Quantum field theory Definition and 558 Threads

According to https://arxiv.org/abs/1407.4569, equation (2.15), the Schwinger electron-positron pair production rate in Minkowski space, ##N_S##, is given in natural units by $$N_S=\exp(-\frac{m}{2T_U})$$ where the `Unruh temperature for the accelerating charge', ##T_U##, is given by...

I've been doing a little bit of reading on string theory, and the very large number of string vacua that are possible (i.e., perhaps 10^500 or more). One thing that is not clear to me is exactly what constitutes a 'vacuum' in string theory. In QFT theory, the vacuum is defined as the state with...

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Propagators Continue reading the Original PF Insights Post.

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Phase Space Continue reading the Original PF Insights Post.

Hi everyone! I'm trying to make a list of recommended books (introductory and advanced). So far, what I was able to search are the following: Particle Physics: - Griffiths: Introduction to Elementary Particles - Thomson: Modern Particle Physics - Nachtmann: Elementary Particle Physics -...

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Observables Continue reading the Original PF Insights Post.

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Symmetries Continue reading the Original PF Insights Post.

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Lagrangians Continue reading the Original PF Insights Post.

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Field Variations Continue reading the Original PF Insights Post.

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Fields Continue reading the Original PF Insights Post.

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Spacetime Continue reading the Original PF Insights Post.

https://www.ma.utexas.edu/users/dafr/OldTQFTLectures.pdf I'm reading the paper linked above (page 10) and have a simple question about notation and another that's more of a sanity check. Given a space ##Y## and a spacetime ##X## the author talks about the associated Quantum Hilbert Spaces...

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Geometry Continue reading the Original PF Insights Post.

Looking for a good quantum field theory book. Any suggestions?

Greg Bernhardt submitted a new PF Insights post A First Idea of Quantum Field Theory - 20 Part Series Continue reading the Original PF Insights Post.

If we were to quantize the Dirac field using commutation relations instead of anticommutation relations we would end up with the Hamiltonian, see Peskin and Schroeder $$ H = \int\frac{d^3p}{(2\pi)^3}E_p \sum_{s=1}^2 \Big( a^{s\dagger}_\textbf{p}a^s_\textbf{p}...

In a thesis, I found double sided arrow notation in the lagrangian of a Dirac field (lepton, quark etc) as follows. \begin{equation} L=\frac{1}{2}i\overline{\psi}\gamma^{\mu}\overset{\leftrightarrow}{D_{\mu}}\psi \end{equation} In the thesis, Double sided arrow is defined as follows...

Back in the 1960s, Richard Feynman worked on quantum gravity for a few years, and most of his notes are collected in the 'Feynman Lectures on Gravitation'. His approach was that of a particle physicist applying the principles of QED to GR, notably the concept of gravitons mediating the force of...

Breaking of a local symmetry is impossible. It is often said that therefore the role of the Higgs mechanism in the standard model is a different one. Namely, Once a gauge is fixed, however, to remove the redundant degrees of freedom, the remaining (discrete!) global symmetry may undergo...

A massless spin 1 particle has 2 degrees of freedom. However, we usually describe it using four-vectors, which have four components. Hence, somehow we must get rid of the superfluous degrees of freedom. This job is done by the Maxwell equations. To quote from Gilmore's "Lie Groups, Physics, and...

Can Lagrangian densities be constructed from the physics and then derive equations of motion from them? As it seems now, from my reading and a course I took, that the equations of motion are known (i.e. the Klein-Gordon and Dirac Equation) and then from them the Lagrangian density can be...

Hi all - forgive me, I'd asked a series of questions in a previous post that was deemed to be circular, but I still didn't obtain a satisfactory answer to the question I was asking. In this post, I'm going to try to be very careful to use terms that are at least less 'misplaced', per se...

I've read Arnold Neumaier's excellent Insight article on virtual particles, but I'm very confused about one thing: Observable particles are considered to be on-shell, and as 'asymptotic states' at time +- infinity. Now, in a scattering experiment, I may produce a new particle, which will travel...

Urs Schreiber submitted a new PF Insights post Introduction to Perturbative Quantum Field Theory Continue reading the Original PF Insights Post.

Hello, I don't know if this is the right place to post this topic, I could not figure out the right one. I have recently finished my Masters in Condensed Matter. Now I want to follow a PhD where I can work/research on the dynamics of the Universe especially on dark energy, modified gravity...

What is the highest loop order in standard model scattering computations that still contributes a measurable effect seen in past and present particle collider experiments? In other words, to which order are loop corrections necessary for accounting for observed high energy physics? I expect it...

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...

Hello! Due to the textbook by Peskin and Schroeder being rather old, I was wondering what are other, more pedagogical textbooks on Quantum Field Theory that you would recommend! Any suggestion is appreciated!

Hello! Manoukian's two books on Quantum Field Theory seem pretty good to me, but before buying them I would like to know your thoughts about them! Bear in mind that I need a pedagogical textbook(with good exercises if possible). Thanks!

