Qft Definition and 956 Threads

Hi guys, I need to get into QFT because of my thesis, yet I study nothing near physics so I need your guidance how to best proceed. I've got two questions, any answers appreciated: 1) how much QM should I learn? In my book (zettili) I'm in chapter about harmonic oscillator and the rest of...

Hello, I've started a course on QFT and I'm having some troubles trying to find the solution of this exercise: Write the action of a non-relativistic spineless free particle in a manifestly hermitian way The problem should be simple but I'm a bit lost in the hermitian way part... What does it...

Homework Statement I'm learning QFT and trying to do a basic problem finding the equations of motion from the Euler-Lagrange equation given a lagrangian. The lagrangian is in terms of: F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu} so then my issue comes in with this part of the...

How to understand the "standard" momentum introduced in Weinberg's QFT I'm reading Weinberg's QFT Volume I. In page 63, you can find a formula (2.5.3) which states that the new state vector obtained by a Lorentz transformation is a linear combination of a whole bunch of other vectors...

Homework Statement From the Lagrangian density L = \frac{1}2 \partial_\mu \phi_a \partial^\mu \phi_a - \frac{1}2 \phi_a \phi_a, where a = 1,2,3 and the transformation \phi_a \to \phi _a + \theta \epsilon_{abc} n_b \phi_c show that one gets the conserved charges Q_a = \int d^3x...

Hey! I'm trying to learn QFT now and I'm currently reading David Tong's online lectures; http://www.damtp.cam.ac.uk/user/tong/qft/one.pdf. At page 17 finds the conserved current j^\mu = - \omega^\rho_{\ \nu} T^{\mu}_{\ \rho} x^\nu where i have understood T to be the energy momentum tensor...

Hello, a confusion has arose during my so far study of the above book. According to the composition rule (2.3.11) it should be: U\left( \Lambda ,a \right)=U\left( \mathbf{1},a \right)U\left( \Lambda \right) and according to transformation law (2.5.3) and the eigenvalue equation which follows...

Homework Statement How does one actually solve the integral for the Wightman function for a massless quantum scalar field in 4D Minkowski spacetime? That is, what is the integration technique to go from: \langle \hat{\phi}(x) \hat{\phi}(y) \rangle = \int_c d^4k \, \frac{1}{(2 \pi...

So I did QFT at university and didn't feel that I really understood what was being done. We just did some calculations, heuristic guesswork and dwelled on phenomenology. I want to do it the way I personally understand things best: by learning the mathematics in detail, almost at the level of a...

Hello, Can anyone tell me how to go about studying Topological QFT. I am fine with QFT, Fibre bundles and currently doing Cohomology from Nakahara. Should i directly start with Witten's paper or are there any more elementary review papers? Thanks.

I have already done quantum mechanics (and general relativity if it is relevant) and have all the associated math prerequisites but not much more than that. Is there anything I should add before attempting QFT and what text would be best for these? In addition, what text would you recommend for...

Hi all, A friend and I are working through Peskin and Schroeder, and we're both stumped with only the fourth equation! The interaction in question is e^+ + e^- \to \mu^+ + \mu^- with a virtual photon as the inner branch. P&S state that \mathcal{M}\propto \langle \mu^+\mu^- | H_I | \gamma...

Hello, I am trying to find out (searching did not return anything useful) what kind of mathematical background one needs to understand QFT comfortably (if such state can ever be attained :D). By comfortably I mean being able to concentrate almost entirely on the physics part rather than pick up...

Hello! I´m currenly considering buying a complete QFT book, I have done some classical field theory and glossed around in Zee's nutshell book. I also have knowledge from advanced QM up to Klein Gordon eqn and 2nd quantization. My question is now which one you think will fit me the best, my...

If it's a dirac delta doesn't it mean it's infinite when x=y? Or is it a sort of kronecker where it's equal to one but the indices x and y are continuous? I'm confused.

Homework Statement I would like to know how to get from eq. (67.3) to (67.4) in Srednicki's book on QFT. The problem is the following: Given the LSZ formula for scalar fields \langle f|i \rangle = i \int d^{4}x_1e^{ik_1x_1}(\partial^{2}+m^{2})\ldots \langle 0|T\phi(x_1)\ldots|0\rangle This...

useage of the term "field" in QFT Wikipedia defines a field as "a physical quantity associated with each point of spacetime". So contrary to a particle, where physical quantities are associated with properties like position or momentum, the field itself is a physical quantity. (This definition...

