Field theory Definition and 523 Threads

In discussing the wave/particle duality, a friend stated basically that the discussion in quantum mechanics is not relevant because quantum mechanics is superseded by quantum field theory. 1. I do not know if this statement is relevant with respect to the wave/particle duality. 2. I am not...

Homework Statement Consider the lagrangian L=\delta_\mu \phi \delta^\mu \phi^* - m^2 \phi \phi^* Show that the transformation: \phi \rightarrow \phi + a \,\,\,\,\,\,\,\,\,\, \phi^* \rightarrow \phi^* + a^* is symmetry when m=0. The attempt at a solution Substituting the transformation...

This isn't a homework problem. I am preparing for a particle physics exam and although I understand the theoretical side of field theory, I have little idea how to approach practical scattering questions like these. THE PROBLEM: Dark matter might be observed at the LHC with monojet and...

Hello, Can someone tell me how to derive: $$ grad\hat{\phi} $$ from: $$ \hat{P}= -:\int \mathrm{d³}x [\pi (x) grad\hat{\phi}(x)]: = \int \mathrm{d³}p [p a⁺(p)a(p)] $$ Are all vectors. Note normal ordering ":" is used. I want to understand well QFT and want to learn to do this calcs...

Is it a good choice to read these books first or there's a better way. My professor recommended me these books but as I started them they had bulk of maths and really matter was not that understandable on my first try. I am an engineer. I read physics in free time I can get , so shall I go ahead...

Hello, I was reading and trying to follow up with Pierre Ramond's "Field theory: A modern primer" and got stuck in his step to step jumping. Kindly, see attachment and note that Eq (1.2.6) = g_{ρσ}=g_{μ\upsilon}\Lambda^{μ}_{ρ}\Lambda^{\upsilon}_{σ}. My question is what do I need from tensor...

At the moment I am trying to understand classical field theory and there's a conceptual problem I encountered, which bothers me a lot and I don't seem to be able to resolve the issue. When making the step to classical field theory, many texts start as follows: First they recall the/a action in...

Good afternoon : I now what I've written here : https://www.physicsforums.com/showthread.php?t=763322 in the first message. I've made the Clebsh Cordon theorem with the components. Which can be represented by the Young tableau. There also the SU(3) and the su(3) representation of dimension...

I stumbled on it while searching for electrodynamics textbooks for undergrads but this seems more advanced than Griffiths. Has anyone else used this book by Marcus Zahn? Is it a worthwhile read for an electrical engineer about to start sophomore year?

Hello Forum, The electromagnetic field EM must be treated relativistically because it travels at the speed of light in a vacuum. However, the idea of quantization forces us to treat the field as a quantum mechanical field. QFT is the answer to that. QFT is quantum mechanics with...

I am reading Dummit and Foote, Chapter 13 - Field Theory. I am currently studying Example 4 [pages 515 - 516] I need some help with what D&F call a simple computation. Example 4 on pages 515-516 reads as follows: Now in the above example, D&F write the following: " ... ... In this case, a...

I am reading Dummit and Foote, Chapter 13 - Field Theory. I am currently studying Theorem 3 [pages 512 - 513] I need some help with an aspect of the proof of Theorem 3 concerning congruence or residue classes of polynomials. D&F, Chapter 13, Theorem 3 and its proof read as...

Homework Statement I uploaded a picture with the question Homework Equations my problem is : How should I find all the symmetries of the action ? Is there an easy way to recognize those symmetries or should I try all the symmetries I know and see if the action doesn't change...

I read a sentence that says if a spherical volume in placed in a quantized space then the maximum entropy of the system can be calculated and it after simple steps found to be: S~V where V is the volume of the spherical volume. "Then the author said: Each local quantum field theory(with UV...

I've been thinking about Magnetic Fields, and I think that I've found a contradiction in conventional physics theory. While comparing the Left-Hand-Rule for Motors (LHR) and the Right-Hand-Rule for Generators (RHR), I found this contradiction: The Left-Hand-Rule states that if the Magnetic...

