Quantum field theory Definition and 587 Threads

Homework Statement Consider the quantum mechanical Hamiltonian ##H##. Using the commutation relations of the fields and conjugate momenta , show that if ##F## is a polynomial of the fields##\Phi## and ##\Pi## then ##[H,F]-i \partial_0 F## Homework Equations For KG we have: ##H=\frac{1}{2} \int...

Consider a ##j## point all massive leg one loop polygonal Feynman diagram ##P## representing some scattering process cut on a particular mass channel ##s_i##. Invoking the relevant Feynman rules and proceeding with the integration via dimensional regularisation for example gives me an expression...

¿How is possible deduce the Lagrangian of the fields of a theory knowing only his Feynman Diagrams?

Hi everyone, I am currently preparing myself for my Bachelor thesis in local quantum field theory. I was encouraged by my advisor to read the books of M. Reed and Simon because of my lag of functional analysis experience but I have quite often problems understand the “obvious” conclusions. For...

I recently read that indexology is the art of writing a Lagrangian by just knowing how many dimensions it has and how to contract tensors. I am very interested in this technique, but I cannot find any reference. Can anyone give me a guidance or a reference?

An element of SU(2), such as for example the rotation around the x-axis generated by the first Pauli matrice can be written as U(x) = e^{ixT_1} = \left( \begin{array}{cc} \cos\frac{x}{2} & i\sin\frac{x}{2} \\ i\sin\frac{x}{2} & \cos\frac{x}{2} \\ \end{array} \right) = \left(...

Assuming that a massive spin-1 particle has momentum only in the z-direction, the polarization vectors are given by \varepsilon_{\mu}(J_z = +1) = (0,-\frac{1}{\sqrt{2}},-\frac{i}{\sqrt{2}},0 ) \varepsilon_{\mu}(J_z = 0) = (\frac{p}{m},0,0, \frac{E}{m}) \varepsilon_{\mu}(J_z = -1) =...

Hello All, I was wondering if anybody could recommend some really good, graduate-level textbooks or sources on quantum field theory and antiparticles. I've browsed through several QFT titles, but if anyone has any books they think would be a good grad-level introduction I'd be grateful...

For instance our quantum vacuum has a certain Cosmological constant and the question is can there be other vacuums with different values and if so where's the evidence for this I would like to read it. How do you derive the Cosmological Constant through something like Quantum field theory or...

According to Peskin, p.414, at the bottom, as part of calculating the ##\beta## functions of a theory, we need to fix the counter terms by setting the "typical invariants" built from the external leg momenta to be of order ##−M^2##. For a 4-point function, these invariants are s, t and u...

I am trying to calculate the ##\beta## functions of the massless pseudoscalar Yukawa theory, following Peskin & Schroeder, chapter 12.2. The Lagrangian is ##{L}=\frac{1}{2}(\partial_\mu \phi)^2-\frac{\lambda}{4!}\phi^4+\bar{\psi}(i\gamma^\mu \partial_\mu)\psi-ig\bar{\psi}\gamma^5\psi\phi.##...

Homework Statement I have to expand the following term: $$\dfrac{1}{4} F_{\mu\nu}F^{\mu\nu} = \dfrac{1}{4} \left(\partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu}\right) \left(\partial^{\mu}A^{\nu} - \partial^{\nu}A^{\mu}\right)$$ to get in the end this form...

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

On page 42 of Peskin, at the bottom they say that the next transformation should follow: ##[i\gamma^\mu\partial_\mu - m ]\psi (x) \rightarrow [i\gamma^\mu(\Lambda^{-1})^\nu_\mu \partial_\nu - m ] \Lambda_{1/2} \psi (\Lambda^{-1}x)## But why does the factor ##\Lambda_{1/2}## appear there...

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...

How might we construct a state most closely corresponding to the idea of a single electron wave packet as some superposition of Fock states?

Homework Statement I'm working on path integrals for fermions and I came across an exercise that ask to compute the three point functions , one of that is the: $$<0|J^{\mu}(x_1)J^{\nu}(x_2)J^{\rho}(x_3)|0> $$ where $$J^{\mu}$$ is the current $$J^{\mu}=\bar{\psi}\gamma^{\mu}\psi$$. ***Can you...

