What is Quantum field theory: Definition and 567 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.

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  1. joebentley10

    I Applying Euler-Lagrange to (real) Klein-Gordon Lagrangian

    I'm currently studying Quantum Field Theory and I have a confusion about some mathematics in page 30 of Mandl's Quantum Field Theory (Wiley 2010). Here is a screenshot of the relevant part: https://www.dropbox.com/s/fsjnb3kmvmgc9p2/Screenshot%202017-01-24%2018.10.10.png?dl=0 My issue is in...
  2. L

    Other Graduate Research topic involving QFT and General Relativity

    Last year I finished the undergraduate course in Mathematical Physics. This year, more precisely in March, I'm going to start the graduate course to acquire a master's degree in Physics. Now, for this course I must choose a research topic and find an advisor. This is being a little bit...
  3. A. Neumaier

    Insights Vacuum Fluctuations in Experimental Practice - Comments

    A. Neumaier submitted a new PF Insights post Vacuum Fluctuations in Experimental Practice Continue reading the Original PF Insights Post.
  4. N

    A Casual dynamical triangulation?

    Is CDT a QFT? Can QFT be used with it to explain fundamental particles?
  5. N

    I What approaches to quantum gravity are QFT's?

    What are the different approaches to solving quantum gravity that are in the framework of quantum field theory?
  6. binbagsss

    A Quantum Field theory profound insight antiparticles

    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...
  7. Q

    Unruh Effect for Standard Model Fields

    I have seen the derivation for Unruh radiation for a massless, non-interacting scalar field (Carroll). Are there interesting differences that arise for more realistic standard model cases. For example, what does QCD look like for an accelerating observer? Any papers that detail this would be...
  8. N

    A Can asymptotic safety in quantum gravity be right?

    Asymptotic safety in quantum gravity is a local QFT. According to many people, local quantum field theories cannot be correct in terms of being a quantum gravity theory. Lubos Motl outlines 4 reasons why they can't be right. "Quantum gravity cannot be described as a local field theory in the...
  9. vishal.ng

    A Taylor series expansion of functional

    I'm studying QFT in the path integral formalism, and got stuck in deriving the Schwinger Dyson equation for a real free scalar field, L=½(∂φ)^2 - m^2 φ^2 in the equation, S[φ]=∫ d4x L[φ] ∫ Dφ e^{i S[φ]} φ(x1) φ(x2) = ∫ Dφ e^{i S[φ']} φ'(x1) φ'(x2) Particularly, it is in the Taylor series...
  10. J

    Quantum Quantum Field Theory books for undergraduates

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

    A How is the invariant speed of light enocded in SL(2,C)?

    In quantum field theory, we use the universal cover of the Lorentz group SL(2,C) instead of SO(3,1). (The reason for this is, of course, that representations of SO(3,1) aren't able to describe spin 1/2 particles.) How is the invariant speed of light enocded in SL(2,C)? This curious fact of...
  12. Luca_Mantani

    Quantum Book on Quantum Field Theory for PhD

    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...
  13. E

    Coulomb scattering of spin-zero particle (QFT)

    I'm looking at Aitchison and Hey's QFT book, trying to verify Eq. 8.27 (which is in fact problem 8.2). It asks us to verify that the matrix element for the scattering of a charged spin zero particle (s^+) is <s^+,p'|j^\mu_{em,s}|s^+,p> = e(p+p')^\mu e^{-i(p-p')\cdot x} where...
  14. N

    A Fetter & Walecka's derivation of second-quantised kinetic term....

    On page 9 of *Quantum theory of many-particle systems* by Alexander L. Fetter and John Dirk Walecka, during the derivation of the second-quantised kinetic term, there is an equality equation below: >\begin{align} \sum_{k=1}^{N} \sum_{W} & \langle E_k|T|W\rangle C(E_1, ..., E_{k-1}, W...
  15. B

    A Spinor Lorentz Transform via Vectors - Cross Product Issue

    The Lorentz transformation operator acting on an undotted, i.e. right-handed, spinor can be expressed as $$e^{-\frac{1}{2} \sigma \cdot \mathbf{\phi} + i\frac{1}{2} \sigma \cdot \mathbf{\theta}}.$$ There is a very cool, almost childlike, derivation of this expression in Landau Vol. 4 S. 18 I've...
  16. F

    I Is the QFT field real or just a mathematical tool?

