Theory Definition and 1000 Threads

Proof: Let ## n\geq 1 ## be a natural number. Then \begin{align*} 2^{5n+1}+5^{n+2}&\equiv (2^{5n}\cdot 2+5^{n}\cdot 5^{2})\pmod {27}\\ &\equiv [(2^{5})^{n}\cdot 2+5^{n}\cdot 25]\pmod {27}\\ &\equiv (32^{n}\cdot 2+5^{n}\cdot 25)\pmod {27}\\ &\equiv (5^{n}\cdot 2+5^{n}\cdot 25)\pmod {27}\\...

Proof Let ## n\geq 1 ## be a natural number. Then \begin{align*} 3^{n+2}+4^{2n+1}&\equiv 3^{n}\cdot 3^{2}+(4^{2})^{n}\cdot 4\pmod {13}\\ &\equiv (3^{n}\cdot 9+16^{n}\cdot 4)\pmod {13}\\ &\equiv (3^{n}\cdot 9+3^{n}\cdot 4)\pmod {13}\\ &\equiv (3^{n}\cdot 13)\pmod {13}\\ &\equiv 0\pmod {13}...

Hello, i need help with the S-matrix. From what i understand, with the S-matrix i would be able to compute the scattering amplitude of some processes, is that correct? If so, how would i be able to do that if i have some field ##\phi(x,t)## in hands? Is that possible?

What do you recommend to read first, Supergravity by Freedman or A First Course in String Theory by Zweibach? For future consideration.

Roughly how many people in this world actually know about string theory? I'm guessing no more than a few hundred because the math of string theory is so esoteric.

This is a continuation of this post, which has been closed to replies: I am also really curious to better understand Jefimenko's theory of gravitation; I have the book, which apparently is no longer available on amazon, and I updated the wikipedia page to include his generalized gravitation...

I was wondering if there is any such textbook which shows how a real physicist actually goes about developing models and or theories to explain experimental observations. I want to see how it is done in practice. Is there such a book? At a level that an undergraduate can understand. It is great...

one of the claimed successes of string theory is its ability to derive the correct Hawking-Bekenstein equations to calculate the quantum entropy of a black hole without any free paramenters, specifically Extremal black hole entropy using supersymmetry and maximal charge. I was wondering if...

Ok for ##1##, we also have, ##a⋅0=a⋅(0+0)=a⋅0 + a⋅0 ## We know that ##a⋅0=0 ## by additive cancellation. For ##2.11##, Number ##2##; We first show and prove that ##-b=-1⋅b## adding ##b## on both sides, ##-b+b=0## for the lhs ##-1⋅b +1⋅b=b(-1+1)=b(0)=0## for the rhs therefore...

Hi, Sorry if this is a stupid question, but I haven't taken fluid mechanics classes and mechanical engineering ones. I understand that sometimes bearings get "dry" and you can regrease them. However I did some searching online and found that it's possible to over grease a bearing which can...

Townsend, quantum mechanics " In our earlier derivation we assumed that each unperturbed eigenstate ##\left|\varphi_{n}^{(0)}\right\rangle## turns smoothly into the exact eigenstate ##\left|\psi_{n}\right\rangle## as we turn on the perturbing Hamiltonian. However, if there are ##N## states ##...

Homework Statement:: See attached Relevant Equations:: Ring Theory Trying to go through my undergraduate notes on Ring Theory ( in appreciation to my Professor who opened me up to the beautiful World of Math)...anyways see attached... I need some clarity on the zero divisor. I am aware that...

McIntyre, quantum mechanics,pg360 Suppose states ##\left|2^{(0)}\right\rangle## and ##\left|3^{(0)}\right\rangle## are degenerate eigenstates of unperturbed Hamiltonian ##H## Author writes: "The first-order perturbation equation we want to solve is ##...

Find a perfect power k^m > 1 where k, m, k^m do not contain 2 in their decimal digits, nor do share any decimal digit, no matter if k^m might possibly be expressed in more than one way for some value, e.g. 8^2 = 4^3. I do not know if such an integer exists at all, or how many and how large they...

