Theory Definition and 1000 Threads

The author start of with $\frac{1}{(y+\sqrt{3})^2} - 2 \cdot \frac{1}{1 + y^2} \left( \frac{y}{\sqrt{1+y^2}} \right) = 0$ and arrives at the equation $y = \frac{(1+y^2)^{3/2}}{2(y+\sqrt{3})^2}$ The solution is merely by iterating (use an initial guess value of y, calculate the RHS, then use this...

In the famous book, Gravitation, by Misner, Thorne and Wheeler, it talks about the stress-energy tensor of a swarm of particles (p.138). The total stress-energy is summed up from all categories of particles. Is summation meaningful in the non-linear theory of Einstein gravitation? Thanks.

Summary:: recommend learning materials Although I took galois theory as an undergraduate, I never really studied it. Any recommendations for good resources?

This is purely a historical question that came up in another thread. I always thought LET was the theory put forward by Lorentz that said the Lorentz-Fitzgerald formula contracts objects moving through the aether. Clocks slowed down due to a shortening of their components. Light was an...

Does the law of conservation of mass fail to meet the first postulate of the special theory of relativity(the laws of physics are the same in all inertial frames of reference)?

Hi everyone! I’ve just discovered Freud‘s theory's, how fascinating! I was searching the web for information on narcissism and stumbled across this. I’ve got a lot of issues from my childhood and have had little help from the mental health sector, not for the lack of trying. I truly believe we...

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Hi, I was looking at this derivation https://en.wikipedia.org/wiki/Derivations_of_the_Lorentz_transformations#From_group_postulates and I was wondering 1- where does the group structure come from? The principle of relativity? or viceversa? or what? 2- why only linear transformations? I remember...

Are there any living Nobel laureates in physics (apart from David Gross, François Englert and perhaps Gerard 't Hooft and Steven Weinberg) who have made research in string theory or at least find it attractive?

When solving "coffee cup calorimeter" problems, you're supposed to include the solute mass with the mass of your solution. However, you're also supposed to assume that dilute solutions have the same density and heat capacity as water. So if I add 5g of NaOH to 500g of water, the solution...

Hello people of physicsforums. Has anyone proved these problems in number theory :Riemann hypothesis, Goldbach conjecture, twin primes conjecture, infinitude of prime numbers? If you want make discussion about them. Thank you for allowing me participate in physicsforums and for wanting to make...

In string theory, physical states satisfy QBΨ = 0, where QB is the BRST operator. This equation of motion can be obtained from an action S = ∫ QBΨ*Ψ + Ψ*Ψ*Ψ There is a gauge invariance under δΨ = QBΛ. what is the framework in which the role of the BRST operator QB is understood in open string...

Hi! I have been looking at differential forms, manifolds and de Rham cohomology. Now I'm trying to figure out the connection from cohomology and equations of motions and topological field theory. Problem is that I am only looking at abelian field theories and I only find introductions into...

It is a long problem, but it is simple to understand. I am having trouble with part A. My attempt: Pressure outside > pressure inside container. pV = constant (isothermal). At equilibrium, all gases are at atmospheric pressure. Because it is quasi-static, the pressures of both compartments are...

I have the following lagrangian density: $$L = \bar{\psi}i \gamma^\mu \partial_\mu \psi - g\bar{\psi}(\sigma + i\gamma^5\pi)\psi + \frac{1}{2}(\partial_\mu \sigma)^2+ \frac{1}{2}(\partial_\mu \pi)^2 -V(\sigma^2 + \pi^2)$$ where $\pi$ and $\sigma$ are scalar fields. I have show that this...

Hi, I would like to know if an undergraduate student in physics could be able to study measure theory in order to have a better understanding of the probability theory and go further in this way (stochastic process) ? Assuming a first year of calculus and the level of "Mathematical methods in...

Hi, I have undergraduate level knowledge about mathematics, quantum physics, and general theory of relativity. Now I am curious about chaos theory, and I would be grateful for suggestions of good introductory books to chaos theory. They may be both introductory and a bit more advanced.Sten Edebäck

I want to find the email of the authors. The problem is I cannot find hers. How to find it? Any help? Thanks in advance!

I am not sure this is the right section to ask this question, but here it goes. So, I was studying Stat. Physics and I came across this paper, A Mathematical Theory of Communication. What it's so important about this paper?

