What is Quantum field theory: Definition and 571 Discussions
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles.
QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory in quantum mechanics.
My discussion (copying this from a Facebook post dated April 29th, 2018):
This weakening of the Wightman axioms is not considered in, for example, Section 3.4 of R F Streater, "Outline of axiomatic relativistic quantum field theory", Rep. Prog. Phys. 38 771-846 (1975), where Streater critiques...
Homework Statement
I am considering the Klein Gordon Equation in a box with Dirichlet conditions (i.e., ##\hat{\phi}(x,t)|_{boundary} = 0 ##). 1-D functions that obey the Dirichlet condition on interval ##[0,L]## are of the form below (using the discrete Fourier sine transform)
$$f(x) =...
In the following there is a proof, for positive values of ##a## only, of (8.18) of Kaku, reference 1, I quote'
$$\int_{-\infty}^\infty~\mathrm{d}p~e^{iap^2+ibp}=\sqrt \frac{i\pi}{a}e^{-ib^2/4a}~~~~~~~~~~~~~(8.18)$$
'. Kaku says this result can be proved by completing the square.
$$iap^2+ibp =...
There is nothing wrong with the well known
$$e^{i\theta}=\cos\theta+i\sin\theta$$
for real ## \theta## but what about
$$\int_{-\infty}^\infty~e^{i\theta(p)}\mathrm{d}p=\int_{-\infty}^\infty~\cos\theta(p)\mathrm{d}p+i\int_{-\infty}^\infty~\sin\theta(p)\mathrm{d}p$$
I have been trying to use...
Homework Statement
Consider four real massive scalar fields, \phi_1,\phi_2,\phi_3, and \phi_4, with masses M_1,M_2,M_3,M_4.
Let these fields be coupled by the interaction lagrangian \mathcal{L}_{int}=\frac{-M_3}{2}\phi_1\phi_{3}^{2}-\frac{M_4}{2}\phi_2\phi_{4}^{2}.
Find the scattering amplitude...
I have found a general result for certain exponential integrals that may be of interest to those involved with using path integrals. I am not certain that I am applying it correctly but it appears to work, and I can reproduce results quoted in various textbooks , using it. This may however be...
Could anyone explain what a quantum field configuration is, and any relation this concept may have to the idea of a wavefunction?
Perhaps for a scalar, quantum field?
Can whatever type of information be encoded in a boundary in holographic principle?
in a question some years ago regarding holography (https://physics.stackexchange.com/questions/75436/are-stokes-theorem-and-gausss-theorem-examples-of-the-holographic-principle)
It is said that AdS/CFT is the...
[Moderator's note: This thread is spun off from another thread since it was dealing with a more technical point that is out of scope for the previous thread. The quote that starts this post is from the previous thread.]
I feel the same about transformations of Dirac matrices and Dirac field...
I am confused about the field transformation under conformal transformation. Consider the scale transformation of field ##\phi## (not necessarily scalar)
In CFT of Francesco et al, formula (2.121), the transformation is
$$ \vec{x}\rightarrow \vec{x}'=\lambda x,\,\,\,\phi(\vec{x}) \rightarrow...
I read somewhere that, suppose a scalar field Σ transforms as doublet under both SU(2)L and SU(2)R, its general rotation is
δΣ = iεaRTaΣ - iεaLΣTa.
where εaR and εaL are infinitesimal parameters, and Ta are SU(2) generators.
I don't quite understand this. First, why does the first term have...
In the algebraic approach, a quantum system has associated to it one ##\ast##-algebra ##\mathscr{A}## generated by its observables and a state is a positive and normalized linear functional ##\omega : \mathscr{A}\to \mathbb{C}##.
Given the state ##\omega## we can consider the GNS construction...
Arnold Neumaier,
I have 2 elementary questions about your article “The Physics of Virtual
Particles”.
1. In the paragraph headed “States.” on p. 4, of 13, you talk about states of a
physical system, with a mixed state specified by a Hermitian operator ρ of trace
1 acting on the Hilbert...
Studying QFT on curved spacetimes I've found the algebraic approach, based on ##\ast##-algebras. In that setting, a quantum system has one associated ##\ast##-algebra ##\mathscr{A}## generated by its observables.
Here we have the algebraic states. These are defined as linear functionals...
This ties into this thread https://www.physicsforums.com/threads/i-want-to-know-the-exact-problems-of-merging-gr-and-qm.939509/ , I would like to know SR/GR's opinion of QM/QFT. I need both sides of the story.
This thread is I want a set of experts in the subject to show me the exact math of why Einstein's field Equations along with Special Relativity and Schrodinger's Equation along with deeper QM like QFT cannot be fused with GR. I want to see the exact anomalies in the equations myself from the...
