Qft Definition and 981 Threads

Hello everybody, I have three quite mathematical questions in modern QFT. 1) Why it's supposed that N=2 SUSY Yang-Mills probably cannot be put on a lattice? 2) What is the recent status of lattice approach to conformal quantum field theories? This question is motivated by the following...

Homework Statement Consider the following scalar theory formulated in two-dimensional Euclidean space-time; S=∫d2x ½(∂μφ∂μφ + m2φ2) , a) Determine the equations of motion for the field φ. b) Compute the propagator; G(x,y) = ∫d2k/(2π)2 eik(x-y)G(k). Homework Equations Euler-Lagrange equations...

I've been trying to teach myself the path integral formulation of quantum field theory and there's a point that's really bugging me: why is the integration measure ##\mathcal{D}\phi(x)## invariant under shifts in the field of the form $$\phi(x)\rightarrow\tilde{\phi}(x)=\phi(x)+\int...

Hi. I'm just starting to self-study QFT and need all the help I can get. I already have "QFT for the Gifted Amateur" and the books by Zee and Schwartz . I am looking for another book that takes things step by step from the very basics. Was looking at the book "Student friendly QFT" by Klauber. I...

Hi. I am just starting to study QFT using the path integral method and for which the main textbook is by Srednicki. Does anyone know of any good online videos which would be suitable Thanks

Hi. I'm just starting QFT for the first time. I've just finished a course in relativity but I'm confused about the index notation I've found in QFT. Here are 2 examples yi = Σ Mij xj and yj = δij yi . These examples don't seem right after what I have learned in relativity unless the index...

Apparently, there are two different routes to get to quantum field theory from single-particle quantum mechanics: (I'm going to use nonrelativistic quantum mechanics for this discussion. I think the same issues apply in relativistic quantum mechanics.) Route 1: Many-particle quantum mechanics...

What are the mathematical relationships (if any) between the particles as described by Quantum Mechanics and the particles described by Quantum Field Theory? A specific question related to the general question above arose in post #14 of the thread: How can a particle be a combination of other...

Hi all -- can anyone offer a qualitative explanation of why it is that couplings run with the energy in *relativistic* quantum theory, and not in non-relativistic? Some insight here would be much appreciated. Thanks.

Is there something wrong with negative probabilities per se? I don't what to hear that they are "unphysical" because it is not clear what reality is. Can negative probabilities (or probabilities > 1) be somehow consistent with macroscopic realism => not causing any macroscopic weirdness (no...

In quantum field theory, a fundamental particle is an excitation in the underlying field, but what does that mean? Do fundamental particles have any physical existence according to QFT?

Hello everybody! I recently started to work in nonperturbative QFT (especially CFT and SUSY models). I love my work but wonder what is the recent development in this subject beyond the SM? It is not hard to see that at the dawn of XX - early 2000's the most exciting results in nonperturbative...

I have been going through chapter 2 of Sakurai; the 1967 edition. Chapter 2 gets into the self energy of the electron, the concept of the bare mass of the electron, and vacuum fluctuations. Would these same concepts (self energy, bare mass, and vacuum fluctuations) apply to a scalar field (e g...

This is more of a QFT question, so the moderator may want to move it to another forum. The simplest example of a QFT that I learned was the scalar field; in Sakurai's 1967 textbook. I know the Higgs is a J=0 particle. Is it described by the simple scalar field discussed in Sakurai's text? I ask...

Hello everyone! I just finished studying basic quantum mechanics, using Liboff's "Introductory Quantum Mechanics", i.e. wavefunctions, uncertainty relations, basic 1D problems, dirac notation, angular momentum (orbital and spin, addition, eigenfunctions, Clebsch-Gordan coefficients etc)...

1. I'm having some trouble with some of the contour integrals covered in Chapter 2 of Peskin & Schroeder's Intro to QTF. I'm not so much as looking for answers to the integral (in fact, the answers are given in the textbook), but I was hoping someone could point me to some resources to use to...

Is probability (or probability current) conserved in RQM/QFT? I have never seen a simple answer to this question. As always, thanks in advance.

