Related papers: Linearized Group Field Theory and Power Counting T…
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not…
We introduce a new family of tensorial field theories by coupling different fields in a non-trivial way, with a view towards the investigation of the coupling between matter and gravity in the quantum regime. As a first step, we consider…
Power counting is applied to relativistic mean-field energy functionals to estimate contributions to the energy from individual terms. New estimates for isovector, tensor, and gradient terms in finite nuclei are shown to be consistent with…
We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S,…
A successful effective field theory program requires besides the most general effective Lagrangian a perturbative expansion scheme for observables in terms of a consistent power counting method. We discuss a renormalization scheme for…
We investigate the possible structures of numbers (as physical quantities) over which accelerated observers can be modeled in special relativity. We present a general axiomatic theory of accelerated observers which has a model over every…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
We propose a novel diagrammatic method for computing transport coefficients in relativistic quantum field theory. The self-consistent equation for summing the diagrams with pinch singularities has a form of a linearized kinetic equation as…
We give a purely algebraic treatment of reduction theory for connections over the formal punctured disc. Our proofs apply to arbitrary connected linear algebraic groups over an algebraically closed field of characteristic 0. We also state…
We revisit the power counting of the Higgs Effective Field Theory (HEFT) from first principles, by requiring that predictions for physical observables follow a series expansion in small, dimensionless quantities. Depending on whether HEFT…
The corepresentation theory of continuous groups is presented without the assumption that the subgroup $G$ of the group with antilinear operations is unitary. The formulas of the corepresentation theory with unitary groups $G$ can be…
A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to…
The power graph $\Gamma_G$ of a finite group $G$ is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. In this paper, we classify the finite groups whose power graphs have…
If we consider a q-analogue of linear differential equation, Galoois group of the q-analogue difference equation is still a linear algebraic group. Namely, by a quantization of linear differential equation, Galois group is not quantized. We…
The power graph of a group $G$ is a graph with vertex set $G$, where two distinct vertices $a$ and $b$ are adjacent if one of $a$ and $b$ is a power of the other. Similarly, the enhanced power graph of $G$ is a graph with vertex set $G$,…
The power graph $\mathcal{P}(G)$ of a finite group $G$ is a graph whose vertex set is the group $G$ and distinct elements $x,y\in G$ are adjacent if one is a power of the other, that is, $x$ and $y$ are adjacent if $x\in\langle y\rangle$ or…
Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms of Group Theory; but some systems are much deeper, such as the axioms of…
We study nonlinear power systems consisting of generators, generator buses, and non-generator buses. First, looking at a generator and its bus' variables jointly, we introduce a synchronization concept for a pair of such joint generators…
Special theory of relativity has been formulated in a vacuum momentum-energy representation which is equivalent to Einstein special relativity and predicts just the same results as it. Although in this sense such a formulation would be at…