Does anyone know a simple explanation for the following statement: Gauge invariance ⇒ $Πμνϒϒ(0) = ΠμνϒZ(0) = 0$ Where ΠVV' is the V to V' one loop correction, ϒ is the photon field and Z is the Z-boson field. The argument of Π is the incoming momentum q2 = 0

The problem statement. When an exercises say " the interaction in a QFT has dimensions Δ" , what does it mean?, it means the field or the Lagrangian has this mass dimension? In this exercise I'm trying to find the classical beta function (β-function) for the assciated couling.

In quantum mechanics, we can define the scattering amplitude f_k(\theta) for two particles as the coefficients of an outgoing spherical wave. More precisely, the asymptotic behaviour (when r\rightarrow\infty) of a wave function of two scattering particles, interacting with some short range...

Homework Statement Homework EquationsThe Attempt at a Solution I've started from writing out the amplitude. Here I know that fermion has definite helicity so I can't sum over spins but I should input explicit forms of spinors. Am I correct? How to do this? I would be grateful for helping me...

Nonlinear sigma models are particular field theories in which the fields take values in some nontrivial manifold. In the simplest cases this is equivalent to saying that the fields appearing in the lagrangian are subject to a number of constraints. Since the lagrangian fields are not independent...

Could you explain what's the interpretation of a before \gamma^{5} in this current: J_{\alpha}=\bar{\psi_{e}}\gamma^{\alpha}\left(1-a\gamma^{5}\right)\psi_{\nu_{e}} +\bar{\psi_{\mu}}\gamma^{\alpha}\left(1-a\gamma^{5}\right)\psi_{\nu_{\mu}}? And will this factor complicate calculations of decay...

Hi. Do you know any book/paper/lecture notes where I can find complete derivation of Feynman rules for both scalar and pseudo-scalar Yukawa theory, and maybe an example of application to decay of fermion?

Problem I have a project for my university class on the Higgs fields and how it impacts the standard model, and how the Higgs particle is formed and decays into particles with the probability of decay based on the mass of the particles it will decay into. I need resources that I can cite like...

Hey guys! I was reading the following paper http://arxiv.org/abs/hep-ph/0703260 for Georgi and I have a conceptual question about it. Howard Georgi was talking about this Unparticle Physics theory and at the base of his analysis is the principle of scale invariance. So Georgi is saying what if...

Hello, I've been trying to find <p'|φ(x)|p> for a free scalar field. and integral of <p'|φ(x)φ(x)|p> over 3d in doing the space In writing φ(x) as In doing the first, I get the creation and annihilation operators acting on |p> giving |p+1> and |p-1> which are different from the bra state |p>...

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...

Hi! I'm desperately trying to develop a list of prerequisites that will enable me to work on topics like quantum gravity, advanced QFT (on curved spacetime etc.) etc. I am currently in the second year of an undergrad theoretical physics degree in the UK, and am heavily unsatisfied with the way...

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...

Homework Statement [/B] Consider a real free scalar field Φ with mass m. Evaluate the following time-ordered product of field operators using Wick's theorem: ∫d^4x <0| T(Φ(x1)Φ(x2)Φ(x3)Φ(x4)(Φ(x))^4) |0> (T denotes time ordering) Homework Equations Wick's theorem: T((Φ(x1)...Φ(xn)) = ...

I am currently studying QFT with 'An Introduction to Quantum Field Theory' by peskin. In part 2 (renormalization) of the book, he introduces counterterms and shows how to compute scattering amplitude with them. Below are counterterms of \phi^4 theory: Then he calculates a 2-2 scattering process...

If I understand what's going on (quite possibly I don't), I think my book is using bad (confusing) notation. Homework Statement As written: "Calculate ##\frac{\delta H[f]}{\delta f(z)} \ \text{where} \ H=\int G(x,y)f(y)dy##" and ##\frac{\delta H[f]}{\delta f(z)}## is the functional derivative...

In QFM, what does it mean to say that an electron is just an excitation of the electron field? Does this apply to all particles? Does it mean to say that an electron is the quanta of the electron field?

1. The problem statement, all variables and given/known I have to prove an equation for the differential cross section of compton scattering of an electron and a photon (electron (P) + photon(K) ⇒ electron(P') + photon (K') ) where P and so on are the inital and final four momenta. Given is...

Hello, I'm looking for a good beginner book about QFT. Thanks!

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...

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...

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...

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 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...

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

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...

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...

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...

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...