For those who forgot the previous chapters: https://www.physicsforums.com/threads/ultra-hyperbolic-pde-and-f-theory.766711/#post-4827614 So I now found in Google the following book which I ran to buy: https://www.amazon.com/dp/3838130510/?tag=pfamazon01-20 unfortunately it's only 200 pages...

Hi, I was working on the following problem: Two classes ## C_1 ## and ## C_2 ## have equal priors. The likelihoods of ## x## belonging to each class are given by 2D normal distributions with different means, but the same covariance: p(x|C _1) = N(\mu_x, \Sigma) \text{and} p(x|C_2) =...

I'm currently a fresh grad student in theoretical physics, and I'm still deciding to choose which research group to join. My current understanding (maybe I'm wrong) is the PhD theme pretty much determines the topic for future post-doc research so I kinda need to choose very carefully. I'm...

In algebraic geometry, the central notion is that of a scheme. This is the replacement for the classical notion of a variety. A scheme is a topological space X equipped with a sheaf of rings. I just assume that this notion of a scheme replaces the idea of a variety? or is that notion still...

I've been assigned to do a problem from Landau which you can read below: I have no problem with finding the energy. Then I write down the equations: \begin{equation*} \begin{cases} (V_{11}-E^{(1)})|c_1|e^{i\alpha_1} + V_{21}e^{i\alpha_2}|c_2| = 0\\ V_{12}e^{i\alpha_1}|c_1| +...

In a inertial frame of reference ##S## body accelerate with constant acceleration ##a##. Can then exist inertial frame of reference ##S'## which moves with speed ##u## relative to ##S## in which body does not accelerate? And why?

Trying to get my head around some basic points of measure theory So rational numbers are dense in the reals. I.e., if with , then there exists an such that . It follows that there are then infinitely many such. The Lebesgue measure of any single irrational (or rational number) is zero in...

This is not my homework. I took it upon myself to answer a textbook question for mental stimulation. I wanted to know if someone can verify if these were the correct values that needed to be solved for, process, and final answer, and if not, what needed to be considered. For the initial...

$$ W_{n,n} = \int_0^{2 \pi} \frac{1}{\sqrt{2 \pi}} e^{-inx} V_0 \cos(x) \frac{1}{\sqrt{2 \pi}} e^{inx} dx $$ $$ = 0 $$ $$ W_{n, -n} = \int_0^{2 \pi} \frac{1}{\sqrt{2 \pi}} e^{-inx} V_0 \cos(x) \frac{1}{\sqrt{2 \pi}} e^{-inx} dx $$ $$ = \frac{a n ( \sin(4 \pi n) + i \cos( 4 \pi n) - i...

Hi, I saw this video by numberphile, and near the end they mention how at the point of a right angle the equation shows infinite velocity for fluids. I'm wondering if this isn't perhaps related to Cantor's solution to Zeno's Paradox of distance (there's always a midpoint). Because I feel like at...

I'm in not too urgent (but a little pressing, i.e. I have an assignment on this due Friday... 😣 ) need of some reference that treats the theory of dislocations in crystal with a mathematical emphasis (i.e. tensors); specifically, pertaining to Burgers' vectors and the strain response to applied...

hello :) i would very much like study some quantum field theorie, but have not previously study any regular quantum mechanic (i am not so interest in regular quantum mechanic, but more the relativistic theories). so i ask, this is possible or not? to what extent knowledge of regular quantum...

Ok, first I want to say that I am an electrical engineer. I want to be very clear that I am trying to understand a specific situation that I came across. I am searching for an answer of why and how this situation could happen. I don't want a solution for the problem, just a theoretical, physical...

From a retiree’s stack of left behind books, I picked up a copy of Two-Person Game Theory (1966) by Rapoport. Is this an acceptable first (and possibly only) reading on the topic?

Assume that I have the Lagrangian $$\mathcal{L}_{UV} =\frac{1}{2}\left[\left(\partial_{\mu} \phi\right)^{2}-m_{L}^{2} \phi^{2}+\left(\partial_{\mu} H\right)^{2}-M^{2} H^{2}\right] -\frac{\lambda_{0}}{4 !} \phi^{4}-\frac{\lambda_{2}}{4} \phi^{2} H^{2},$$ where ##\phi## is a light scalar field...