Hi everyone, I am currently preparing myself for my Bachelor thesis in local quantum field theory. I was encouraged by my advisor to read the books of M. Reed and Simon because of my lag of functional analysis experience but I have quite often problems understand the “obvious” conclusions. For...

During a course of QFT my teacher said that in this theory is not possible to use the operator X for the position in order to construct with the momentum P and the spin S a set of irreducible operators that charachterize particles, and that we need a different point of wiev: the irreducible...

In the canonical formulation of QFT (to which I've been exposed), it is always argued that only differences in energy are physically observable and so we can deal with the fact that the vacuum energy is infinite by redefining the vacuum such that its energy is zero and we subsequently measure...

As far as I understand it gravity is sensitive to absolute energies, as seen directly through Einstein's equation G_{\mu\nu}=8\pi GT_{\mu\nu} Thus the local geometry of spacetime is directly affected by the local energy density (and not just differences in energy). So whenever gravity is taken...

Hello everybody! I've recently decided that I'm interested in supersymmetric solitons and want to work in this area for future 2 undergrad years. I wonder what is the best place to study the general theory of solitons in QFT? Is Rubakov "Classical gauge fields" really the best book for those who...

Hi all, I have a question about the ground state of an interacting quantum field theory. The state space in non-interacting QFT is a space where each field mode (with specified momentum p) has some occupation number n. These modes are interpreted as n particles with momentum p. The vacuum is...

Hi all, can anybody help me to find literature that takes the reader on a step-by-step path from non-relativistic quantum theory to relativistic quantum theory? I imagine something like that: it starts with a single harmonic oscillator, analyzes the non-harmonic oscillator (does the...

Why is it required that interactions between fields must occur at single spacetime points in order for them to be local? For example, why must an interaction Lagrangian be of the form \mathcal{L}_{int}\sim (\phi(x))^{2} why can't one have a case where \mathcal{L}_{int}\sim\phi(x)\phi(y) where...

Hello everybody. I'm interested in some problems of bound states in external fields in QFT (especially QED). I wonder are there any lectures/books or reviews which provide modern treatment of this subject? I would like to learn more about general formalism and applications in QED (I allready...

I've been trying to fill in my mathematical blanks of things I just took as dogma before. Especially, not having a background in functional analysis, the functional derivatives often seem to me mumbo jumbo whenever things go beyond the "definition for physicists". In particular I tried looking...

I'm aware that most modern textbooks gloss over relativistic qm and jump to qft. Since I'm not that brilliant of a student I'm thinking that i should firstly familiarize myself with relativistic and then go to qft. So my first question: Is it worth it to study relativistic qm or should i jump...

I've read in a set of lecture notes that the requirement of locality and unitarity in QFT imply that the vacuum must have a non-zero energy associated with it (http://arxiv.org/pdf/1502.05296v1.pdf , top of page 3 under heading "What is the problem?"). My question is, why does the locality and...

I am slightly unsure as to whether I have understood the notion of locality correctly. As far as I understand it locality is the statement that if two events occur simultaneously (i.e. at the same time) then no information can be shared between them (they are causally disconnected). Thus a...

First of all, sorry if this is in the wrong forum, wasn't quite sure which one to post it in given the question. My question is, given two space-time points ##x^{\mu}## and ##y^{\mu}##, if the events that occur at these points are simultaneous, i.e. ##x^{0}=y^{0}##, are the two events...

On page 12 of Zee's QFT in a nutshell, he rewrites an integral from dirac notation to a mixture of schrodinger/dirac My question is, since , what happened to the integrals, and shouldn't there be four wave functions instead of two? I tried writing out the integrals explicitly, thinking maybe...

I'm relatively new to QFT and was wondering how the QED vacuum has a dormant zero average-field condition if there is a zero-point energy of the field as well? How is there a zero average and a zero point energy?

I'm looking at the simplest example of an interacting theory, and this is the theory of a neutral scalar boson $\phi$ with $\lambda \phi^4$ interaction term. Can I ask: is there a physical interpretation of the `charge' through which this field interacts with itself? In particular, is \lambda...

Hello I am an incoming Biology student (college), i really wanted to take applied physics as my course but my parents told me that it is better to be a doctor, anyways, it's summer here and I started taking Calculus 1 in coursera.com (i have NO backgroud in calculus because we don't have...