Every time I try to read Peskin & Schroeder I run into a brick wall on page 15 (section 2.2) when they quickly derive the Euler-Lagrange Equations in classical field theory. The relevant step is this: \frac{∂L}{∂(∂_{μ}\phi)} δ(∂_{μ}\phi) = -∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) + ∂_{μ}...

Every time I try to read Peskin & Schroeder I run into a brick wall on page 15 (section 2.2) when they quickly derive the Euler-Lagrange Equations in classical field theory. The relevant step is this: \frac{∂L}{∂(∂_{μ}\phi)} δ(∂_{μ}\phi) = -∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) + ∂_{μ}...

One page 24 of his book on classical field theory (4th edition), Landau derives the relativistic equation of motion for a uniformly accelarated particle. How does he get the differential equation that leads him to his result?

What ever happened with QFT? Heard so much about it years ago now only once in a while will a past Nobel laureate state it is real. I know string is the thing now. Any thoughts? Sussan

Homework Statement Consider a spherical dielectric shell so that ε = ε_0ε_r for a < r < b and ε = ε_0 for 0 < r < a. If a charge Q is placed at the center of the shell, find a) P for a < r < b b) ρ_pv for a < r b c) ρ_ps at r = a and r = b Homework Equations ρ_pv = -div(P) ρ_ps = P...

Hi everyone, I'm having a lot of troubles learning QFT, personally I find it very challenging, besides that my professor has a very difficult accent and given that I'm not an English native speaker it is really hard for me to follow him. I would like to hear your experience learning QFT, Was it...

Why do we know that particle physics/quantum field theory is a physics of symmetries?What leads we to the gauge symmetries of all interactions?.Why we can not assume a physics without symmetry?

There's very few problems in Landau's books. I'm the kind of guy that properly learns material by doing tons of problems. Of course I can pull from other textbooks but there's the issue of different notation, extra material within chapters, etc... Does anyone know of a good resource that can...

I am pursuing electrical engineering and I am currently in my 3rd semester. I have field theory or Engineering electromagnetics as a subject. It seems very interesting but I am not able to figure how to approach the subject to enjoy it. Hence I need to change my perspective from just...

Hello, I understand the classical Lagrangian which follows the Principle of Least Action(A) A=∫L dt But what is Lagrangian density? Is it a new concept? A=∫Lagrangian density dx^4 Here 4 is the four vector? One time-like and 3 space-like co-ordinates? QFT uses Lagrangian to...

Copper (ii) chloride is a light brown solid, which slowly absorbs moisture to form a blue-green dihydrate. According to ligand field theory, water is a stronger field ligand than chloride. As a result, the dihydrate form should have a larger d orbital splitting than the anhydrous form. Thus...

Would it be right to say that QFT tries to bring together the many-particles(many-body) discrete systems of quantum mechanics and the relativistic fields that are basically continuous systems? Of course the discrete particle of classical mechanics that when found in big numbers must be dealt...

I have recently been learning CTF and energy differences and orbital splitting is starting to make sense to me a bit more. I have not seen any definitive answers yet so any help would be great. In CTF, octahedral complexes are most common and there are 5 d orbitals that participate. Whether it...

Recently, I read a review on magnetic monopole published in late 1970s, wherein some conjectures of properties possibly possessed by a longingly desired quantum field theory of monopoles are stated. My question is what our contemporary understanding of the quantum field theory of monopoles...

The bare cosmological constant in field theory is needed to cancel the infinite vacuum zero-point energy. Then you get a renormalized cosmological constant. There are three quantites at play, Ω=E+Ω0, where E is the infinite vacuum zero-point energy, and Ω is the renormalized cosmological...

Solid State Physics Quantum mechanics and quantum nature of solids, properties of materials. Band theory in metals and semiconductors. Conduction processes, the p-n junction, transistors and other solid state devices. Field Theory Review of vector analysis and coordinate systems...

I am reading Nicholson: Introduction to Abstract Algebra, Section 6.3 Splitting Fields. Example 1 reads as follows: (see attachment) -------------------------------------------------------------------------------------------------- Example 1. Find an extension E \supseteq \mathbb{Z}_2 in...

