Theory Definition and 1000 Threads

Lattices are studied in mathematics. What physicists call a "lattice theory" uses the mathematical object that is a lattice, but it involves other things, such as associating elements of a group with the links between nodes of a lattice. Is there a mathematical term for lattices with this...

If (u,v) = 1, prove that (u+v,u-v) is either 1 or 2. Where (,) means: $$ux_1 + vx_2 = 1$$ $$u + v(x_2/x_1) = 1/x_1, u(x_1/x_2) + v = 1/x_2$$ $$u + v = 1/x_1 + 1/x_2 - v x_2/x_1 - u x_1/x_2$$ $$u - v = 1/x_1 - 1/x_2 + u x_1/x_2 - v x_2/x_1$$ Now we can express (u+v,u-v). But i am not sure if...

why the general wave vector q (in the proof of Bloch theorem in Ashcroft Mermin) is represented by k-K, where k is in the 1st BZ ? why not q=k+K ( usual vector form) what is special about k-K?

Is it possible to have some kind of General Relativistic Quantum Theory without passing through the stage of Quantum Field Theory (where Quantum Theory is married to Special Relativity)? Einstein attached primary significance to the concept of general covariance as shown in this letter in 1954...

As I've been studying statistical mechanics as well as some other things, I keep hearing about "information theory". For instance, I've heard about information theory as it relates to entropy, regarding some theorems of statistical mechanics, and I even heard about it in a Carl Bender lecture...

In the book: SET THEORY AND LOGIC By ROBERT S.STOLL in page 19 the following theorem ,No 5.2 in the book ,is given: If,for all A, AUB=A ,then B=0 IS that true or false If false give a counter example If true give a proof

I am self-studying Ivan Niven's An Introduction to the Theory of Numbers. Unfortunately, I find myself stuck while doing the problems. With this in mind, I would like to ask whether anyone here has the solution manual for Niven's textbook. Hopefully a softcopy version is available? Thank you in...

Hello there. What will physicists do after a theory of quantum gravity is found?Will they ask, if it is found ,more questions about it and try to develop it?What other questions will they make probably?Thank you.

Some good introductory string theory books that I know are GSW Polchinski McMahon Becker What are the good books at a more advanced level? Are there any such books, or do I have to dig it out of the research papers? There is a set of books called "mirror symmetry" and "dirichlet branes and...

Summary:: Good introductory book about Group Theory? Hi, I am looking for a good introductory book about Group Theory for physicists.

Consider the following scenario. A material has the E-k band scheme as shown in the figure (extended scheme of zones). Could anyone give me a suggestion regarding the following : Electrical character of the material with the temperature. Sign of the Hall coefficient. Sign of the effective mass...

So I know Dalton's law as stated above which I think is applicable in this question. Then I know the effusion rate is ##\frac{1}{4} n \bar{v}##, and from this we can make a differential for the time evolution of the number density of the gas in the container which is: ##\frac{dn}{dt} =...

Every second the universe branches into 5000 universes and each of those 5000 universes branches into 5000 more after one more second. Now, consider an 80 year old person, he has lived close to 80*365*24*60*60 seconds, which is 2.5 Billion seconds. So, in his life time, universe has branched...

Hi, I'm reading the following paper (L. Chua) about the state-of-art of dynamic non linear circuit analysis -- Chua_Dynamic_Circuits I've a doubt about Theorem 2 on section 3.2 On the Existence of the Resistor Function that establishes sufficient conditions for the existence of network...

From the german Version of Carlo Rovellis book "La realtà non è come ci appare. La struttura elementare delle cose" I have learned about the theory of Loop Quantum Gravity that space and time arise through the interactions of gravitational quanta, the space quanta have discrete volume spectra...

Cosmological inflationary models are general models in the sense that they could be applied to a variety of fundamental theories. Most physicists working in inflation assume that there is only one (but yet unknown) fundamental theory which through inflation would produce multiple regions or...

