Theory Definition and 1000 Threads

What's the difference between relativistic quantum mechanics and quantum field theory? In principle, my guess is that to do the former, one needs to express the Hamiltonian in a relativistic, Lorentz invariant, form, because it seems to be the only frame-related term in the wave equation. (Is...

I have some questions about scalar field Lagrangians, using the box notation defined as \Box \equiv \frac{\partial^2}{\partial t^2} - \nabla^2 . It's a basic, perhaps silly issue, but somehow I've managed to sweep it under the rug for a long time. So, usually, the Lagrangian of a free scalar...

Hello! Recently I found this article: http://quantum-journal.org/papers/q-2017-07-14-13/pdf/ Being familiar with some basis of quantum formalism, I, nevertheless, experienced several difficulties with understanding of the theorem described in this paper. I would really appreciate if someone...

And if I can extend this further, for liquids?

In the multiverse theory, I keep on hearing that our observable universe is one of many universes. Is that saying that our universe ends at the point we can no longer see it - at the end of the observable universe. That would mean that the Earth is the literal centre of our universe. Am I...

I'm interested in the the band theory of solids for semiconductor modeling. I haven't solved the Schrodinger equation for multiple atoms, but I'd like to know some details that experienced physicists might already know. Several texts show how the bands develop from molecular coupling of...

According to classical electromagnetic theory,for acceleration a particle must not only change its direction but it should also increase its speed. But Maxwell said that a particle accelerates then it radiates energy.(this is with reference to Rutherford model). But actually the particle is not...

Hello. I will be attending a course on Group theory and the book that the professor suggests is Georgi's Lie Algebras in Particle Physics. As I liked Zee's book on General Relativity, I thought that it would be a blast to also use his Group theory textbook for the course. Problem is that I don't...

I just wanted to share this idea with other people who may be interested: I watched a PBS Space Time episode about the speed of light more accurately described as the speed of causality. And I Submit! That "time" is simply a interaction between atoms. And though an interaction can be...

Hello! I am reading some representation theory (the book is Lie Algebra in Particle Physics, by Georgi, part 1.17) and the author solves a problem of 3 bodies connected by springs forming a triangle, aiming to find the normal modes. He builds a 6 dimensional vector formed of the 3 particles and...

Homework Statement ##1)## Which one of the following is an example of a set ##S## such that the language ##S^*## has the same number of 8-letter words as 4-letter words? 1) ##S = \{aaaa \quad bbbb\}## 2) ##S = \{bbbb \quad bbbbbb\}## 3) ##S = \{aa \quad bb\}## 4) ##S = \{a \quad bbbb\}##...

We can prove that When A and B are two sets(A≠B) (A-B) = (A∩B') = (A-(A∩B)) {We can also confirm them using venn diagram} From first and third relation A-B = A - (A∩B) By cancelling A from both side I get B = (A∩B) Which is only possible when A and B are same set. What is wrong in my proof , is...

My physics teacher, who dislikes the idea of dark matter, told me that a physicist created an alternative explanation to the phenomena caused by dark matter. Is there something I missed on the news? What is the alternative theory to dark matter and how does it explain 'things' ?

Hi everyone, I have a question that, when came to me, sounded a bit silly to me as well, but then I realized, I myself maybe don't understand the logic behind this 100%, so why not discussing with you about it. So my question is the following. Usually we are used to do quantum field theory...

Emission theories propose that the velocity of light depends on the velocity of the light source. But the ordinary Doppler effect assumes the velocity of light remains as ##c## with respect to the ether medium, even when the light source is moving at speed ##v## with respect to the ether. They...

I saw a documentary the other day where Michio Kaku said something that really peaked my interest. He said that Einstein in his last days was working on something having to do with how small geometries of some sort being the cause of gravity. Does anyone know the details of Einstein's Unified...