Do you have an opinion about my summary above? Do you understand the relation between irreversible logic and irreversible process? According to Landauer, logical irreversibility implies physical irreversibility. This is still a topic of debate it seems to me. Is the debate also about what logic...

I'm probably inadequately equipped to understand this paper by Bucholtz, Longo and Rehren on "Causal Lie products of free fields and the emergence of quantum field theory", but I decided to give it a try. Alas, I got stuck in the 1st para of sect 2 where it says: Although I've seen the term...

Merely studying formalism and theory in quantum mechanics is too dry and demotivating for me. I would appreciate being able to do more practical calculations and realistic applications instead of canned problems. Is there a way to balance this theory and applications? I have thought of doing...

In quantum field theory, we have the following expansion on a scalar field (I follow the convention of Schwarz's book) $$\phi(\vec{x},t)=\int d^3 p \frac{a_p exp(-ip_\mu x^\mu)+a_p^{\dagger}exp(ip_\mu x^\mu)}{(2\pi)^3 \sqrt{2\omega_p}} \quad p^{\mu}=(\omega_p,\vec{p})$$ With commutation relation...

Hello, I am better studying the theory that is the basis of Bayesian optimization with a Gaussian Process and the acquisition function EI. I would like to expose what I think I understand and ask you to correct me if I'm wrong. The aim is to find the best ##\theta## parameters for a parametric...

About the mathematical expressions of the first law of thermodynamics

Proof: Suppose that all primes except for 3 must have remainder of 1 or 2 when divided by 3. Then we have the form 3p+1 or 3p+2. Note that the product of integers of the form 3p+1 also have the form...

I tried to use the degenerated perturbation theory but I'm having problems when it comes to diagonalizing the perturbation q1ˆ3q2ˆ3 which I think I need to find the first order correction.

I came across this upcoming book -- https://press.princeton.edu/books/hardcover/9780691174297/quantum-field-theory-as-simply-as-possible -- peer reviewed as it is published by Princeton University Press, which is due to be published in October. I've already ordered a copy coming from the UK. It...

I’m looking for a book treating the fluid dynamics of solidification, in particular in the presence of solute concentration gradients. I have found an amazing article by G. Worster titled “Perspectives in fluid dynamics; solidification of fluids”. Are there others?

ok we shall have ##(A-B)∩(A-C)= [1,y]∩[1,2,x,y]=[1,y]## correct?

In my lecture, it was explained that Kirchhoff's Rule is used when circuits are too "complicated" to simplify by combining resistances in series and parallel. I do not understand in which cases I can simplify circuits by combining resistances, and on which cases I can only use Kirchoff's Rule...

Proof: Suppose for the sake of contradiction that gcd(a, b) \neq 1. Then there exists a prime number k that divides both a+b and ab. Note that k divides either a or b. Since k divides a+b, it follows that k divides b. Thus, this is a...

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.040403 In QM, I was taught that the imaginary unit ##i## in wave functions is merely a mathematical tool. It has no physical meaning. We can always take the real part of the complex wave functions. Therefore, there should be some...

I apologize for the simple question, but it has been bothering me. One can write a relationship between groups, such as for example between Spin##(n)## and SO##(n)## as follows: \begin{equation} 1 \rightarrow \{-1,+1 \} \rightarrow \text{Spin}(n) \rightarrow \text{SO}(n) \rightarrow 1...

Hello, can somebody help me out please? just watched this video so far understood but if motion changes the now frame its logic if the alien cylcles to the guy sitting that his time is slower and the guys time will be in the future (time delitation). but when the alien is moving away how can...

I'm trying to prove the following: ##wt(x+y) \leq wt(x) + wt(y)##, where "wt(x)" is referring to the weight of a specific code word. Proof: For two code words ##x, y \in F^{n}_2##, we have the inequalities ##0 \leq wt(x)## and ##0 \leq wt(y)##. Adding these together, we have ##0 \leq wt(x) +...

