What is Field theory: Definition and 551 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. M

    Relativity What is Field Theory and How Can I Build a Strong Foundation in the Subject?

    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...
  2. V

    I Why are scalar fields Lorentz invariant?

    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...
  3. 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...
  4. 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...
  5. LarryS

    I Classical Field Theory for a system of particles

    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...
  6. GIM

    A Good slides or summaries for Field theory, Lie algebra, etc.

    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...
  7. 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...
  8. T

    I Space and time as fields of mass-energy

    In my post graduate course, several years now, our professor in field theory have mentioned that in field theory the fields of mass-energy seem to be space and time themselves, like electric and magnetic fields in ElectroMagnetism. Specificaly he said that "the problem is that in...
  9. 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...
  10. S

    Nonlinear gravity as a classical field theory

    Homework Statement In this problem, you will calculate the perihelion shift of Mercury simply by dimensional analysis. (a) The interactions in gravity have ##\mathcal{L}=M^{2}_{Pl}\Big(-\frac{1}{2}h_{\mu\nu}\Box...
  11. S

    Scale Invariant Classical Field Theory

    Homework Statement A class of interesting theories are invariant under the scaling of all lengths by ##x^{\mu} \rightarrow (x')^{\mu}=\lambda x^{\mu}## and ##\phi(x) \rightarrow \phi'(x) = \lambda^{-D}\phi(\lambda^{-1}x)##. Here ##D## is called the scaling dimension of the field. Consider...
  12. S

    Maxwell's equations in Lagrangian classical field theory

    Homework Statement Given the Maxwell Lagrangian ##\mathcal{L} = -\frac{1}{2} (\partial_{\mu}A_{\nu})(\partial^{\mu}A^{\nu}) + \frac{1}{2} (\partial_{\mu}A^{\mu})^{2}##, show that (a) ##\frac{\partial \mathcal{L}}{\partial (\partial_{\mu}A_{\nu})} = -...
  13. 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})##...
  14. S

    I Einstein's Unified Field Theory: Approaches Explored

    Hi, Does anyone have details about what Einstein at a higher level tried in his last 30 years when he was working on Unified field theory. What approaches he tried?
  15. 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
  16. D

    Quantum Le Bellac "Quantum and Statistical Field Theory" solutions?

    Hello, Does anyone know if there is a solutions manual or any other source of solutions for the book Quantum and Statistical Field theory by Le Bellac? Thanks!
  17. M

    Polynomial splits over simple extension implies splitting field?

    This is a question that came about while I attempting to prove that a simple extension was a splitting field via mutual containment. This isn't actually the problem, however, it seems like the argument I'm using shouldn't be exclusive to my problem. Here is my attempt at convincing myself that...
  18. 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...
  19. S

    Principle of least action in field theory

    In page 15, Peskin and Schroeder states that The principle of least action states that when a system evolves from one given configuration to another between times ##t_1## and ##t_2##, it does so along the path in configuration space for which ##S## is an extremum. What is the definition of...
  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. J

    Violation of Bell inequalities for classical fields?

    There is a recent article (Optics July 2015) claiming violation of Bell inequalities for classical fields: "Shifting the quantum-classical boundary: theory and experiment for statistically classical optical fields" https://www.osapublishing.org/optica/abstract.cfm?URI=optica-2-7-611...
  22. 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
  23. gonadas91

    Field Theory vs Lattice: Exploring Differences in Calculations and Results"

    Hello guys! I just just wondering a general thing about calculations done in the field theory and those made in the lattice. In the field theory we have some results that in principle should match with the lattice ones in the thermodynamic limit. However, when we tried to solve the same problem...
  24. 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...
  25. 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...
  26. P

    Why Kink can not tunnel to vacuum, and is topologically stable

    Why the kink (\phi(x)=tanh(\frac{x}{\xi})), can not tunnel into vacuum +v or -v (Spontaneous symmetry breaking vacuum). From the boundary condition(x\rightarrow \pm\infty, \phi(x)\rightarrow \pm v), it is self-evident. but the book states: Due to the infinite high energy barrier, the kink...
  27. bhobba