I am studying field theory. A general question I have is the following: Let E \supseteq F be fields and let u \in E . Now, if I determine an irreducible polynomial f in F[x] such that f(u) = 0 in E, can I conclude that I have found the minimal polynomial of u over F. Can someone...

I am reading Nicholson: Introduction to Abstract Algebra, Section 6.2 - Algebraic Extensions. Example 15 on page 282 (see attachment) reads as follows: --------------------------------------------------------------------------------------------------------------------------------- Example 15...

xample 13 from Nicholson: Introduction to Abstract Algebra, Section 6.2, page 282 reads as follows: (see attachment) ------------------------------------------------------------------------------------------------------------------ Example 13: If u = \sqrt[3]{2} show that \mathbb{Q}(u) =...

I am reading Nicholson: Introduction to Abstract Algebra, Section 6.2 Algebraic Extensions. Example 14 on page 282 (see attachment) reads as follows: ------------------------------------------------------------------------------------------- Example 14. Let E \supseteq F be fields and let...

I am reading Nicholson: Introduction to Abstract Algebra, Section 6.2 Algebraic Extensions. Example 13 on page 282 (see attachment) reads as follows: "If u = \sqrt[3]{2} show that \mathbb{Q}(u) = \mathbb{Q}(u^2) " In the third line of the explanation - see page 282 of attachment - we...

I am reading Nicholson: Introduction to Abstract Algebra Section 6.2 Algebraic Extensions. On page 282 the Corollary to Theorem 5 states the following: (see attachment for Theorem 5 and the Corollary)...

Field Theory - Element u transcendental over F In Section 10.2 Algebraic Extensions in Papantonopoulou: Algebra - Pure and Applied, Proposition 10.2.2 on page 309 (see attachment) reads as follows...

I am reading Dummit and Foote (D&F) Section 13.1 Basic Theory of Field Extensions. I have a question regarding the nature of extension fields. Theorem 4 (D&F Section 13.1, page 513) states the following (see attachment)...

The title says it all. I'm sorry if you get annoyed because of my "noobishness", but I'm still a physicist in training (taking undergrad Classical Mechs). I'm really interested in Quantum Theory and I keep hearing about Quantum Field Theory, but not a single website accurately explains what it...

------------------------------------------------------------------------------------------------ 7. Prove that \mathbb{Q} ( \sqrt{2} + \sqrt{3} ) = \mathbb{Q} ( \sqrt{2} , \sqrt{3} ). Conclude that [\mathbb{Q} ( \sqrt{2} + \sqrt{3} ) \ : \ \mathbb{Q} ] = 4 . Find an irreducible...

Can someone help me get started on the following problem. Determine the degree over \mathbb{Q} of \ 2 + \sqrt{3} and of 1 + \sqrt[3]{2} + \sqrt[3]{2} Peter [This has also been posted on MHF]

Dummit and Foote Exercise 2, Section 13.2, page 529 reads as follows: ------------------------------------------------------------------------------------------------------------------ 2. Let g(x) = x^2 + x -1 and let h(x) = x^3 - x + 1 . Obtain fields of 4, 8, 9 and 27 elements by...

I am reading Dummit and Foote on algebraic extensions. I am having some issues understanding Example 2 on page 526 - see attachment. Example 2 on page 526 reads as follows...

I am trying to clarify my understanding of Proposition 11 of Dummit and Foote Ch13 Field Theory concerning the degree of \alpha over F. Proposition 11 reads as follows...

I am studying Dummit and Foote Chapter 13: Field Theory. Exercise 1 on page 519 reads as follows: =============================================================================== "Show that p(x) = x^3 + 9x + 6 is irreducible in \mathbb{Q}[x] . Let \theta be a root of p(x). Find the...

The new geometric version of quantum field theory could also facilitate the search for a theory of quantum gravity that would seamlessly connect the large- and small-scale pictures of the universe https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/ I...

What kind of background do I need to study many-body quantum field theory?

In QFT, which have infinite degree of freedom, there exlst infinite unitary nonequvilent representation. Expecially after phase transition, the two representation are unitary nonequvilent. So can we say that unitary are broken in QFT? Or a pure state can evolved to a mixed state which is a...