    Sorry, I know this has been talked about many times before but I like to put the question in a direct way so I may understand. Since there are more than 10^80 particles and radiation, how can a single point in space carry the values for all these fields at the SAME time all the time if they are...
  17. Q

    A Does an infinitesimal generator of acceleration exist?

    I am trying to determine what types of field theories have a Lagrangian that is symmetric under an Infinitesimal acceleration coordinate transformations. Does an infinitesimal generator of acceleration exist? How could I go about constructing this matrix?
  18. G

    A Wave of an outgoing anti-particle in quantum field theory?

    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...
  19. A

    B Quantum field theory VS Quantum mechanics

    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?
  20. M

    A Quantized E field, Coulomb Gauge with Interactions

    The common presentation for free field quantization proceeds with the Lorentz and Coulomb (##\phi = 0, \,\nabla \cdot \mathbf{A} = 0 ##) constraints. Then ##A## can be defined $$\mathbf{A} \propto \iint \frac{d^3 p}{\sqrt{2\omega_p}}\sum_{\lambda} \Big(e^{i\mathbf{p}\cdot...
  21. D

    A Quantum Field Theory - Why quantise fields?

    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...
  22. Indiana

    A Where does statistical physics/mechanics fit in with QFT,GR?

    We have two theories namely,Quantum Field Theory which works very well at sub-atomic scales, and the General Relativity which works very well at very large scales.So, my question is where does statistical physics/mechanics fit in? What role statistical physics/mechanics play in today's modern...
  23. S

    A Partition function in quantum field theory

    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...
  24. A

    A Quantum Field Theory for the Gifted Amateur: Fourier Transforms & Excitations

    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
  25. S

    A Relevant interactions in quantum field theory

    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...
  26. A. Neumaier

    A States in relativistic quantum field theory

    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...
  27. john baez

    Insights Struggles with the Continuum - Conclusion - Comments

    john baez submitted a new PF Insights post Struggles with the Continuum - Conclusion Continue reading the Original PF Insights Post.
  28. john baez

    Insights Struggles with the Continuum - Part 7 - Comments

    john baez submitted a new PF Insights post Struggles with the Continuum - Part 7 Continue reading the Original PF Insights Post.
  29. Romanopoulos Stelios

    Differentiation of unitary operator U(t,t') in Peskin and Schroeder

    How the authors came to the conclusion (eq. 4.25) that $$ U(t,t')=e^{iH_0(t-t_0)} e^{-iH(t-t')} e^{-iH_0(t'-t_0)} $$
  30. S

    Quantum Particles & Quantum Fields - Hagen Kleinert

    I've discovered a potential treasure horde tucked away in the deep dark folds of the world wide web. A 1625 page mammoth on all aspects of quantum field theory by Prof. Hagen Kleinert. There's a draft ed. for free available here -...
  31. I

    B Shape of elementary particles in QFT, etc?

    Hello, I hope this is not a stupid question as I am not a physicist. But I was curious about how contenders for the so-called Theory of Everything view the shape of the elementary particles. I know that the basic idea of string theory is related to the shape of elementary particles as one...
  32. qqbar

    Peskin and Schroeder eq. 18.84

    Homework Statement So I am self-studying the book of Peskin&Schroeder, and there is something I don't understand on page 616. In eq. 18.80, there is a numerical factor of ½ and going from e2 to α will introduce a factor 4π when proceeding to eq. 18.84. But then there should be a numerical...
  33. J

    A Srednicki's QFT: Feynman Rules and Feynman Diagrams

    I'm reading Srednicki's Quantum Field Theory. I 'm trying to read Srednicki's presentation of Feynman Diagrams in the chapter Path Integral for the Interacting Field Theory. Link to the book: The path integral for the phi-cubed theory is equation 9.11 in the book. Please read that. I get the...
  34. Luca_Mantani

    A Quantum Field Theory vs Effective Field Theory

    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...
  35. J

    A How to understand the electric-field operator?

    I know the positive field operator E+ is actually an annihilation operator a while the negative field E- is a creation operator a+. I also learned that the absorption process can be represented as E-E+, which should be the number of photons n accroding to the principle of ladder operator. Also...
  36. hilbert2

    A QFT and transitions between momentum states

    Hi, I'm trying to learn some QFT at the moment, and I'm trying to understand how interactions/nonlinearities are handled with perturbation theory. I started by constructing a classical mechanical analogue, where I have a set of three coupled oscillators with a small nonlinearity added. The...
  37. M

    Zee, Quantum Field Theory in a Nutshell, problem 1.3.1

    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...
  38. Kfir Dolev

    A Renormalization Scheme Dependence of Vevs

    Is the one-loop corrected vacuum expectation value of a field renormalization scheme independent?
  39. Kfir Dolev

    A Why are the Tadpole Equations Called so?

    I know that the nth order tadpole equations give you the value of constant field configurations for which the first derivative of the nth order effective potential is 0, but what does this have to do with the tadpole graphs?
  40. F

    How Do You Diagonalize the Chiral Symmetry Breaking Term for Pion Masses?

    Homework Statement I want to diagonalize the quadratic form $$ m_0((m_u+m_d)\pi^3\pi^3+\frac{2}{\sqrt{3}}(m_u-m_d)\pi^3\pi^8+\frac{1}{3}(m_u+m_d+4m_s)\pi^8\pi^8)$$ which can be found under equation 5.47, in order to get the mass of the η and ##\pi^0## pions. This quadratic form is produced by...
  41. H

    Quantum Appropriate pre requisites for quantum field theory?

    I have just finished working through Jackson's Electrodynamics and Sakurai's Modern Quantum Mechanics and was wondering if this was sufficient background for me to start studying qft. Also, would Weinberg's Books be a good place to dive in given my background or is there are a more suitable...
  42. S

    A Calculation of S-matrix elements in quantum field theory

    Consider the following extract taken from page 60 of Matthew Schwartz's 'Introduction to Quantum Field Theory':We usually calculate ##S##-matrix elements perturbatively. In a free theory, where there are no interactions, the ##S##-matrix is simply the identity matrix ##\mathbb{1}##. We can...
  43. C

    A Q: Scalar Boundary Condition & U(1) Isometry - Lewkowycz & Maldacena

    I have a simple question about Lewkowycz and Maldacena's paper http://arxiv.org/abs/1304.4926v2'][/PLAIN] http://arxiv.org/abs/1304.4926v2 In section 2, they consider the scalar field in BTZ background ground and require boundary condition of the scalar field, $\phi \sim e^{i\tau}$ . This...
  44. C

    A Time-ordering fermion operators

    If A and B are fermionic operators, and T the time-ordering operator, then the standard definition is T(AB) = AB, if B precedes A = - BA, if A precedes B. Why is there a negative sign? If A and B are space-like separated then it makes sense to assume that A and B anticommute. But...
  45. J

    Geometry Book on Differential Geometry/Topology with applications

    Hello! I want to learn about the mathematics of General Relativity, about Topology and Differential Geometry in general. I am looking for a book that has applications in physics. But, most importantly, i want a book that offers geometrical intuition(graphs and illustrations are a huge plus) but...
  46. F

    I Why do we require locality in quantum field theory?

    In quantum field theory (QFT) from what I've read locality is the condition that the Lagrangian density ##\mathscr{L}## is a functional of a field (or fields) and a finite number of its (their) spatial and temporal derivatives evaluated at a single spacetime point ##x^{\mu}=(t,\mathbf{x})##...
  47. D

    A How to derive general solution to the Klein-Gordon equation

    I understand that the ansatz to $$(\Box +m^{2})\phi(\mathbf{x},t)=0$$ (where ##\Box\equiv\partial^{\mu}\partial_{\mu}=\eta^{\mu\nu}\partial_{\mu}\partial_{\nu}##) is of the form ##\phi(\mathbf{x},t)=e^{(iE_{\mathbf{k}}t-\mathbf{k}\cdot\mathbf{x})}##, where...
  48. A. Neumaier

    Insights Misconceptions about Virtual Particles - Comments

    A. Neumaier submitted a new PF Insights post Misconceptions about Virtual Particles Continue reading the Original PF Insights Post.
  49. H

    A QED vs Scalar QED: Proving Divergence in P&S 10.1

    In Peskin and Schroeder problem 10.1 is about showing that superficially divergent diagrams that would destroy gauge invariance converge or vanish. We are supposed to prove it for the 1-photon, 3-photon, and 4-photon vertex diagrams. Does this change for scalar QED?
  50. A. Neumaier

    Insights The Physics of Virtual Particles - Comments

    A. Neumaier submitted a new PF Insights post The Physics of Virtual Particles Continue reading the Original PF Insights Post.
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