Quantum field theory Definition and 558 Threads

In Peskin and Schroeder problem 10.1 is about showing that superficially divergent diagrams that would destroy gauge invariance converge or vanish. We are supposed to prove it for the 1-photon, 3-photon, and 4-photon vertex diagrams. Does this change for scalar QED?

A. Neumaier submitted a new PF Insights post The Physics of Virtual Particles Continue reading the Original PF Insights Post.

My question is, how does one get a wave function for a 'combined' spin-1 and a spin-0 field? How is this possible? I have only been able to find combined states for equal spin identical particles. If you don't understand my question, I'll be glad to reword it.

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

In the srednicki notes he goes from $$H = \int d^{3}x a^{\dagger}(x)\left( \frac{- \nabla^{2}}{2m}\right) a(x) $$ to $$H = \int d^{3}p\frac{1}{2m}P^{2}\tilde{a}^{\dagger}(p)\tilde{a}(p) $$ Where $$\tilde{a}(p) = \int \frac{d^{3}x}{(2\pi)^{\frac{3}{2}}}e^{-ipx}a(x)$$ Is this as simple as...

Derive Vacuum permittivity and permeability using Quantum Field theory or String theory! If QFT or String theory is real fundamental theory, it can be derived the permittivity and permeability of vacuum. << Moderator's note: personal contact details deleted>>

I'm not sure if I posted this in the right category, it's something that came up just after the quantum mechanics section so I just chose this one. I've come across something that I simply can not find an answer for on my own. I'm taking Modern Physics course and the last chapter is some...

Given a Yukawa coupling as a function of scale and a vev, how can I compute the corresponding pole mas? Understandably most paper explain how from a measured pole mass one can compute the running mass, for example, Eq. 19 here. However I want to compute the pole mass from the running mass. In...

For the Gordon identity $$2m \bar{u}_{s'}(\textbf{p}')\gamma^{\mu}u_{s}(\textbf{p}) = \bar{u}_{s'}(\textbf{p}')[(p'+p)^{\mu} -2iS^{\mu\nu} (p'-p)_{\nu}]u_{s}(\textbf{p}) $$ If I plug in $\mu$=5, what exactly does the corresponding $(p'+p)^{5}$ represent? 4 vectors can only have 4 components so...

Are spacetime and the gravitational quantum field (still hypothetical) separate entities? Would the gravitational field be more fundamental, one of the various entities from which spacetime as a whole is composed? Gravitons, which are believed to transmit the force of gravity, would surely be...

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...

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.

In QFT particles are described by fields, but AFAIK these fields are mathematical since we don't measure values of fields at a particular spacetime. So what does it mean to say a higgs field exist! I mean it is one thing to say Higgs particle exists (in LHC), but I have not seen anybody measure...

On page 164-165 of srednicki's printed version (chapter 27) on other renormalization schemes, he arrives at the equation $$m_{ph}^{2} = m^2 \left [1 \left ( +\frac{5}{12}\alpha(ln \frac{\mu^2}{m^2}) +c' \right ) + O(\alpha^2)\right]$$ But after taking a log and dividing by 2 he arrives at...

What is the intuition behind divergences for the sunset diagram? I know that there is quadratic divergence by why no quartic divergence or higher?

Does anyone know any good references for discussion of ##\overline{MS}## theory in phi^4 theory?

As I understand it, the 2-point fnuction is for 1 particle incoming, 1 particle outgoing. The 4-point function is for 2 particles incoming, 2 particles outgoing. Is this correct? So an N-point function describes N/2 incoming particles and N/2 outgoing particles? Thanks!

Given a diagram, how is one supposed to apply the feynman rules to calculate the feynman amplitude?

For quartic scalar field theory these are some of the lowest order diagrams (taken from the solutions to 9.2 srednicki). I'm wondering if someone can give me an intuition of how to actually calculate them. What I'm thinking is that vertices are $$\int \frac{d^{4}x}{(2\pi)^{4}}$$ and for the...

Could someone please tell me the difference between tree diagrams and loop diagrams? If I'm thinking correctly tree diagrams are before contracting? Also how do vacuum diagrams fit into the picture? Thanks!

On page 60 of srednicki (72 for online version) for the $$\phi^{3}$$ interaction for scalar fields he defines $$Z_{1}(J) \propto exp\left[\frac{i}{6}Z_{g}g\int d^{4}x(\frac{1}{i}\frac{\delta}{\delta J})^{3}\right]Z_0(J)$$ Where does this come from? I.e for the quartic interaction does this...

I asked this question to PhysicsStackExchange too but to no avail so far. I'm trying to understand the way that the Higgs Mechanism is applied in the context of a U(1) symmetry breaking scenario, meaning that I have a Higgs complex field \phi=e^{i\xi}\frac{\left(\rho+v\right)}{\sqrt{2}} and...

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

When we observe an electron it is always a localized excitation in the electron field. But when it's not being observed, does the excitation begin to spread through space and become a delocalized excitation?

I will start with a summary of my confusion: I came across seemingly contradictory transformation rules for left and right chiral spinor in 2 books, and am unable to understand what part is Physics and what part is convention. Or is it that one of the two books incorrectly writes the...

Let's take a quantum state ##\Psi_p##, which is an eigenstate of momentum, i.e. ##\hat{P}^{\mu} \Psi_p = p^{\mu} \Psi_p##. Now, Weinberg states that if ##L(p')^{\mu}\,_{\nu}\, p^{\nu} = p'##, then ##\Psi_{p'} = N(p') U(L(p')) \Psi_{p}##, where ##N(p')## is a normalisation constant. How to...

Hello everyone, I'm a senior undergraduate and I'm planing to do a Monograph related to Quantum effects in Gravity (Hawking radiation or something similar(?)) or even some QFT in curved space-time (maybe ambitious since I know this is VERY HARD and I don't have much time), the thing is I can't...

In 'an introduction to quantum field theory' by peskin, he writes: To analyze the photon one-point function, note that the external photon must be attached to a QED vertex. Neglecting the external photon propagator, this amplitude is therefore: I really cannot justify this equation. Can...

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...

In quantum field theory, a fundamental particle is an excitation in the underlying field, but what does that mean? Do fundamental particles have any physical existence according to QFT?

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...

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...

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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.