What is Quantum field theory: Definition and 576 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. 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...
  2. 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...
  3. 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...
  4. 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...
  5. 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})##...
  6. 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...
  7. 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.
  8. 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?
  9. 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.
  10. P

    I Coupling Spin-0 and spin-1 fields

    My question is, how does one get a wave function for a 'combined' spin-1 and a spin-0 field? How is this possible? I have only been able to find combined states for equal spin identical particles. If you don't understand my question, I'll be glad to reword it.
  11. S

    Quantum Quantum Field Theory: The Why, What and How by T. Padmanabhan

    Author: T. Padmanabhan Title: Quantum Field Theory: The Why, What and How Amazon Link: https://www.amazon.com/dp/3319281712/?tag=pfamazon01-20 Springerlink (Previews of chapters): http://link.springer.com/book/10.1007%2F978-3-319-28173-5
  12. H

    A Canonical quantization of scalar fields

    In the srednicki notes he goes from $$H = \int d^{3}x a^{\dagger}(x)\left( \frac{- \nabla^{2}}{2m}\right) a(x) $$ to $$H = \int d^{3}p\frac{1}{2m}P^{2}\tilde{a}^{\dagger}(p)\tilde{a}(p) $$ Where $$\tilde{a}(p) = \int \frac{d^{3}x}{(2\pi)^{\frac{3}{2}}}e^{-ipx}a(x)$$ Is this as simple as...
  13. Y

    B Derive Vacuum permeability and permeability....

    Derive Vacuum permittivity and permeability using Quantum Field theory or String theory! If QFT or String theory is real fundamental theory, it can be derived the permittivity and permeability of vacuum. << Moderator's note: personal contact details deleted>>
  14. A

    I Quantum field and mediating particles

    I'm not sure if I posted this in the right category, it's something that came up just after the quantum mechanics section so I just chose this one. I've come across something that I simply can not find an answer for on my own. I'm taking Modern Physics course and the last chapter is some...
  15. unknown1111

    A Computing the pole mass from a given MS mass?

    Given a Yukawa coupling as a function of scale and a vev, how can I compute the corresponding pole mas? Understandably most paper explain how from a measured pole mass one can compute the running mass, for example, Eq. 19 here. However I want to compute the pole mass from the running mass. In...
  16. H

    Confusion with the Gordon identity

    For the Gordon identity $$2m \bar{u}_{s'}(\textbf{p}')\gamma^{\mu}u_{s}(\textbf{p}) = \bar{u}_{s'}(\textbf{p}')[(p'+p)^{\mu} -2iS^{\mu\nu} (p'-p)_{\nu}]u_{s}(\textbf{p}) $$ If I plug in $\mu$=5, what exactly does the corresponding $(p'+p)^{5}$ represent? 4 vectors can only have 4 components so...
  17. H

    Can Gordon Identity Be Adapted for Different Spinor Equations?

    The Gordon identity allows us to solve using $$2m \bar{u}_{s'}(\textbf{p}')\gamma^{\mu}u_{s}(\textbf{p}) = \bar{u}_{s'}(\textbf{p}')[(p'+p)^{\mu} -2iS^{\mu\nu} (p'-p)_{\nu}]u_{s}(\textbf{p}) $$ But how would we solve for $$2m \bar{u}_{s'}(\textbf{p}')\gamma^{\mu}v_{s}(\textbf{p}) $$ Would a...
  18. R

    Difference between spacetime and the gravitational field?

    Are spacetime and the gravitational quantum field (still hypothetical) separate entities? Would the gravitational field be more fundamental, one of the various entities from which spacetime as a whole is composed? Gravitons, which are believed to transmit the force of gravity, would surely be...
  19. A. Neumaier

    A Particles in quantum field theory

    In this thread, I want to discuss the implications of quantum field theory for the interpretation of quantum mechanics. To set the stage I'll import in the next few posts a number of posts from other threads. The latest of these is the following: Only if it is the sole particle in the whole...
  20. edguy99

    Quantum Field Theory intro with flying field disturbances

    Great youtube introduction video about Quantum Field Theory (QFT) from a couple of days ago by Dr Don Lincoln @fermilab. The video and description of a particle being a disturbance in a field and flying through the air at 3:25 is especially compelling.
  21. F

    Does the Higgs field truly exist if it cannot be directly measured?