Hello everyone! I'm studying the physics of complex systems and I'm approaching probability theory. I understand that we need a ## \sigma-algebra ## and the Kolmogorov axioms in order to define a probability space but then I bumped into the following relation: $$ p(A_1 \cup A_2 ) = p( A_1 ) + p(...

I'm not a math machine, but I dabble in dimensional stuff. I think this falls under knot theory. I have built several prototypes of a tesseract. Each of them sits in a little case in my office. One of them is made from truncated cubes, held together with elastic cord: In theory, the...

I've been studying TQFT and gauge theory. Dijkgraaf-Witten theory in particular. One learns that a topological field theory applied to a manifold outputs the number of principal G bundles of a manifold. My question is for the Physicists in the room, why do you want to know the number of...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] I think I understand part b) . The idea is to move the operator that annihilates to the RHS via the commutator relation. However I can't seem to get part a. I have: ## [ P^u, P^v]= \int \int \frac{1}{(2\pi)^6} d^3k d^3 k'...

Homework Statement Question: To find/ explain why there exists a continuous lorentz transformation that flips the sign for space-like separation but not time-like. Homework Equations Signature ## (-,+,+...) ## Definition of lorentz transformation: ##x^u=\lambda^u_v x^v ##...

Homework Statement Action attached: To find the EoM of ##\phi ## / ##\phi^* ## Homework Equations The Attempt at a Solution [/B] Without deriving from first principles, using E-L equations I have: ## \partial_{u}\frac{\partial L}{\partial_u \phi} - \frac{\partial L}{\partial \phi} =0 ##...

I study control theory and robotics. Recently I figured out that I have a much deeper understanding of probability and statistics compared to my colleagues. Is this 'talent' valuable in my field and if so, where? We used this theory to define white noise, but nothing more...as of now. Also I am...

Urs Schreiber submitted a new PF Insights post Super p-Brane Theory Emerging from Super Homotopy Theory Continue reading the Original PF Insights Post.

Hi everyone, I remember years ago at school memorising the derivation of the formula for pressure in the kinetic theory of gases, as explained in this Youtube video: Thinking a little more deeply about this derivation there are two things I don't get: 1) At 0:53, the video says the molecule...

Suppose there is a charged particle far enough of any mass so that there is no gravitational interaction between the particle and any other body. The trajectory of the particle in space-time would appear to us like this (we are at the origin of our coordinate system). Consider that at...

1. Homework Statement Hello all. It is not a homework actually. I just didn't know at which forum I should post. I am working on a MATLAB code solving the finite wing properties iteratively by using the Anderson's Numerical Lifting Line Method. However, I got some wrong results. The...

Hi there. It is well known from the theory of differential equation the Sturm-Liouville theory, concerning with the eigenvalue problem: ##\displaystyle \frac{d}{dx} \left ( p(x) \frac{dy_n}{dx} \right ) - q(x) y_n(x)=\lambda_n w(x) y_n(x)## with prescribed boundary condtitions for ##a\leq x...

Hello ! I have just graduated from high school but I have a big interest in the strings theory. I am trying to understand its roots aka from where/ how did it come! To that I Need some references for my research, references to make me understand the bases only ! Thank you!

Hi I was hoping someone could advise me on a textbook/platform where I can learn more about the perturbation theory applied to helium and the perturbation theory time depedant. Thanks

Hey everyone ! I am trying to learn how to mathematically prove that a steel tube (with wall thickness of ~ 1mm and external diameter of ~ 15 mm) will have ... At any point along its length, the shaft must : 1) bend in such a way that the deflection is the same regardless of how the shaft is...

Hi , everyone! This is my first post/thread/anything on this forum so first I apologise if I slip up or make any mistakes. Anyway, my question is about recommendations for textbooks for Undergraduate Number Theory. So far, I have studied Calculus 1-3 (including things like line integrals...

ShayanJ submitted a new PF Insights post Entanglement Entropy – Part 2: Quantum Field Theory Continue reading the Original PF Insights Post.