In this case, the lagrangian density would be $$\mathcal{L}=\frac{1}{2}((\partial_{\mu}\Phi)^2-m^2\Phi^2)-\frac{\lambda}{4!}\Phi^4$$ whe $$\Phi$$ is the scalar field in the Heisenburg picture and $$\ket{\Omega}$$ is the interacting ground state. Was just curious if there were ways to do Feynman...

I know in the Heisenburg picture, $$\Phi(\vec{x},t)=U^{\dagger}(t,t_0)\Phi_{0}(\vec{x},t)U(t,t_0)$$ where $$\Phi_{0}$$ is the free field solution, and $$U(t,t_0)=T(e^{i\int d^4x \mathcal{L_{int}}})$$. Is there a way I could solve this using contractions or Feynman diagrams? Because otherwise, it...

Hello everybody, I hope it is the right section to post. For an exam, I should delve into a topic concerning graph theory. My work should include theoretical explanation, pseudo code, correctness analysis, complexity analysis and code implementation (C ++, python or other). Could someone...

Hi, I was recently being taught a control theory course and was going through a 'derivation' of the controllable canonical form. I have a question about a certain step in the process. Question: Why does the coefficient ## b_0 ## in front of the ## u(t) ## mean that the output ## y(t) = b_0 y_1...

We know about the Higg's field and boson, so what if gravity is the same. There has long been a dispute as to weather gravity is a field or a particle. Why can't it be like the Higg's boson.

I am studying the 'toy' Lagrangian (Quantum Field Theory In a Nutshell by A.Zee). $$\mathcal{L} = - \frac{1}{4} F_{\mu \nu}F^{\mu \nu} + \frac{m^2}{2}A_{\mu}A^{\mu}$$ Which assumes a massive photon (which is of course not what it is experimentally observed; photons are massless). The...

Hello, I am spending time learning more about the theory of special relativity and string theory. One of the things that I have read about string theory is that it includes other dimensions in relation to space (space has 9 dimensions in string theory, supposedly). However, from what I...

Hi, I have a course on calculus of variations and Sturm Liouville theory and was wondering if anyone had any good textbook suggestions? If they had questions and solutions it would be a bonus! I have put all the subtopics of the course below. Calculus of variations Variation subject to...

Relevant Equations:: ##\ket{\vec{p}}=\hat{a}^{\dagger}(\vec{p})\ket{0}## for a free field with ##[\hat{a}({\vec{k})},\hat{a}^{\dagger}({\vec{k'})}]=2(2\pi)^3\omega_k\delta^3({\vec{k}-\vec{k'}})## $$ \bra{ \vec{ p'}} T_{\mu,\nu} \ket{ \vec...

$$ \bra{ \vec{ p'}} T_{\mu,\nu} \ket{ \vec {p}}=\bra{\Omega}\hat{a}(\vec{p'})(\partial^{\mu}\Phi\partial^{\nu} \Phi-g^{\mu \nu}\mathcal{L})\hat{a}^{\dagger}(\vec{p})\ket{\Omega}=\bra{\Omega}(\hat{a}(\vec{p'})\partial^{\mu}\Phi\partial^{\nu} \Phi\hat{a}^{\dagger}(\vec{p})\\...

Not sure where to start!

There are several models of brane cosmology (https://en.wikipedia.org/wiki/Brane_cosmology) and several physicists working in this field (e.g Lisa Randall and Raman Sundrum), but as you will notice, apparently they are all directly related to string theory. This has several consequences, for...

A neutral uranium atom has 92 electrons and 92 protons. in a violent nuuclear event a uranium nucleus is stripped of all 92 electrons. The resulting bare nucleus captures a single free electron from the surroundings. Given that the ionization energy for hydrogen is ##13.6eV##, derive the...

. I should preface by saying I'm a geologist not a physicist... Gotta say I usually avoid people who talk about the simulation stuff but I just saw a Tedx by George Smoot and it wound me up... Anyway, the simulation hypothesis seems to me, and most other scientists to basically be a bit of a...

Hello. What are the problems specifically or mathematically or physically that physicists find difficulty in solving to make a theory of quantum gravity? Thank you.