    In QFT particles are described by fields, but AFAIK these fields are mathematical since we don't measure values of fields at a particular spacetime. So what does it mean to say a higgs field exist! I mean it is one thing to say Higgs particle exists (in LHC), but I have not seen anybody measure...
  22. H

    Error in Srednicki renormalization?

    On page 164-165 of srednicki's printed version (chapter 27) on other renormalization schemes, he arrives at the equation $$m_{ph}^{2} = m^2 \left [1 \left ( +\frac{5}{12}\alpha(ln \frac{\mu^2}{m^2}) +c' \right ) + O(\alpha^2)\right]$$ But after taking a log and dividing by 2 he arrives at...
  23. H

    Intuition for divergences in sunset diagram

    What is the intuition behind divergences for the sunset diagram? I know that there is quadratic divergence by why no quartic divergence or higher?
  24. H

    ##\overline{MS}## in scalar theory references

    Does anyone know any good references for discussion of ##\overline{MS}## theory in phi^4 theory?
  25. H

    Difference between 2-point and 4-point function in QFT

    As I understand it, the 2-point fnuction is for 1 particle incoming, 1 particle outgoing. The 4-point function is for 2 particles incoming, 2 particles outgoing. Is this correct? So an N-point function describes N/2 incoming particles and N/2 outgoing particles? Thanks!
  26. H

    Using Feynman rules to calculate amplitude

    Given a diagram, how is one supposed to apply the feynman rules to calculate the feynman amplitude?
  27. H

    How to calculate Feynman diagrams in phi^4

    For quartic scalar field theory these are some of the lowest order diagrams (taken from the solutions to 9.2 srednicki). I'm wondering if someone can give me an intuition of how to actually calculate them. What I'm thinking is that vertices are $$\int \frac{d^{4}x}{(2\pi)^{4}}$$ and for the...
  28. H

    Vacuum diagrams vs. tree diagrams vs. loop diagrams

    Could someone please tell me the difference between tree diagrams and loop diagrams? If I'm thinking correctly tree diagrams are before contracting? Also how do vacuum diagrams fit into the picture? Thanks!
  29. H

    Order of scalar interaction impact Feynman diagrams

    On page 60 of srednicki (72 for online version) for the $$\phi^{3}$$ interaction for scalar fields he defines $$Z_{1}(J) \propto exp\left[\frac{i}{6}Z_{g}g\int d^{4}x(\frac{1}{i}\frac{\delta}{\delta J})^{3}\right]Z_0(J)$$ Where does this come from? I.e for the quartic interaction does this...
  30. K

    Is the Higgs mechanism a gauge transformation or not?

    I asked this question to PhysicsStackExchange too but to no avail so far. I'm trying to understand the way that the Higgs Mechanism is applied in the context of a U(1) symmetry breaking scenario, meaning that I have a Higgs complex field \phi=e^{i\xi}\frac{\left(\rho+v\right)}{\sqrt{2}} and...
  31. S

    Quantum Field Theory: Project Topic Ideas

    Dear All I am currently taking " Introduction to Quantum field theory", And I have to do a project by the end of the course. I have searched and i find : QFT in curved space, QFT for higher spins... But i need other suggestion of topics I can do as a project. Thank you
  32. A

    Is an electron a delocalized excitation before measurement?

    When we observe an electron it is always a localized excitation in the electron field. But when it's not being observed, does the excitation begin to spread through space and become a delocalized excitation?
  33. P

    Lorentz Transformation on Left & Right Chiral Spinors

    I will start with a summary of my confusion: I came across seemingly contradictory transformation rules for left and right chiral spinor in 2 books, and am unable to understand what part is Physics and what part is convention. Or is it that one of the two books incorrectly writes the...
  34. terra

    Lorentz transforming a momentum eigenstate

    Let's take a quantum state ##\Psi_p##, which is an eigenstate of momentum, i.e. ##\hat{P}^{\mu} \Psi_p = p^{\mu} \Psi_p##. Now, Weinberg states that if ##L(p')^{\mu}\,_{\nu}\, p^{\nu} = p'##, then ##\Psi_{p'} = N(p') U(L(p')) \Psi_{p}##, where ##N(p')## is a normalisation constant. How to...
  35. loops496

    Advice on choosing a Monograph topic

    Hello everyone, I'm a senior undergraduate and I'm planing to do a Monograph related to Quantum effects in Gravity (Hawking radiation or something similar(?)) or even some QFT in curved space-time (maybe ambitious since I know this is VERY HARD and I don't have much time), the thing is I can't...
  36. T

    Why Is the Photon One-Point Function Zero in QED?

