The Polyakov action is an important concept in theoretical physics, particularly in the context of string theory. It is a two-dimensional field theory that describes the dynamics of strings in spacetime. Named after the physicist Alexander Polyakov, the action provides a framework to model how strings propagate and interact in a background spacetime.
The term "primary field" can refer to different concepts depending on the context in which it's used. Here are a few interpretations: 1. **Data Management**: In databases, a primary field (or primary key) is a unique identifier for each record in a table. It ensures that each entry can be uniquely identified and accessed, preventing duplicates.
The RST model, or Rhetorical Structure Theory, is a framework used to analyze the structure of discourse and the relationships between different parts of text or conversation. It was developed by William Mann and Sandra Thompson in the late 1980s. The model provides a way to understand how various components of a text connect with each other to convey meaning and achieve communicative goals.
The term "scaling dimension" can refer to different concepts depending on the context in which it is used, particularly in physics and mathematics. Here are a couple of relevant interpretations: 1. **In Physics (Statistical Mechanics and Quantum Field Theory)**: The scaling dimension is a property of operators in conformal field theories (CFTs). It describes how the correlation functions of those operators change under rescaling of the coordinates.
The Coase Conjecture is a concept in economics proposed by economist Ronald Coase. It addresses the behavior of firms when they sell durable goods, particularly how they set prices over time. The conjecture suggests that if a firm sells a durable good (a product that lasts a long time, like cars or appliances) and has market power, it will face a challenge in setting prices optimally.
The Conley Conjecture is a proposition in the field of dynamical systems, particularly related to the study of Hamiltonian systems and their behavior in the context of symplectic geometry. Formulated by Charles Conley in the early 1970s, the conjecture specifically concerns the existence of certain types of periodic orbits for Hamiltonian systems.
De Branges's theorem, often referred to in the context of de Branges spaces, is a significant result in the theory of entire functions, specifically related to the representation of certain types of entire functions through Hilbert spaces. The theorem addresses the existence of entire functions that can be represented in terms of their zeros and certain properties related to their growth and behavior. More formally, it provides conditions under which a function defined by its Taylor series can be expressed in terms of its zeros or certain integral representations.
Superconformal algebra is an extension of the conformal algebra that incorporates supersymmetry, a key concept in theoretical physics. Conformal algebra itself describes the symmetries of conformal field theories, which are invariant under conformal transformations—transformations that preserve angles but not necessarily distances. These symmetries are important in various areas of physics, particularly in the study of two-dimensional conformal field theories and in string theory.
In the context of theoretical physics—particularly in string theory—the term "twisted sector" refers to a particular construction related to the compactification of extra dimensions and the nature of string states. In string theory, especially in theories involving compactification (where extra dimensions are rolled up to a small scale), the Hilbert space of string states can be divided into different sectors based on how the strings wrap around the compact dimensions.
The Virasoro conformal block is a fundamental concept in conformal field theory (CFT), particularly in two-dimensional CFTs. It plays an important role in the study of correlation functions of primary fields in such theories. ### Key Points: 1. **Virasoro Algebra**: The Virasoro algebra is an extension of the Lie algebra of the conformal group, which arises in the context of 2D conformal field theories.
The Witt algebra is a type of infinite-dimensional Lie algebra that emerges prominently in the study of algebraic structures, particularly in the context of mathematical physics and algebra. It can be thought of as the Lie algebra associated with certain symmetries of polynomial functions.
The Ibragimov–Iosifescu conjecture pertains to the behavior of certain types of stochastic processes, particularly concerning the convergence of $\phi$-mixing sequences. A sequence of random variables \((X_n)_{n \in \mathbb{N}}\) is said to be $\phi$-mixing if it satisfies a certain criterion that measures the dependence between random variables that are separated by a certain distance.
Selberg's 1/4 conjecture, proposed by the Norwegian mathematician Atle Selberg, is a conjecture in the field of number theory and specifically related to the distribution of the zeros of the Riemann zeta function and other Dirichlet series.
The Arnold conjecture, proposed by the mathematician Vladimir Arnold in the 1960s, is a statement in the field of symplectic geometry and dynamical systems. It relates to the fixed points of Hamiltonian systems, which arise in the study of physics and mechanics.
The Calogero conjecture, proposed by Salvatore Calogero in the early 1990s, is a conjecture in the field of mathematical physics, specifically in the study of integrable systems. It generally concerns certain mathematical structures known as "Calogero-Moser systems," which are defined on a set of particles interacting through a specific type of potential. The conjecture itself relates to the behavior of the eigenvalues of certain matrices that arise in the context of these systems.
The Chronology Protection Conjecture is a theoretical idea in physics that was proposed by physicist Stephen Hawking. It suggests that the laws of physics may prevent time travel to the past in order to avoid potential paradoxes and violations of causality.
Ehrhart's volume conjecture is a conjecture in the field of combinatorial geometry and involves the study of convex polytopes and their integer lattice points. More specifically, it relates the number of integer points in dilates of a polytope to the volume of the polytope.
The Duffin–Schaeffer theorem is a result in the field of number theory, specifically in the study of Diophantine approximation. It addresses the question of how well real numbers can be approximated by rational numbers under certain conditions.
Khabibullin's conjecture, proposed by the mathematician Ildar Khabibullin, revolves around integral inequalities related to certain classes of functions, particularly focusing on the relationships that hold for integrals of products of functions and their transformations. The conjecture suggests specific bounds and properties for these integrals, often drawing upon known results in functional analysis, inequalities, and perhaps the theory of convex functions.
Lafforgue's theorem is a result in the field of mathematics, specifically in the area of number theory and the theory of automorphic forms. It is associated with Laurent Lafforgue and pertains to the Langlands program, which aims to connect number theory and representation theory.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. - Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact