Field theory Definition and 523 Threads

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.

This question is more about the maths than the physics. So I am reading the textbook by Bergersen and Plischke, and they get the following: $$m= \tanh [ \beta (qJm+h)]$$ where ##m## is the magnetization, ##q## is the number of nearest neighbours of site ##0##, ##J## and ##h##are the...

In quantum gravity, I get 'mixed signals' as regards renormalizability. My state of confusion is being caused, I suspect, by an incomplete understanding of what is covered under t'Hooft's 1972 proof that non-Abelian gauge theories are renormalizable. ( = Nobel Prize 1999). Specifically, some...

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...

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

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...

I have some questions about scalar field Lagrangians, using the box notation defined as \Box \equiv \frac{\partial^2}{\partial t^2} - \nabla^2 . It's a basic, perhaps silly issue, but somehow I've managed to sweep it under the rug for a long time. So, usually, the Lagrangian of a free scalar...

Hi everyone, I have a question that, when came to me, sounded a bit silly to me as well, but then I realized, I myself maybe don't understand the logic behind this 100%, so why not discussing with you about it. So my question is the following. Usually we are used to do quantum field theory...

I saw a documentary the other day where Michio Kaku said something that really peaked my interest. He said that Einstein in his last days was working on something having to do with how small geometries of some sort being the cause of gravity. Does anyone know the details of Einstein's Unified...

I'm trying to derive the Klein Gordon equation from the Lagrangian: $$ \mathcal{L} = \frac{1}{2}(\partial_{\mu} \phi)^2 - \frac{1}{2}m^2 \phi^2$$ $$\partial_{\mu}\Bigg(\frac{\partial \mathcal{L}}{\partial (\partial_{\mu} \phi)}\Bigg) = \partial_{t}\Bigg(\frac{\partial \mathcal{L}}{\partial...

Context The following is from the book "Ideas and methods in supersymmetry and supergravity" by I.L. Buchbinder and S.M Kuzenko, pg 56-60. It is about realizing the irreducible massive representations of the Poincare group as spin tensor fields which transform under certain representations of...

I'm a rising physics sophomore at a Japanese university. I've studied general physics, linear algebra, and analysis (actually, calculus of single and several variables with emphasis on analysis, everything was proven and the theoretical background was well explained) Other than that, I've...

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

Double field theory [1] is an attempt to realize T-duality of string theory at the level of field theory. For instance, if a field in ordinary field theory lives in 4 non-compact spacetime dimensions, then a field in double field theory lives in 8 non-compact spacetime dimensions. I don't...

Suppose one starts with the standard Klein-Gordon (KG) Lagrangian for a free scalar field: $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^{2}\phi^{2}$$ Integrating by parts one can obtain an equivalent (i.e. gives the same equations of motion) Lagrangian...

Hello friends. I'm trying to compute an EoS to walecka model of barion interaction, but I'm having trouble to solve this equation by bisection. M*=M-gs²*nb/ms² where nb= (M*)*( kf*Ef- (M*)²* ln (kf+Ef)/M*) , using Ef= sqrt( kf²+(M*)²) and Cs²= gs² M² / ms² = 267.1 I'm using J. D. Walecka...

What is the intuitive reasoning for requiring that a Lagrangian describing a free-field contains terms that are at most quadratic in the field? Is it simply because this ensures that the EOM for the field are linear and hence the solutions satisfy the superposition principle implying (at least...

Hi, i would be curious to know what would be the prerequisites for learning the classical field theory !

In field theory a typical Lagrangian (density) for a "free (scalar) field" ##\phi(x)## is of the form $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi -\frac{1}{2}m^{2}\phi^{2}$$ where ##m## is a parameter that we identify with the mass of the field ##\phi(x)##. My question is...

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...

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...

In classical field theory, translational (in space and time) symmetry leads the derivation of the energy-momentum tensor using Noether's theorem. From this it is possible to derive four conserved charges. The first turns out to be the Hamiltonian, and thus we have energy conservation. The...

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...

The thread https://www.physicsforums.com/threads/qft-operators-time-space-asymmetry.906369/ contains the first recommendation I have seen in these forums for Klauber's book, and instead of hijacking that thread I thought I might ask a question here. I find the book more readable than many for...

The mantra in theoretical physics is that global gauge transformations are physical symmetries of a theory, whereas local gauge transformations are simply redundancies (representing redundant degrees of freedom (dof)) of a theory. My question is, what distinguishes them (other than being...

Hi, I have recently began studying quantum field theory and have just seen how the quantization of the complex scalar field, noting that there is invariance of the action under a phase rotation shows the existence of antiparticles. I just have a couple of questions, apologies in advance if...

Hello, I would appreciate it if someone would suggest some Quantum Field Theory books that an advanced undergraduate could read. Thank you!