If I place an insulated container of gas on the edge of a turntable and then rotate the container as a constant angular velocity, what happens to the gas? Does the temperature of the gas increase? If so, how was work done on the gas?

Hello everyone. Iam working on a course in multivariable control theory and I stumbled over the Identity Matrix. I understand what the identity matrix is, though the use of it is a mistery... I was reading about going from state space to transfer functions and I found this expressions...

I want to study Electromagnetic theory from Zero.Although i have basic knowledge of electrostatics and magnets but i do not feel confident about EM theory.I am undergraduate with Instrumentation and Control Engineering.I am preparing for National level exam in which question related to Emt...

I am reading Dummit and Foote, Chapter 14 - Galois Theory. I am currently studying Section 14.2 : The Fundamental Theorem of Galois Theory ... ... I need some help with Corollary 10 of Section 14.2 ... ... and the definition of \text{Aut}(K/F) ... ... Corollary 10 reads as follows: Now...

I am reading Dummit and Foote, Chapter 14 - Galois Theory. I am currently studying Section 14.2 : The Fundamental Theorem of Galois Theory ... ... I need some help with Corollary 10 of Section 14.2 ... ... and the definition of ##\text{Aut}(K/F)## ... ... Corollary 10 reads as follows: Now...

I need recommendations on literature to read. Basically i do not understand these section of Frank Harary's book on graph theory since the definition of what a boundary and a cycle vector is not clearly defined. I have googled literature on it but I am having a tough time finding the right...

Homework Statement Attached Homework EquationsThe Attempt at a Solution [/B] where ##\tau## and ##\sigma## are world-sheet parameters. where ##h_{ab}## is the world-sheet metric. To be honest, I am trying to do analogous to general relativity transformations, since this is new to me, so in...

I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 8: Galois Theory, Section 1: Automorphisms of Field Extensions ... ... I need help with Proposition 11.1.11 on page 560 ... ...Proposition 11.1.11 reads as follows...

I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 8: Galois Theory, Section 1: Automorphisms of Field Extensions ... ... I need help with Proposition 11.1.11 on page 560 ... ...Proposition 11.1.11 reads as follows: In the...

Hey, My question isn't exactly a problem,it's just a doubt which occurred in my mind,while studying current electricity.The potential difference across the emf of an ideal battery is considered to be constant,whereas if the battery has an internal resistance (the case for all real life...

I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 8: Galois Theory, Section 1: Automorphisms of Field Extensions ... ... I need help with Example 11.1.10 on page 560 ... ...Example 11.1.10 reads as follows: My questions...

I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 8: Galois Theory, Section 1: Automorphisms of Field Extensions ... ... I need help with Example 11.1.10 on page 560 ... ...Example 11.1.10 reads as follows: My questions...

Magnetic braking is a theory explains the loss of stellar angular momentum and is used extensively to describe the given rotation stars. However, on a smaller and more directly observable level, when we consider Jupiter's rapid rotation rate of less than ten hours and its accompanying powerful...

Hi All This is in relation to the folllowing paper: https://arxiv.org/pdf/1402.6562.pdf See section 3 on examples where standard probability theory is discussed. Is it valid? To me its rather obvious but I had had a retired professor of probability say probability theory doesn't have a state...

Is there a guide, based on existing evidence, that I could use to infer realistically how color would be affected on alien worlds due to factors like star class, luminosity, atmospheric composition, etc? I'm planning to develop a not-too-too-distant future scenario where all the stars in...

Double field theory [1] is an attempt to realize T-duality of string theory at the level of field theory. For instance, if a field in ordinary field theory lives in 4 non-compact spacetime dimensions, then a field in double field theory lives in 8 non-compact spacetime dimensions. I don't...

Hi all, Clarification question: I've read that string theory is manifestly Lorentz invariant - however, I'm confused about this being true in 4D spacetime or in the full 10D setting of the theory (well, one version anyway). At some point I'd also read in a paper that 4D Lorentz invariance...