I only see it brought up in creationist attacks on evolution, definitely NOT trying to bring that up - curious if and how real biological science uses it. There are a couple of (expensive) older books and paywalled papers that seem legit, but cannot find much else for example...

Let us first take the S-matrix expansion (i.e. Dyson's formula) \begin{align*} S_{fi}&=\langle f | T \left\{ \exp\left( i\frac{\lambda_3}{3!}\int d^4 x :\phi \phi \phi (x) : + i\frac{\lambda_4}{4!}\int d^4 x :\phi \phi \phi \phi (x) : \right) \right\}| i \rangle \\ &= \langle f | i...

With free part L=-½(∂Φ)^2 -½m^2 Φ^2 and interaction term L=½gΦ^2Any help would be appreciated, thank you.

(NOTE: "$" == "String") https://getpocket.com/explore/item/dark-energy-may-be-incompatible-with-string-theory

YouTube has been suggesting videos about category theory of late, and I have spent some time skimming through them, without really understanding where it's all going. A question came to mind, namely: It seems reasonably conceivable that group theory could perhaps supply a vital key to the...

The claim states the following: Let ##(X,\mathcal{A},\mu)## be a measurable space, ##E## is a measurable subset of ##X## and ##f## is a measurable bounded function which has a bounded support in ##E##. Prove that: if ##f\ge 0## almost everywhere in ##E##, then for each measurable subset...

I was reading the book "A Fortunate Universe" by Geraint Lewis and Luke Barnes and something caught my attention: At page 195 the authors say that universes with different symmetries could be modeled and they would have dramatic results like having different conservation laws. I asked Mr...

Hey guys, I decide I need to learn the mathematics of molecular-orbital theory, to build on the qualitative approach of my chemistry coursee. To do this I also first need to study single-electron systems and then many-electron systems, the Born-Oppenheimer approximation, and relevant topics...

I've completed my PhD and am leaving the field to take up a career elsewhere, however I'm interested in developing my knowledge of string theory as a (potentially lifelong) side project. I have a solid understanding of GR and some extensions (my PhD was in relativistic effects in cosmology, and...

I know $$ i\mathcal{M}(\vec {k_1}\vec{k_2}\rightarrow \vec{p_1}\vec{p_2})(2\pi)^4\delta^{(4)}(p_1 +p_2-k_1-k_2) $$ =sum of all (all connected and amputated Feynman diagrams), but what is meant by 1 loop order? In other words, when I take the scattering matix element...

Hello. I do not understand how to solve systems of three or two congruences of one unknown of first order, a congruence of one unknown of second order and a system of diophantine equations of two or three unknowns. Could someone help me by providing examples in these cases? Thank you.

I’m reading Lancaster & Blundell, Quantum field theory for the gifted amateur (even tho I”m only an amateur...) and have a problem with their explanation of symmetry breaking from page 242. They start with this Lagrangian: ## \mathcal{L} = (\partial_{\mu} \psi^{\dagger} - iq...

Hi all, I was reading this article https://asiatimes.com/2020/11/the-big-bang-never-happened-but-fusion-will/ And I got somewhat confused. As most I've been taught that BB has succeeded in giving most of the cosmological predictions that we observe [nucleosynthesis, formation of galaxies, cmb...

For the first question, i believe that mechanical energy is conserved hence we can derive the total energy i think. In regards to the second question, I'm assuming its at room temperature, so helium is monotonic therefore it has 3 degrees of freedom, therefore its internal energy is 3/2KT. I am...

Hello there.Questions I have: what is the value of group theory?I am not trying to say that it is not important I want to know what made mathematicians study these objects and we still study them today.I know there are very interesting for me at least examples of groups like the Lie group but...

Is the partition function used in number theory and statistical mechanics the same thing?

I was wondering that if there was a theory that didn't have a mathematical formula yet but had experimental data how would a scientist go about publishing it? This isn't what I'm doing I'm just trying to see a possible process. Additional circumstances would be that the person publishing is a...