Homework Statement I think the in equation ##(28.2)##,##x^i## in ##\frac{dx^i}{dt}## and the ##x^i## decides ##\rho## is not the same,if they are equaivalent,##\rho## can not vary with position changing and time fixed, because ##\frac{dx^i}{dt}## indicate the ##x^i(t)## which means if position...

Homework Statement I am not sure whether the meaning of the equation ##(3)## which used for deriving momentum is as same as equation ##(4)##.I will make a detailed description below. The lagrangian function for a free particle is ##L=-mc^2\sqrt{1-\frac{v^2}{c^2}} \quad (1)## The action from...

Hi all. I am looking for a book in Quantum Field Theory, not for the first read. I have already studied it for university purpose, but now i would like to study the subject again from a book to cover holes and have a deeper understanding before starting a possible PhD. I heard about Srednicki...

Classical fields are usually constructed using a collection of classical harmonic oscillators, e.g. masses connected to springs. The energy of a classical harmonic oscillator is proportional to the amplitude squared. QFT uses quantized versions of those same classical fields. But, in the...

Hello. I'm studying a course of the Quantum Field Theory and I got a question in a canonical quantization of a scalar field. I don't write a full expression of the field quantization here but the textbook said terms with ei(p⋅x - Ept) are associated with an incoming particle and terms with...

Hello I am little bit confused about one topic on theoretical Physics and that is If we want to describe our Quantum world (example atoms in metal) then should I use Quantum field theory or Quantum mechanics?

Currently working through some exercises introducing myself to quantum field theory, however I'm completely lost with this problem. Let $$L$$ be a Lagrangian for for a real vector field $$A_\mu$$ with field strength $$F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$$ gauge parameter...

As I understand it, the need for quantum field theory (QFT) arises due to the incompatibility between special relativity (SR) and "ordinary" quantum mechanics (QM). By this, I mean that "ordinary" QM has no mechanism to handle systems of varying number of particles, however, special relativity...

Why is the partition function ##Z[J]=\int\ \mathcal{D}\phi\ e^{iS[\phi]+i\int\ d^{4}x\ \phi(x)J(x)}## also called the generating function? Is the partition function a q-number or a c-number? Does it make sense to talk of a partition function in classical field theory, or can we define...

Consider the partition function ##Z(\lambda)## of the ##0##-dimensional scalar ##\phi^{4}## theory ##Z(\lambda)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}d\phi\ \exp\{-\frac{1}{2}\phi^{2}-\frac{\lambda}{4!}\phi^{4}\}.## It can be shown that...

Dear Sir, P 25 in quantum field theory for the gifted amateur One makes Fourier transforms from the position to the frequency space for the system of linear chain of N atoms. How can I see that in the frequency space the excitations are uncoupled . I also don’t understand equation 2.50

For a ##\phi^{3}## quantum field theory, the interaction term is ##\displaystyle{\frac{g}{3!}\phi^{3}}##, where ##g## is the coupling constant. The mass dimension of the coupling constant ##g## is ##1##, which means that ##\displaystyle{\frac{g}{E}}## is dimensionless. Therefore...

No. This is a noncovariant, observer-specific view.In the covariant, observer-independent view of fields, states are labeled instead by the causal classical solutions of hyperbolic field equations. On the collection of these the Peierls bracket is defined, which is the covariant version of the...

Hello. In my university the course of the Field theory was based on Landau's book, which of course, is a quiet rough book to introduce a subject with - so all I was left with was superficial knowledge of the branch. I would like to read another book (introductory level is preferred) about the...

Hi. This question most probably shows my lack of understanding on the topic: why are scalar fields Lorentz invariant? Imagine a field T(x) [x is a vector; I just don't know how to write it, sorry] that tells us the temperature in each point of a room. We make a rotation in the room and now...

Hi everyone, I'm approaching the study of EFT but I'm facing some problems. While in QFT usually we want renormalizable theories, in EFT we don't want this costraint anymore and this opens up space for a lot more terms in the Lagrangian. My problem is that when we want to calculate amplitudes...

Homework Statement I'm working through Zee for some self study and I'm trying to do all the problems, which is understandably challenging. Problem 1.3.1 is where I'm currently stuck: Verify that D(x) decays exponentially for spacelike separation. Homework Equations The propagator in question...

In classical field theory, the field, φ, is usually constructed from a very large number of coupled harmonic oscillators. Let's say our φ consists of just electrons. What does φ best represent physically, a very large number of electrons or can it represent just a few electrons? Which is the...

Hello! I am a diploma student at HEP section. I am going to have an interview for PhD within a week. I've finished the course and learned a lot about Lie algebra, quantum field theory, general relativity, standard model, etc. How can I review everything as soon as possible? For example, Mark...