    Comments - Some Useful Integrals In Quantum Field Theory

    bhobba submitted a new PF Insights post Some Useful Integrals In Quantum Field Theory Continue reading the Original PF Insights Post.
  28. Xenosum

    Mean Field Theory for Fermions/Bosons

    I'm not really sure if this counts as a homework problem (I was reluctant to post in that section since they evidently force you to ensure you've used the template, even though it's not very applicable here) so much as a general misunderstanding of mean field theory. So, in Michale Plischke and...
  29. H

    Self consistency and mean field theory

    Homework Statement I am a little confused about the how self consistency conditions work and I was wondering if in the following case I have correctly understood the details? Homework Equations [/B] Say we have a harmonic oscillator with a perturbation...
  30. L

    In the interacting scalar field theory, I have a question.

    First of all, I copy the text in my lecture note. - - - - - - - - - - - - - - - - - - - In general, $$e^{-iTH}$$ cannot be written exactly in a useful way in terms of creation and annihilation operators. However, we can do it perturbatively, order by order in the coupling $$ \lambda $$. For...
  31. HaLAA

    Show √ 2 + √ 3 algebraic over Q

    Homework Statement Show √ 2 + √ 3 algebraic over Q. Find its degree over Q. Prove the answer. Homework EquationsThe Attempt at a Solution Let ##\alpha= \sqrt{2}+\sqrt{3}\in \mathbb{R}##, then ##\alpha^4-10\alpha^2+1=0## which is a root of ##f(x)=x^4-10x^2+1## where ##f(x)## in...
  32. HaLAA

    FInd non-zero elements are primitive in a field

    Homework Statement Construct $\mathbb{F}_{16}$ as a quotient of $\mathbb{Z}_2[X]$. How many non-zero elements are primitive in this field? Calculate $|GL2_(\mathbb{F}_16)|$. Homework Equations Primitive Theorem The Attempt at a Solution For the first question, I don't know how to construct...
  33. M

    EM: Vector potential vs. Field tensor: Which is fundamental?

    In my lecture we were discussing the Lagrangian construction of Electromagnetism. We built it from the vector potential ##A^\mu##. We introduced the field tensor ##F^{\mu \nu}##. We could write the Langrangian in a very short fashion as ##-\frac{1}{4}F_{\mu \nu}F^{\mu \nu}## In the end we...
  34. S

    What is the meaning of local field theory in classical field theory?

    In page of 15 of 'An Introduction to Quantum Field Theory,' Peskin and Schroeder writes In a local field theory the Lagrangian can be written as the spatial integral of a Lagrangian density, ... , which is a function of one of more fields and their derivatives. Can you explain what the term...
  35. Isaac0427

    Independent project on field theory

    Hi all, I am in 7th grade science, but I have a lot of interest in advanced physics (and I am really bored in class), so I am currently working on an independent project on field theory (both classical and quantum). I understand it well, although my background in calculus is not great (I have...
  36. M

    New properties of "standard model effective field theory"

    http://arxiv.org/abs/1409.0868 Holomorphy without Supersymmetry in the Standard Model Effective Field Theory Rodrigo Alonso, Elizabeth E. Jenkins, Aneesh V. Manohar (Submitted on 2 Sep 2014 (v1), last revised 6 Nov 2014 (this version, v2)) The anomalous dimensions of dimension-six operators in...
  37. C

    Why is the solution of the phi^6 potential not a soliton?

