These lectures review the formalism of renormalization in quantum field theories with special regard to effective quantum field theories. While renormalization theory is part of every advanced course on quantum field theory, for effective theories so...
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection "Mathematica...
A particular exact solution of Einstein's Hermitian theory of relativity is examined, after recalling that there is merit in adding phenomenological sources to the theory, and in choosing the metric like it was done long ago by Kursunoglu and Hely....
In this article, we further the study of higher K-theory of dg categories via universal invariants, initiated by the second named author. Our main result is the co-representability of non-connective K-theory by the base ring in the universal locali...
This paper proposes a gravitodynamic theory because there are similarities between gravitational theory and electrodynamics. Based on Einstein's principle of equivalence, two coordinate conditions are proposed into the four-dimensional line element...
This is a survey article that advertizes the idea that there should exist a theory of p-adic local analogues of Shimura varieties. Prime examples are the towers of rigid-analytic spaces defined by Rapoport-Zink spaces, and we also review their theory...
We construct a version of Beilinson's regulator as a map of sheaves of commutative ring spectra and use it to define a multiplicative variant of differential algebraic K-theory. We use this theory to give an interpretation of Bloch's construction of...
Involutive category theory provides a flexible framework to describe involutive structures on algebraic objects, such as anti-linear involutions on complex vector spaces. Motivated by the prominent role of involutions in quantum (field) theory, we de...
Theory of digital signal processing (DSP): signals, filtration (IIR, FIR, CIC, MAF), transforms (FFT, DFT, Hilbert, Z-transform) etc. (⭐ 1186)
It has been shown that double field theory (DFT) action can be constructed in a perturbative manner up to cubic order by using double copy of Yang-Mills. This construction can also be extended by starting with higher-derivative Yang-Mills theory to o...
We provide exposition into the field of projection theory, which lies at the intersection of incidence geometry and geometric measure theory. We first give the necessary preliminaries in Chapter 2, focusing on incidences between points and lines and...
The string theory introduced in early 1971 by Ramond, Neveu, and myself has two-dimensional world-sheet supersymmetry. This theory, developed at about the same time that Golfand and Likhtman constructed the four-dimensional super-Poincaré algebra,...
The theory of eleven dimensional supergravity on R^10 x S^1/Z_2 with super Yang-Mills theory on the boundaries is reconsidered. We analyse the general solution of the modified Bianchi identity for the four-form field strength using the equations of...
We describe a refinement of the general theory of higher rank Euler, Kolyvagin and Stark systems in the setting of the multiplicative group over arbitrary number fields. We use the refined theory to prove new results concerning the Galois structure o...
The BMN Matrix model can be regarded as a theory of coincident M-theory gravitons, which expand by Myers dielectric effect into the 2-sphere and 5-sphere giant graviton vacua of the theory. In this note we show that, in the same fashion, Matrix Str...
This article is devoted to the status of the electroweak theory on the eve of experimentation at CERN's Large Hadron Collider. A compact summary of the logic and structure of the electroweak theory precedes an examination of what experimental tests...
We propose a double-scaling limit of $β$-deformed ABJM theory in three-dimensional $\mathcal{N} = 2$ superspace, and a non-local deformation thereof. Due to the regular appearance of the theory's Feynman supergraphs, we refer to this superconformal...
This short note is devoted to the representative dynamics, which realizes a link between the theory of controlled systems and representation theory. Dynamical inverse problem of representation theory for controlled systems is considered: to solve i...
Since Wilson's work on lattice gauge theory in the 1970s, discrete versions of field theories have played a vital role in fundamental physics. But there is recent interest in certain higher dimensional analogues of gauge theory, such as p-form elec...
We begin with a context more general than set theory. The basic ingredients are essentially the object and functor primitives of category theory, and the logic is weak, requiring neither the Law of Excluded Middle nor quantification. Inside this we f...