Quantum field theory Definition and 559 Threads

The Klein-Gordon equation has the Schrodinger equation as a nonrelativistic limit, in the following sense: Start with the Klein-Gordon equation (for a complex function ##\phi##) ## \partial_\mu \partial^\mu \phi + m^2 \phi = 0## Now, define a new function ##\psi## via: ##\psi = e^{i m t}...

Homework Statement Hi, I am looking at the attached question, parts a) and b).Homework Equations The Attempt at a Solution so for part a) it vanishes because in the ##lim \epsilon \to 0 ## we have a complete derivative: ## \int d\phi \frac{d}{d\phi} (Z[J]) ## for part b) we attain part a)...

Hello all, Can you tell me what is the best book to study QFT when you are thinking to follow a PhD in cosmology (Dark energy, scalar fields, extension to GR, string theory).

I am trying to read about and understand string theory. But in trying to understand how it reconciles with the world of quantum field theory and quantum mechanics, I am getting a little confused. How does the string move through and propagate through the quantum field? Does string theory...

Although the question came to my mind while studying Weinberg's QFT books, the doubt is much more general than that, and is not a doubt about physics, but rather about how to actually study and learn the topic alone from the book. From one point I agree that coming up with this doubt nearly...

Homework Statement Given the spinors: \Psi_{1}=\frac{1}{\sqrt{2}}\left(\psi-\psi^{c}\right) \Psi_{2}=\frac{1}{\sqrt{2}}\left(\psi+\psi^{c}\right) Where c denotes charge conjugation, show that for a vector boson #A_{\mu}#; A_{\mu}\overline{\Psi_{1}}\gamma^{\mu}\Psi_{2} +...

There seem to be two ways of defning what a vacuum is in QFT: 1. It is state $|0\rangle$ such that $$a_k|0\rangle = 0$$ for all anihilation operators $$a_k$$, with creation operators $$a_k^{\dagger}$$. Thus, it is defined in Fock space. 2. It is state $$|0\rangle$$ such that derivative...

Homework Statement https://i.imgur.com/sI3JiB4.jpg https://i.imgur.com/PLpnPZw.jpg I have no idea how to solve the first question about the vacuum energy. I solved the second and third problems, but I'm hopelessly stuck at the first. 2. Homework Equations The Hamiltonian can be written as...

Quantum mechanics replaces the classical concept of cause and effect with probabilities. The best explanation: it just is. While the Heisenberg Uncertainty Principles hold in quantum field theory does QFT offer a different interpretation to this concept? Or at least mitigate some of the...

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.

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

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.

"It is easily shown" that the gamma 5 matrix anticommutes with the four gamma matrices. Can someone tell me how or provide a link to such proof?

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Quantization 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 >> [/color] 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...

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

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)[SIZE=16px] 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...

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

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...