Field theory Definition and 554 Threads

For a ##\phi^{3}## quantum field theory, the interaction term is ##\displaystyle{\frac{g}{3!}\phi^{3}}##, where ##g## is the coupling constant. The mass dimension of the coupling constant ##g## is ##1##, which means that ##\displaystyle{\frac{g}{E}}## is dimensionless. Therefore...

No. This is a noncovariant, observer-specific view.In the covariant, observer-independent view of fields, states are labeled instead by the causal classical solutions of hyperbolic field equations. On the collection of these the Peierls bracket is defined, which is the covariant version of the...

Hey, I am about to do my bachelor project in physics and I really want to dive into the classical theory of fields, this could be General Relativity (GR) and/or Electrodynamics (ED). I have some books on the subject: Barut, ED and classical theory of fields and particles, and Landau&Lifshitz...

Hello. In my university the course of the Field theory was based on Landau's book, which of course, is a quiet rough book to introduce a subject with - so all I was left with was superficial knowledge of the branch. I would like to read another book (introductory level is preferred) about the...

Hi. This question most probably shows my lack of understanding on the topic: why are scalar fields Lorentz invariant? Imagine a field T(x) [x is a vector; I just don't know how to write it, sorry] that tells us the temperature in each point of a room. We make a rotation in the room and now...

Hi everyone, I'm approaching the study of EFT but I'm facing some problems. While in QFT usually we want renormalizable theories, in EFT we don't want this costraint anymore and this opens up space for a lot more terms in the Lagrangian. My problem is that when we want to calculate amplitudes...

Homework Statement I'm working through Zee for some self study and I'm trying to do all the problems, which is understandably challenging. Problem 1.3.1 is where I'm currently stuck: Verify that D(x) decays exponentially for spacelike separation. Homework Equations The propagator in question...

In classical field theory, the field, φ, is usually constructed from a very large number of coupled harmonic oscillators. Let's say our φ consists of just electrons. What does φ best represent physically, a very large number of electrons or can it represent just a few electrons? Which is the...

Hello! I am a diploma student at HEP section. I am going to have an interview for PhD within a week. I've finished the course and learned a lot about Lie algebra, quantum field theory, general relativity, standard model, etc. How can I review everything as soon as possible? For example, Mark...

I have just finished working through Jackson's Electrodynamics and Sakurai's Modern Quantum Mechanics and was wondering if this was sufficient background for me to start studying qft. Also, would Weinberg's Books be a good place to dive in given my background or is there are a more suitable...

In my post graduate course, several years now, our professor in field theory have mentioned that in field theory the fields of mass-energy seem to be space and time themselves, like electric and magnetic fields in ElectroMagnetism. Specificaly he said that "the problem is that in...

Consider the following extract taken from page 60 of Matthew Schwartz's 'Introduction to Quantum Field Theory':We usually calculate ##S##-matrix elements perturbatively. In a free theory, where there are no interactions, the ##S##-matrix is simply the identity matrix ##\mathbb{1}##. We can...

Homework Statement In this problem, you will calculate the perihelion shift of Mercury simply by dimensional analysis. (a) The interactions in gravity have ##\mathcal{L}=M^{2}_{Pl}\Big(-\frac{1}{2}h_{\mu\nu}\Box...

Homework Statement A class of interesting theories are invariant under the scaling of all lengths by ##x^{\mu} \rightarrow (x')^{\mu}=\lambda x^{\mu}## and ##\phi(x) \rightarrow \phi'(x) = \lambda^{-D}\phi(\lambda^{-1}x)##. Here ##D## is called the scaling dimension of the field. Consider...

Homework Statement Given the Maxwell Lagrangian ##\mathcal{L} = -\frac{1}{2} (\partial_{\mu}A_{\nu})(\partial^{\mu}A^{\nu}) + \frac{1}{2} (\partial_{\mu}A^{\mu})^{2}##, show that (a) ##\frac{\partial \mathcal{L}}{\partial (\partial_{\mu}A_{\nu})} = -...

In quantum field theory (QFT) from what I've read locality is the condition that the Lagrangian density ##\mathscr{L}## is a functional of a field (or fields) and a finite number of its (their) spatial and temporal derivatives evaluated at a single spacetime point ##x^{\mu}=(t,\mathbf{x})##...