Hi there - just a quick question about Fourier transforms: When learning about quantum mechanics, I found that the Fourier transform and inverse Fourier transform were both defined with constants of ##{ \left( 2\pi \right) }^{ -d/2 }## in front of the integral. This is useful, as...

I am studying quantum field theory from [David Tong's lecture notes][1] and I am stuck at a particular place. In Page 52., under the heading *3.1.1 Dyson's Formula*, Tong introduces an unitary operator U(t, t_0) = T \exp(-i\int_{t_0}^{t}H_I(t') dt') He then introduces the usual definition of...

Consider the Dirac Lagrangian, L =\overline{\psi}\left(i\gamma^{\mu}\partial_{\mu}-m\right)\psi, where \overline{\psi}=\psi^{\dagger}\gamma^{0} , and show that, for \alpha\in\mathbb{R} and in the limit m\rightarrow0 , it is invariant under the chiral transformation...

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

There are several reasons given in the literature, why UV infinities arise in QFT in the first place. My problem is putting them together, i.e. understand how they are related to each other. So... UV divergences arise and thus we need to renormalize, because: We have infinite number of...

If I have a particle with: Momentum: p Spin: s Energy: E Position: x Time coordinate: t Charge: q And I preform a CPT transformation on said particle, what will these variables become? Can you show me mathematically? Also, could you show me how this effects the wavefunction/quantum state of...

Last year I've finished the undergraduate course in Mathematical-Physics and Mathematics and this year I've started on graduate school on Physics in order to obtain a master's degree. What I'm really interested are two main topics: general relativity and quantum field theory. I also like...

In string theory, particles is vibrating strings. However, QFT treats particles as excitations in a quantum field. Can both of these theories be correct? If so, how does them fit together?

Hi all, Another naive question related a previous post (where the topic diverged somewhat). I'm wondering about the following thought experiment: Consider the field associated with a single electron. Now, confine the field to a region (volume) of radius R - that is, field values outside of R...

Hi all, This is likely a naive question, following up on something @vanhees71 posted some time ago in another thread: My question is the following - if we take an electron that has, for example, absorbed a photon, is the portion of the wavefunction representing the electron in a lower energy...

Homework Statement Consider the process of decay of a muon into one electron, one electron antineutrino and one muon neutrino using the Fermi theory. Assume the matrix element is, ignoring the electron's and the two neturino's masses, |\mathcal{M}|^2 = 32G_F^2(m^2-2mE)mE being E the electron...

Hello, I am new to this. As I understand it, the difference between the quantum field theory and string theory is that in the former, physical field is considered as the fundamental reality, while in the latter it is believed that everything comes out of strings. My question is, by everything do...

Homework Statement STATEMENT ##\hat{H}=\int \frac{d^3k}{(2\pi)^2}w_k(\hat{a^+(k)}\hat{a(k)} + \hat{b^{+}(k)}\hat{b(k)})## where ##w_k=\sqrt{{k}.{k}+m^2}## The only non vanishing commutation relations of the creation and annihilation operators are: ## [\alpha(k),\alpha^{+}(p)] =(2\pi)^3...

Hi all - apologies, I'm starting a new thread here for something buried at the end of another thread - but I think the topic of that thread had changed sufficiently to warrant a more succinct top-level post. Thanks very much to PeterDonis for his very useful answers in the previous thread...

Hello, I know QED and QCD as isolated theories but now I thought about particle interactions with QED and QCD processes (like fpr proton-antiproton scattering). But I'm not sure how to interpret this mathematically. As I understood my Feynman diagrams are nothing more like pictures for the...

Homework Statement Consider the free real scalar field \phi(x) satisfying the Klein-Gordon equation, write the Hamiltonian in terms of the creation/annihilation operators. Homework Equations Possibly the definition of the free real scalar field in terms of creation/annihilation operators...

Hello! I read several books and took courses on quantum mechanics and particle physics and I understood the topics. However I feel that I have only pieces of informations without a global image of what is going on. For example in the particle physics classes we were given Feynman rules without...

I am getting started with QFT and I'm having a hard time to understand the quantization procedure for the simples field: the scalar, massless and real Klein-Gordon field. The approach I'm currently studying is that by Matthew Schwartz. In his QFT book he first solves the classical KG equation...

I'm studying Quantum Field Theory and the first example being given in the textbook is the massless Klein Gordon field whose equation is just the wave equation \Box \ \phi = 0. The only problem is that I'm not being able to get the same solution as the book. In the book the author states that...

I have an acquaintance who maintains that in quantum field theory, primarily the cgs system is used. OK, I know it's not really important, but I was under the impression that everyone had switched to SI. (My book on quantum field theory has very few actual quantities with units outside of GeV...

In classical mechanics, the Hamiltonian and the Lagrangian are Legendre transforms of each other. By analogy, in quantum mechanics and quantum field theory, the relationship between the Hamiltonian and the Lagrangian seems to be preserved. Where can I find a derivation of the Lagrangian...