    In 'an introduction to quantum field theory' by peskin, he writes: To analyze the photon one-point function, note that the external photon must be attached to a QED vertex. Neglecting the external photon propagator, this amplitude is therefore: I really cannot justify this equation. Can...
  37. S

    Quantum Field Theory Online Courses?

    I wanting to do an introductory Quantum Field theory course in my spare time. And although there are a couple available, they are not very beneficial without solutions to the problem sets. I am also looking at the course on the MIT open courseware website: "8.323: Relativistic Quantum Field...
  38. A

    What is a fundamental particle according to QFT?

    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?
  39. S

    Quantum Field Theory: Exploring Positive and Negative Energies

    Hi all I am studying quantum field theory and i want to just to check something. We have said that the problem with klein gordon equation for real field is that is predict positive and negative energies in addition to the negative probability density. For the complex klein gordon field we have...
  40. loops496

    Klein-Gordon Hamiltonian commutator

    Homework Statement Consider the quantum mechanical Hamiltonian ##H##. Using the commutation relations of the fields and conjugate momenta , show that if ##F## is a polynomial of the fields##\Phi## and ##\Pi## then ##[H,F]-i \partial_0 F## Homework Equations For KG we have: ##H=\frac{1}{2} \int...
  41. C

    Cuts of a Feynman diagram and the massless limit

    Consider a ##j## point all massive leg one loop polygonal Feynman diagram ##P## representing some scattering process cut on a particular mass channel ##s_i##. Invoking the relevant Feynman rules and proceeding with the integration via dimensional regularisation for example gives me an expression...
  42. G

    Lagrangian of fields from Feynman diagrams

    ¿How is possible deduce the Lagrangian of the fields of a theory knowing only his Feynman Diagrams?
  43. FreeBiscuits

    Creation Operator is not a densely defined operator....

    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...
  44. T

    Learn the Art of Indexology to Writing Lagrangians with Tensors

    I recently read that indexology is the art of writing a Lagrangian by just knowing how many dimensions it has and how to contract tensors. I am very interested in this technique, but I cannot find any reference. Can anyone give me a guidance or a reference?
  45. Dilatino

    How can I construct the 4D real representation of SU(2)?

    An element of SU(2), such as for example the rotation around the x-axis generated by the first Pauli matrice can be written as U(x) = e^{ixT_1} = \left( \begin{array}{cc} \cos\frac{x}{2} & i\sin\frac{x}{2} \\ i\sin\frac{x}{2} & \cos\frac{x}{2} \\ \end{array} \right) = \left(...
  46. Dilatino

    Demystification of the spin-sum for massive spin-1 particles

    Assuming that a massive spin-1 particle has momentum only in the z-direction, the polarization vectors are given by \varepsilon_{\mu}(J_z = +1) = (0,-\frac{1}{\sqrt{2}},-\frac{i}{\sqrt{2}},0 ) \varepsilon_{\mu}(J_z = 0) = (\frac{p}{m},0,0, \frac{E}{m}) \varepsilon_{\mu}(J_z = -1) =...
  47. F

    Quantum Recommended Textbooks for Quantum Field Theory and Antiparticles

    Hello All, I was wondering if anybody could recommend some really good, graduate-level textbooks or sources on quantum field theory and antiparticles. I've browsed through several QFT titles, but if anyone has any books they think would be a good grad-level introduction I'd be grateful...
  48. quantumfunction

    How different can quantum vacuums be?

    For instance our quantum vacuum has a certain Cosmological constant and the question is can there be other vacuums with different values and if so where's the evidence for this I would like to read it. How do you derive the Cosmological Constant through something like Quantum field theory or...
  49. G

    Typical Momentum Invariants of a 3-Point Function

    According to Peskin, p.414, at the bottom, as part of calculating the ##\beta## functions of a theory, we need to fix the counter terms by setting the "typical invariants" built from the external leg momenta to be of order ##−M^2##. For a 4-point function, these invariants are s, t and u...
  50. G

    Trouble Finding Renormalization Conditions in Yukawa Theory

    I am trying to calculate the ##\beta## functions of the massless pseudoscalar Yukawa theory, following Peskin & Schroeder, chapter 12.2. The Lagrangian is ##{L}=\frac{1}{2}(\partial_\mu \phi)^2-\frac{\lambda}{4!}\phi^4+\bar{\psi}(i\gamma^\mu \partial_\mu)\psi-ig\bar{\psi}\gamma^5\psi\phi.##...
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