Hi, Does anyone have details about what Einstein at a higher level tried in his last 30 years when he was working on Unified field theory. What approaches he tried?

Author: T. Padmanabhan Title: Quantum Field Theory: The Why, What and How Amazon Link: https://www.amazon.com/dp/3319281712/?tag=pfamazon01-20 Springerlink (Previews of chapters): http://link.springer.com/book/10.1007%2F978-3-319-28173-5

Hello, Does anyone know if there is a solutions manual or any other source of solutions for the book Quantum and Statistical Field theory by Le Bellac? Thanks!

This is a question that came about while I attempting to prove that a simple extension was a splitting field via mutual containment. This isn't actually the problem, however, it seems like the argument I'm using shouldn't be exclusive to my problem. Here is my attempt at convincing myself that...

In this thread, I want to discuss the implications of quantum field theory for the interpretation of quantum mechanics. To set the stage I'll import in the next few posts a number of posts from other threads. The latest of these is the following: Only if it is the sole particle in the whole...

In page 15, Peskin and Schroeder states that The principle of least action states that when a system evolves from one given configuration to another between times ##t_1## and ##t_2##, it does so along the path in configuration space for which ##S## is an extremum. What is the definition of...

Great youtube introduction video about Quantum Field Theory (QFT) from a couple of days ago by Dr Don Lincoln @fermilab. The video and description of a particle being a disturbance in a field and flying through the air at 3:25 is especially compelling.

There is a recent article (Optics July 2015) claiming violation of Bell inequalities for classical fields: "Shifting the quantum-classical boundary: theory and experiment for statistically classical optical fields" https://www.osapublishing.org/optica/abstract.cfm?URI=optica-2-7-611...

Dear All I am currently taking " Introduction to Quantum field theory", And I have to do a project by the end of the course. I have searched and i find : QFT in curved space, QFT for higher spins... But i need other suggestion of topics I can do as a project. Thank you

Hello guys! I just just wondering a general thing about calculations done in the field theory and those made in the lattice. In the field theory we have some results that in principle should match with the lattice ones in the thermodynamic limit. However, when we tried to solve the same problem...

I wanting to do an introductory Quantum Field theory course in my spare time. And although there are a couple available, they are not very beneficial without solutions to the problem sets. I am also looking at the course on the MIT open courseware website: "8.323: Relativistic Quantum Field...

Hi all I am studying quantum field theory and i want to just to check something. We have said that the problem with klein gordon equation for real field is that is predict positive and negative energies in addition to the negative probability density. For the complex klein gordon field we have...

Why the kink (\phi(x)=tanh(\frac{x}{\xi})), can not tunnel into vacuum +v or -v (Spontaneous symmetry breaking vacuum). From the boundary condition(x\rightarrow \pm\infty, \phi(x)\rightarrow \pm v), it is self-evident. but the book states: Due to the infinite high energy barrier, the kink...

bhobba submitted a new PF Insights post Some Useful Integrals In Quantum Field Theory Continue reading the Original PF Insights Post.

I'm not really sure if this counts as a homework problem (I was reluctant to post in that section since they evidently force you to ensure you've used the template, even though it's not very applicable here) so much as a general misunderstanding of mean field theory. So, in Michale Plischke and...

Homework Statement I am a little confused about the how self consistency conditions work and I was wondering if in the following case I have correctly understood the details? Homework Equations [/B] Say we have a harmonic oscillator with a perturbation...

First of all, I copy the text in my lecture note. - - - - - - - - - - - - - - - - - - - In general, $$e^{-iTH}$$ cannot be written exactly in a useful way in terms of creation and annihilation operators. However, we can do it perturbatively, order by order in the coupling $$ \lambda $$. For...

Homework Statement Show √ 2 + √ 3 algebraic over Q. Find its degree over Q. Prove the answer. Homework EquationsThe Attempt at a Solution Let ##\alpha= \sqrt{2}+\sqrt{3}\in \mathbb{R}##, then ##\alpha^4-10\alpha^2+1=0## which is a root of ##f(x)=x^4-10x^2+1## where ##f(x)## in...