All definitions of entanglement, that I have encountered, were expressed in the language of non-relativistic QM. Suppose a free, massive particle decays into 2 other massive particles. The 2 new particles would be entangled in linear momentum. Can QFT define that type of entanglement? Any...

In the Klein-Gordon equation (spin 0), the mass dependence is (only) through m^2, whereas in the Dirac equation (spin 1/2) it's through m. Does this mean that for spin 0 particles, we can just as well describe them as having negative mass without changing any of the physics (whereas for the...

For physics between QM and String Theory I've heard a lot of different names. Quantum Electrodynamics seems to be the physics of the electron and the photon. Quantum Chromodynamics seems to be the physics of quarks. But High Energy/Nuclear/Particle Physics, Atomic physics, QFT, I don't...

Hi everybody! Please explain to me how can we consider static electromagnetic field in point of view of Quantum Field Theory.Because varying electromagnetic field can quantize to photons,so we can consider varying electromagnetic field like a ''set'' of photons. Thanks very much in advance.

In QFT of a real Klein-Gordon-Field, the field operator \phi(x) is an observable. Mathematically, this is the case because it is a sum (over all k) of a and a^\dagger and this yields a Hermitian operator. Physically, I can understand this because this equation would describe, for example, a...

When we talk about the vacuum in qft, what are we referring to? The lowest state vector of the Fock space or the lowest energy field configuration that minimize the Lagrangian? Also related, when we sandwich the free field between two vacuum states, we get zero plus quantum fluctuations. But...

I'm currently trying to make some intuitive sense out of Quantum field theory, but I'm not really understanding the vacuum. Consider a real (or complex, with + in the right places) scalar particle (a Klein-Gordon field). Now consider the propagator (or correlation function) G(x-y)=...

I just happily bought a used copy of Dirac's Lectures on Quantum Mechanics from Amazon.com. I also want his Lectures on Quantum Field Theory but they don't carry it. Anyone know where I can find a copy?

Question about this "interaction" in QFT Hi, I started two months ago my course in QFT, and since I heard about the fact that the bare mass appearing in the Lagrangian of a theory isn't the physical mass of a particle (due to self interaction, I guess), I tried to find an example explicitly...

Weinberg in his 1st book on QFT writes in the paragraph containing 2.5.12 that we may choose the states with standard momentum to be orthonormal. Isn't that just true because the states with any momentum are chosen to be orthonormal by the usual orthonormalization process of quantum mechanics...

Special relativity gives that time for a (traveler on) photon do not run. It also gives that every moving elementary particle rest in some inertial system, but photon does not rest in any inertial system. But how this can be visible in Quantum field theory or in QED? An electron and a photon...

Hi, I am reading through Section 3.4 of Lewis Ryder's QFT book, where he makes the statement, This makes some sense intuitively, but can someone please explain this direct product equivalence to me as I do not have a firm background in topology (unfortunately, I need some of it for a...

In non-relativistic QM, we spend a lot of time examining bound states--energy levels, spatial distributions, and all that. We can determine that an electron put into a Coulomb potential will have certain Hamiltonian eigenstates, which correspond to the orbitals of a hydrogen atom. However, in...

I have the basics of CM, relativity and non relativistic QM but never went much beyond KG and the Dirac equation. So I need a good intro to QFT, particle physics and the SM. Ideally with an emphasis more on the theoretical side than only experimental. I had a good feeling with "An...

Does the cutoff really have to go to infinity in QFT? It seems that once we replace bare parameters by experimental (i.e. physical) parameters, the cutoff vanishes from the expressions for physical quantities, so it didn't matter what the value of the cutoff was, whether it's 0, 10000000000, or...

The axiom says: "The interaction between two observations is constrained by causality |x-y|^2 <0 \Rightarrow [\phi(x),\phi(y)]=0 " But |x-y|^2<0 is always false that means the if the condition applies then by simple logic the consequnet of the condition can occur or not occur, I don't...