Summary:: Control Theory root equation pole Hi, I ran into a simple question but somehow I can't get it right. My work this far: ## G_0(s) = G(s) \cdot K \cdot \frac{1}{T_I s} = \frac{k}{\tau s +1} \cdot \frac{2\beta \tau -1}{k} \cdot \frac{2\beta^2 \tau}{Kks} = \frac{2\beta^2\tau}{s(\tau s...

Hi! So I have just been studying Yang-Mills theory advanced quantum field theory. In chapter 72 of Srednicki's book Quantum Field Theory they list the Feynman rules for non-abelian gauge theory. I was asked if I could show some sample allowed diagrams but I could not.. In standard particle...

Cumrun Vafa and colleagues have recently posted a new theory of the early universe in the paper: https://arxiv.org/abs/2009.10077 If anyone could explain the main themes of the paper in laymen friendly manner that would be really appreciated. In particular what is topological gravity ? how is...

Could you recommend a book to study the big bang theory and the background necessary, mainly in math, to understand the theory rigorously?

For any physical theory to be accepted, the consensus is that there must be a radical categorical separation between the formalism in which the theory is described (using exact mathematical language) and the empirical situation in which it is validated (using real world tools, materials and...

Before I attempt to delve into the math of tensors and curved spacetime, I'm hoping to get a more general intuitive grasp of things. As such, I'm parsing through a lot of lower level articles on these topics, and several that I've come across have argued that Newtonian gravity can be thought of...

Hopefully, I am in the right forum. I am trying to get an intuitive understanding of how fiber bundles can describe gauge theories. Gauge fields transform in the adjoint representation and can be decomposed as: Wμ = Wμata Gauge field = Gauge group x generators in the adjoint...

Given that Penrose now got the Nobel prize for a theory that is almost impossible to verify experimentally in a near future (that is, for theorems that predict singularities inside black holes), does it mean that now string theory can also get a Nobel prize? (If so, Witten and Schwarz would be...

Summary:: Need lecture notes for many body I want a lecture notes of a many body introduction course according to the book of "many body theory of solids" by John C.Inkson, Could anyone help me?

It is a wonderful book for learning QFT. Interesting problems with detailed solutions. I have tried the problems from chapter 1 to chapter 7. In most chapters, I could at least solve some part of the problems. But I got stuck in chapter 4, the Dirac equation. I could not solve any of the...

"The dual space is the space of all linear maps from the original vector space to the real numbers." Spacetime and Geometry by Carroll. Dual space can be anything that maps a vector space (including matrix and all other vector spaces) to real numbers. So why do we picked only a vector as a...

Quantum mechanics has argued for years that space is not a vacuum. Arguments attempting to brush aside quantum mechanics vacuum theory claiming, it's 'just a quantum mathematical theory' can now put to rest. In this article, laboratory experimentation demonstrates that the Casimir Effect can...

hi guys i saw this problem : if G is a group and a,b belongs to G and O(a) = e , b.a =a.b^2 then find O(b) , but i want to tackle this problem using Cayley diagrams , so my attempt is as following : $$ba =ab^{2}$$ then i might assume b as flipping , a as rotation : $$ fr = rf^{2}$$ then...

Hi, I just had a quick question about conventions in potential flow theory: Question: What is the convention for ## \Gamma ## for the streamline ## \Psi = \frac{\Gamma}{2\pi} ln(\frac{r}{a} ) ## and how can we interpret the Kutta-Jukowski Theorem ## Lift = - \rho U \Gamma ##? Approach: For the...

Hi everyone, I'm working through some group theory questions online. But unfortunately they don't have answers to go with them. So, I'm hoping you can say if I'm on the right track. If this is a binary operation on ℝ, am I right in thinking it satisfies the closure and associativity axioms...

I'm trying to dig up anything that supports or discounts Schommers' theory as it relates to Projection Theory. Tried some Googling and came up with naught.