Homework Statement Construct $\mathbb{F}_{16}$ as a quotient of $\mathbb{Z}_2[X]$. How many non-zero elements are primitive in this field? Calculate $|GL2_(\mathbb{F}_16)|$. Homework Equations Primitive Theorem The Attempt at a Solution For the first question, I don't know how to construct...

In my lecture we were discussing the Lagrangian construction of Electromagnetism. We built it from the vector potential ##A^\mu##. We introduced the field tensor ##F^{\mu \nu}##. We could write the Langrangian in a very short fashion as ##-\frac{1}{4}F_{\mu \nu}F^{\mu \nu}## In the end we...

In page of 15 of 'An Introduction to Quantum Field Theory,' Peskin and Schroeder writes In a local field theory the Lagrangian can be written as the spatial integral of a Lagrangian density, ... , which is a function of one of more fields and their derivatives. Can you explain what the term...

Hi all, I am in 7th grade science, but I have a lot of interest in advanced physics (and I am really bored in class), so I am currently working on an independent project on field theory (both classical and quantum). I understand it well, although my background in calculus is not great (I have...

http://arxiv.org/abs/1409.0868 Holomorphy without Supersymmetry in the Standard Model Effective Field Theory Rodrigo Alonso, Elizabeth E. Jenkins, Aneesh V. Manohar (Submitted on 2 Sep 2014 (v1), last revised 6 Nov 2014 (this version, v2)) The anomalous dimensions of dimension-six operators in...

Homework Statement Consider a theory with a \phi^6-scalar potential: \mathcal{L} = \frac{1}{2}(\partial_\mu\phi)^2-\phi^2(\phi^2-1)^2. Why is the solution to the equation of motion not a soliton? Homework Equations \phi''=\frac{\partial V}{\partial\phi} The Attempt at a Solution...

Homework Statement [/B] So, I need to show Lorentz covariance of a Proca field E-L equation, conceptually I have no problems with this, I just have to make one final step that I cannot really justify. Homework Equations "Proca" (quotation marks because of the minus next to the mass part, I...

I created this thread to notify people about to the online resources for Tong's QFT course. Lecture videos: Blackboard screens and Videos: http://pirsa.org/C09033 Lecture notes: http://www.damtp.cam.ac.uk/user/tong/qft.html Course text: Peskin and Schroeder (search for it)

Hello over the summer I would like to study quantum field theory. I took two semesters of undergraduate quantum mechanics using Griffith's textbook. We covered the entire book in those two semesters. I also know my special relativity pretty well. Is that enough to self study quantum field theory...

I have been meaning to ask this one for a while - but never seem to get around to it. In MW its sometimes said it's simply the working out of the universal wave-function via Schroedinger's Equation. Of course Schroedinger's Equation is only valid non-relativistically. Wallace doesn't really...

I would appreciate any help with the following question: I know that for relativistic field theories, the stress tensor can be obtained from the classical action by differentiating with respect to the metric, as is explained on the wikipedia page...

Hi all, my question is rather a simple one and regards conformal transformations. On "Applied CFT" by P.Ginsparg, http://arxiv.org/pdf/hep-th/9108028.pdf , on page 10, gives the transformation rule of a quasi primary field and relates the exponent of 1.12 to the one of 1.10. My first question...

I have been studying quantum field theory and I am currently in the Lagrangian field theory chapter in my book. Now it says that the energy momentum tensor is as follows: Tμν= [∂L/∂(∂μφ) * ∂νφ] - δμνL Note: I am using L to symbolize Lagrangian density and not just Lagrangian since the latex...

Hi I understand that Maxwell's equations, and General Relativity are both field theories. I am trying to understand what the opposite of a field theory is, or what is not a field theory. For example, am I correct in believing that Newton's Laws are not a field theory? Is that is true then...

I was looking for explanation why x^0=1. thread https://www.physicsforums.com/threads/my-simple-proof-of-x-0-1.172073/ is locked and i did't found solution in it from axioms. People using exp(x) and log(x) and xa-a=xax-a as given. If you have xa-a=xax-a for a∈ℤ and x∈ℕ+ then there is no...

for a given diagram in some interacting theory that needs a momentum cutoff shouldn't the same momentum cutoff be used for diagrams that don't need a momentum cutoff for convergence for example, phi3 theory has a self energy diagram that diverges, so if one imposed a momentum cutoff there...