In quantum mechanics, most wave functions are normalized with \int |\phi|^2 dx^3 =1. But I did not see any field in the quantum field theory is normalized. I understand they maybe just plain waves and does not need to be normalized. But in some cases, if we do not expand the field as plain wave...

I like the way quantum mechanics can be expressed as a set of five or six axioms, like in Daniel T. Gillespie's A Quantum Mechanics Primer or David McMahon's Quantum Mechanics Demystified. Is there a similar set of axioms for quantum field theory?

Hi everyone. Many texts when describing QFT start immediately discussing about free field theories, Fock spaces etc.. I want to understand general properties of the Hilbert space, and how to find a basis of it, and how to find a particle interpretation. I know there are very mathematical...

According to Peterdonis in an old thread According to Matterwave in https://www.physicsforums.com/showthread.php?t=573589 msg #11: Peterdonis said Time is a parameter in non-relativistic QM while as a coordinate in relativistic QM/QFT. But Matterwave said parameter and coordinate has...

"Smeared" quantum fields in everyday QFT Hello everyone. I have a question regarding algebraic QFT. I read that, in order to avoid ill-defined, divergent expressions like the mode expansions for spacetime-dependent field operators φ(x), one starts from the (Wightman?) axioms, using...

There is this paper that someone posted in a thread: http://arxiv.org/abs/0904.2287 Called "QFT as pilot-wave theory of particle creation and destruction" Which talks mainly about Bohmian interpretations applied to QFT (the whole paper is in QFT scheme). However, in chapter 3, it talks...

I noticed a few sources that seem to indicate that Clifford algebra may be used in both QFT and GR. I've seen where the Clifford algebra is a type of associative algebra that generalizes the real numbers, complex numbers, quaternions, and octonions, see Wikipedia on Clifford Algebra. And I've...

If I may, I would like to give this question another try, especially if guys with some cabala in QFT can address it. Is it possible to show in the relativistic quantum theory, that the hydrogen atom is stable? (Electron will not fall onto the proton)? I explain. In the non-relativistic...

In QFT, Lagrangian is often mentioned. While in QM, it's the Hamiltonian, Is the direct answer because in QFT "position" of particle is focused on and Lagrangian is mostly about position and coordinate while in QM, potential is mostly focus on and Hamiltonian is mostly about potential and...

I'm wondering, is there still a sharp distinction between Bosons and Fermions in a rigorous QFT, if exsits? My question is motivated by the following, consider one of the equations of motion of QED: \partial_\nu F^{\nu \mu} = e \bar{\psi} \gamma^\mu \psi In our familiar perturbative QED (Here...

Please teach me this: In the book writing: ...consider the color invariant: (t^{a})_{ij}(t^{a})_{kl}(18.38).The indices i,k transform according to to 3 representation of color; the indices j,l transform according to 3^{-}.Thus,(18.38) must be a linear combination of the two possible way to...

Just read Feynmen's QFT and been wondering the difference between photon reflection by a perfect mirror and photon scatter by say a rough surface. In both cases, photons are said to be absorbed by electrons and re-emitted. But in reflection case, photons get to "preserve" its wave...

To people familiar with QFT. You know quantum fields are non-interacting and they use perturbations methods. Is there other studies or programme that would replace conventional QFT with full fledged interacting quantum fields? Also about Second Quantization where they treat the Klein-Gorden...

I'm trying to understand the basics of convensional QFT versus QM. There are too many books about QM in the introductory level for layman but too rare for QFT. But the public needs to be adept about QFT too not just particle-wave duality, entanglement and other attractions in QM. Let's start...

Hi, I have just started to try to understand some ‘basic’ quantum field theory (QFT), if this is even possible, but not sure that I have any real understanding of the scope of the fields implied within the QFT model. As such, the following description may be completely wrong, but may serve as a...

Hello, I've been reading a book on QFT (specifically, Atchison and Hey) and they say that a classical field can be expanded into an integral of harmonic oscillators. When you quantize the scalar field \phi, it becomes an operator. Now, this is an infinite number of quantum oscillators. Do...

From what little I have read about QFT, apparently the position of a particle is not a observable - it is more like an index for a collection of quantum harmonic oscillators. Thus there is no QFT equivalent to the position probability density in QM. So, how does QFT predict or describe a...