Hello, does anyone can help me with these tasks: I have no idea how to solve it

I am reading pretty much everywhere that LET (Lorentz Ether Theory, or call it Neo-Lorentzian Relativity, or whatever theory that involves a preferred undetectable frame with some yet unknown properties that make all the moving objects with respect to this frame length contact and time dilate)...

Hi all, I just graduated from my master's program in theoretical physics. I did 60% of the coursework in high energy physics and rest in condensed matter theory plus a few experimental physics courses. I did my master's thesis in what can be called as theoretical cosmology, studying particle...

Research into the Higgs boson suggest that the universe is in a false vacuum but I heard many physicists do not take it seriously as they think that if it were true we cannot even exist as it would have wiped us out billions of years ago. For example Katie Mack said that its like a piece of...

Hello, all. First, I want to apologize if this is not the correct forum or area of the forum for this question. Please direct me if I should be posting this somewhere else. I have some questions regarding what I believe is best described as the "theory" of electrical capacitance. As my...

For example, after the Lagrangian is renormalized at 1-loop order, it is of the form $$\mathcal{L}=\frac{1}{2}\partial^{\mu}\Phi\partial_{\mu}\Phi-\frac{1}{2}m^2\Phi^2-\frac{\lambda\Phi^4}{4!}-\frac{1}{2}\delta_m^2\Phi^2-\frac{\delta_{\lambda}\Phi^4}{4!}$$. So if I were to attempt to find the...

Hey guys, I just wanted to know if you think that a membrane field theory could ellucidate the non-perturbative framework of M-theory? Let me specify and explain what I mean by that: String field theory was intoduced to study the non-perturbative regime of string theory and some achievements in...

DLVO theory gives the curve of potential energy vs distance of two colloid particles. Potential energy curve is derived for colloids being only electrostatically stabilized and not sterically. Looking at the image below which shows potential energy curve, we can see two local minima and one...

Hello! I'm a physics graduate who is interested to work in Mathematical Physics. I haven't taken any specialized maths courses in undergrad, and currently I have some time to self-learn. I have finished studying Real Analysis from "Understanding Analysis - Stephen Abbott" and I'm currently...

I'm not sure the following passage is so trivial as it was supposed to be: I mean, what does exactly prove it? That's my question. The step is the following: if ##P## has a root ##\alpha## in ##\mathbf L## - an extension of ##\mathbf K## of degree <= ##\frac n 2## where n is the degree of ##P##...

I understand that string theory has almost no testable predictions, however loop quantum gravity is an enticing candidate for only quantum gravity and it doesn't explain much of symmetry, constants, mixing angles etc in Standard model. There is obviously not enough evidence to create a full...

I'd like someone to check that this solution is right, and if not, give me the point of failure and not the answer. Thanks!

Given the unperturbed Hamiltonian ##H^0## and a small perturbating potential V. We have solved the original problem and have gotten a set of eigenvectors and eigenvalues of ##H^0##, and, say, two are degenerate: $$ H^0 \ket a = E^0 \ket a$$ $$ H^0 \ket b = E^0 \ket b$$ Let's make them...

Or will confirm its predictions? As far as I can tell, you can only raise the bar on the energies required from the accelerator, but you cannot give an upper bound, where beyond it the theory is doomed... This isn't science... we might as well say we need infinite energies. 🙃

So far, I've taken Ordinary Differential Equations and Introduction to Mathematical Proof. My plan is to take "Introduction To Number Theory" for next semester in Spring 2022. But my professor told me that she won't use a textbook for this class. I was wondering what are some of the good...

I am doing private studies in string theory and am reading "A first course in string theory" by Barton Zwiebach. Below equation 6.52 the author says "Since the second term on the right-hand side must vanish...". I do not understand why this term must vanish, and I would be grateful for an...

Hello folks, I am currently studying from Griffiths' Introduction to Quantum Mechanics and I've got a doubt about good quantum numbers that the text has been unable to solve. As I understand it, good quantum numbers are the eigenvalues of the eigenvectors of an operator O that remain...

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