormalizable models on non-commutative spaces constitutes a big challenge. Only few examples of renormalizable theories are known, such as the scalar Grosse-Wulkenhaar model. Gauge fields are even more difficult, since new…
We report on a comprehensive analysis of the renormalization of noncommutative \phi^4 scalar field theories on the Groenewold-Moyal (GM) plane. These scalar field theories are twisted Poincar\'e invariant. Our main results are that these…
Graphical models are an important tool in exploring relationships between variables in complex, multivariate data. Methods for learning such graphical models are well developed in the case where all variables are either continuous or…
We present a covariant decomposition of Einstein's Field Equations which is particularly suitable for perturbations of spherically symmetric -- and general locally rotationally symmetric -- spacetimes. Based upon the utility of the 1+3…
We investigate the phase structure of non-commutative scalar field theories and find evidence for ordered phases which break translation invariance. A self-consistent one-loop analysis indicates that the transition into these ordered phases…
In this work a class of massive scalar field theories with self-interactions described by a general potential is studied. Under the sole condition that the potential admits the Fourier representation, it is shown that such theories may be…
Model fusion seeks to combine independently trained neural networks into a single model without retraining, but is complicated by representational divergence arising from permutation invariance, random initialization, and heterogeneous…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is presented. The paradigm example studied in this paper is the Euclidean scalar field with a…
The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel…
Theory of massless scalar field $\phi$ with interaction $g \phi^3$ in six-dimensional space is considered. A possibility of initial scale invariance breaking, which results in a spontaneous arising of effective interaction $G \phi^4$, is…
Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…
New developments on the symmetries of non-relativistic field theoretical models on the non commutative plane are reviewed. It is shown in particular that Galilean invariance strongly restricts the admissible interactions. Moreover, if a…
We present globally supersymmetric models of gauged scale covariance in ten, six, and four-dimensions. This is an application of a recent similar gauging in three-dimensions for a massive self-dual vector multiplet. In ten-dimensions, we…
Multilevel modeling extends traditional modeling techniques with a potentially unlimited number of abstraction levels. Multilevel models can be formally represented by multilevel typed graphs whose manipulation and transformation are…
Most general renormalizable interaction in the system with a set of scalar fields having identical quantum numbers generates naturally mixed kinetic terms in the Lagrangian. Taking into account these terms leads to modification both the…
New classes of classically integrable models in the cosmological theories with a scalar field are obtained by using freedoms of defining time and fields. In particular, some models with the sum of exponential potentials in the flat spatial…
Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…
In this work we study various aspects of supersymmetric three-dimensional higher-derivative field theories. We classify all possible models without derivative terms in the auxiliary field of the fermionic sector and find that scalar field…