According to our best theories of physics, the fundamental building blocks of matter are not particles, but continuous fluid-like substances known as 'quantum fields'. David Tong explains what we know about these fields, and how they fit into our understanding of the Universe.
According to our best theories of physics, the fundamental building blocks of matter are not particles, but continuous fluid-like substances known as 'quantum fields'. David Tong explains what we know about these fields, and how they fit into our understanding of the Universe.
Homework Statement
Derive, using the canonical commutation relation of the position space representation of the fields φ(x) and π(y), the corresponding commutation relation in momentum space.Homework Equations
[φ(x), π(y)] = iδ3(x-y)
My Fourier transforms are defined by: $$ φ^*(\vec p)=\int...
I will soon start with the course introduction to QFT and are hence an amateur on the subject.
However I could not help but wonder,
If particles are describes by oschlliations in a field, how can a "bigger body" be made up of several such oscillation? (A bigger particle is made out of several...
Greg Bernhardt submitted a new PF Insights post
Mathematical Quantum Field Theory - Interacting Quantum Fields
Continue reading the Original PF Insights Post.
According to [Dark Energy and the Accelerating Universe](https://ned.ipac.caltech.edu/level5/March08/Frieman/Frieman5.html) quantum field theory says that the energy density of the vacuum, ##\rho_{vac}##, should be given by
$$\rho_{vac}=\frac{1}{2}\sum_{\rm...
Hi!
I will soon begin my third year at the theoretical physics program. I have done a bunch of classical & Lagrangian mechanics, SP, atomic physics, electromagnetism, and basic particle physics.
Is it a good idea to study general relativity and quantum field theory with this knowledge, what...
Greg Bernhardt submitted a new PF Insights post
Mathematical Quantum Field Theory - Free Quantum Fields
Continue reading the Original PF Insights Post.
Hi,
I'm trying to calculate an integral which looks unfortunately divergent. The structure is similar to a loop integral but the appendix in the Peskin textbook didn't have a useable form. The integral form is (I did a u substitution to make it easier to look at)
\int_x^{\infty}du...
<< Mentor note -- posts broken off from an Insights comment thread >>
Ok, this is where I show my ignorance, but all this is theoretical and why I get lost with these academia discussions. Time is just a mathmatical construct to measure the motion of two or more objects relative to each other...
Hi!
I have studied about 70% of the textbook QFT for the Gifted Amateur by Lancaster and Blundell and I think that I am now ready to go to more advanced treatments.
My thoughts were to go to Klauber's Student Friendly Quantum Field Theory as I have read that it is very pedagogical. Problem is...
Greg Bernhardt submitted a new PF Insights post
Mathematical Quantum Field Theory - Reduced Phase Space
Continue reading the Original PF Insights Post.
Quantum mechanics does a good job in describing the hydrogen atom. Are there any views either mathematically or conceptually in describing the hydrogen atom?
I've done some recent reading on IR divergences (propagators becoming singular, etc.). I believe I understand collinear divergences (to some extent)... but I'm not sure about total energies for (primarily) soft photons.
In all scattering experiments, total energy should be conserved - but if...
Greg Bernhardt submitted a new PF Insights post
Interview with Mathematician and Physicist Arnold Neumaier
Continue reading the Original PF Insights Post.
Arnold will welcome science questions and comments only.
I have read( even Peter Donis mentioned it) that the derivation of the potential between two particles is not a true QFT, why is that? if not, then what is it?
Thanks in advance.
I would like to know where one may operate with tensor quantities in quantum field theory: Minkowski tensors, spinors, effective lagrangians (for example sigma models or models with four quark interaction), gamma matrices, Grassmann algebra, Lie algebra, fermion determinants and et cetera.
I...
How would sliding the plates parallel to each other in order to separate them (they are prevented from contacting to avoid friction) require the same amount of energy as pulling them apart? You're not pushing against the force (the net force at the edges pulling it back is balanced by opposite...
I'm trying to work through a scattering calculation in the Peskin QFT textbook in chapter 5, specifically getting equation 5.10. They take two bracketed terms
4[p'^{\mu}p^{\nu}+p'^{\nu}p^{\mu}-g^{\mu\nu}(p \cdot p'+m_e^2)]
and
4[k_{\mu}k'_{\nu}+k_{\nu}k'_{\mu}-g_{\mu\nu}(k \cdot...
Consider a free real scalar field. The quadratic term in field of spacetime implies that a universe of these free particles is created, annihilated, recreated, and so on moment by moment.
In this video Susskind explains the quadratic term in the Lagrangian
youtu.be/D7yXoNAg3J8
(At minute...
I have a major in mathematical physics and mathematics and currently I'm on a graduate course in Physics working on a master's thesis. When I started the graduate course I was going to work on General Relativity and Quantum Field Theory on Curved Spacetimes (QFTCS). It turns out that by several...
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...
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
-...