Homework Statement I'm working on path integrals for fermions and I came across an exercise that ask to compute the three point functions , one of that is the: $$<0|J^{\mu}(x_1)J^{\nu}(x_2)J^{\rho}(x_3)|0> $$ where $$J^{\mu}$$ is the current $$J^{\mu}=\bar{\psi}\gamma^{\mu}\psi$$. ***Can you...

I've been working through a qft book by Sadovskii (while I wait for my Peskin book to come in) and I've used some later chapters of Griffith's Into to Elementary Particles as an introduction to some qft. My issue with both of these is that, where in classical mechanics we have the Lagrangian...

The problem statement. When an exercises say " the interaction in a QFT has dimensions Δ" , what does it mean?, it means the field or the Lagrangian has this mass dimension? In this exercise I'm trying to find the classical beta function (β-function) for the assciated couling.

In quantum mechanics, we can define the scattering amplitude f_k(\theta) for two particles as the coefficients of an outgoing spherical wave. More precisely, the asymptotic behaviour (when r\rightarrow\infty) of a wave function of two scattering particles, interacting with some short range...

The spin observable for spin 1/2 particles is represented by Pauli Matrices acting upon a 2-dimensional Hilbert Space. In RQM, forgetting about the matter-antimatter duality for the moment, that TWO-state Hilbert Space is directly related, through the Lorentz Group, to the TWO separate...

In QFT vol 3 of Weinberg write:''For d=11 the spin 2 graviton representation of little group O(9) is a symmetric traceless tensor with 9x10/2-1=44 independent components:there is one 2+(-)i3,2+(-)i3 component with J23=+(-)2, seven2+(-)i3,k components with J23=+(-)1; and twenty eight k,l...

I recently learned that with (local) gauge invariance, functional quantization needs to factor out volume factor(Faddeev-Popov procedure). Why does this has to be done?Just to remove infinity? As far as I am concerned, ##\phi^4## theory contains invariance(for example ##\phi\to\phi\cdot e^{i...

Hey guys! I was reading the following paper http://arxiv.org/abs/hep-ph/0703260 for Georgi and I have a conceptual question about it. Howard Georgi was talking about this Unparticle Physics theory and at the base of his analysis is the principle of scale invariance. So Georgi is saying what if...

The Feynman propagator is $$ G_{F}(x) = \int d^4p \, \frac{e^{-ip x}}{p^2 - m^2 + i\epsilon}. $$ I want to understand why the directions of Wick rotation in position space and momentum space are contrary. Every book I find says something like "we should keep ##xp## unchanged", but why? As we...

Can one apply the Hubbard-Stratonovich transformation to the exponential of the Laplace–Beltrami operator?

(I hope this post goes in this part of the forum) Hi, I was wondering if someone could help me with the following: I have a (1+1) scalar field decomposed into two different sets of modes. One set corresponds to a Minkowski frame in (t,x) coordinates, the other to a Rinder frame in conformal...

Hi all, so I've come across the following Gaussian integral in QFT...but it has a denominator and I am completely stuck! \int_{0}^{\infty} \frac{dx}{(x+i \epsilon)^{a}}e^{-B(x-A)^{2}} where a is a power I need to leave arbitrary for now, but hope to take between 0 and 1, and \epsilon is...

Hi all, I have an undergraduate degree in Physics, but I've since specialized in more environmental applications of Physics. I've taken a few quantum Physics courses as part of my degree, but, if I'm being honest, what I took from those courses was more of a mathematical view of the field, such...

I am working on Schwartz QFT book problem 14.3, particularly part (c). Basically, it asks us to evaluate the following integration. \int \cfrac{d^3 p}{2\pi^3} \omega_p e^{i \vec{p} \cdot (\vec{x}-\vec{y})} where \omega_p = \sqrt{p^2 + m^2} I could perform the angular integration, and the...

Hi! I'm desperately trying to develop a list of prerequisites that will enable me to work on topics like quantum gravity, advanced QFT (on curved spacetime etc.) etc. I am currently in the second year of an undergrad theoretical physics degree in the UK, and am heavily unsatisfied with the way...