    Homework Statement Consider a theory with a \phi^6-scalar potential: \mathcal{L} = \frac{1}{2}(\partial_\mu\phi)^2-\phi^2(\phi^2-1)^2. Why is the solution to the equation of motion not a soliton? Homework Equations \phi''=\frac{\partial V}{\partial\phi} The Attempt at a Solution...
  38. VintageGuy

    Tensor indices (proving Lorentz covariance)

    Homework Statement [/B] So, I need to show Lorentz covariance of a Proca field E-L equation, conceptually I have no problems with this, I just have to make one final step that I cannot really justify. Homework Equations "Proca" (quotation marks because of the minus next to the mass part, I...
  39. craigi

    David Tong: Lectures on Quantum Field Theory

    I created this thread to notify people about to the online resources for Tong's QFT course. Lecture videos: Blackboard screens and Videos: http://pirsa.org/C09033 Lecture notes: http://www.damtp.cam.ac.uk/user/tong/qft.html Course text: Peskin and Schroeder (search for it)
  40. X

    Studying Quantum Field Theory without taking graduate QM?

    Hello over the summer I would like to study quantum field theory. I took two semesters of undergraduate quantum mechanics using Griffith's textbook. We covered the entire book in those two semesters. I also know my special relativity pretty well. Is that enough to self study quantum field theory...
  41. bhobba

    Many Worlds and Quantum Field Theory

    I have been meaning to ask this one for a while - but never seem to get around to it. In MW its sometimes said it's simply the working out of the universal wave-function via Schroedinger's Equation. Of course Schroedinger's Equation is only valid non-relativistically. Wallace doesn't really...
  42. C

    Stress tensor from action in Landau-Ginzburg field theory

    I would appreciate any help with the following question: I know that for relativistic field theories, the stress tensor can be obtained from the classical action by differentiating with respect to the metric, as is explained on the wikipedia page...
  43. Ace10

    Conformal Field Theory: Questions & Answers

    Hi all, my question is rather a simple one and regards conformal transformations. On "Applied CFT" by P.Ginsparg, http://arxiv.org/pdf/hep-th/9108028.pdf , on page 10, gives the transformation rule of a quasi primary field and relates the exponent of 1.12 to the one of 1.10. My first question...
  44. S

    Properties of fields in quantum field theory

    I have been studying quantum field theory and I am currently in the Lagrangian field theory chapter in my book. Now it says that the energy momentum tensor is as follows: Tμν= [∂L/∂(∂μφ) * ∂νφ] - δμνL Note: I am using L to symbolize Lagrangian density and not just Lagrangian since the latex...
  45. resurgance2001

    What is the opposite of a field theory?

    Hi I understand that Maxwell's equations, and General Relativity are both field theories. I am trying to understand what the opposite of a field theory is, or what is not a field theory. For example, am I correct in believing that Newton's Laws are not a field theory? Is that is true then...
  46. W

    My simple proof of x^0=1 part 2 (axioms)

    I was looking for explanation why x^0=1. thread https://www.physicsforums.com/threads/my-simple-proof-of-x-0-1.172073/ is locked and i did't found solution in it from axioms. People using exp(x) and log(x) and xa-a=xax-a as given. If you have xa-a=xax-a for a∈ℤ and x∈ℕ+ then there is no...
  47. T

    Momentum cutoffs free field theory

    for a given diagram in some interacting theory that needs a momentum cutoff shouldn't the same momentum cutoff be used for diagrams that don't need a momentum cutoff for convergence for example, phi3 theory has a self energy diagram that diverges, so if one imposed a momentum cutoff there...
  48. Coffee_

    Classical field theory, initial and boundary conditions

    Hello, I am taking an introductory class on non relativistic classical field theory and right now we are doing the more mathematical aspect of things right now. The types of differential equations in the function ##f(\vec{r},t)## that are considered in this course are linear in the following...
  49. B

    Heisenberg equation of motion - field theory.

    Hi, I'm completely stuck with problem 3a). I have no idea of how to start. Anyone have any clue?http://speedy.sh/9JkCf/handin1-4.pdf
  50. S

    Degree of freedom of gravitino

    Please tell me how to count the degree of freedom of gravitino on the mass-shell? I read http://arxiv.org/abs/1112.3502, but I can't understand it. How about supervielbein?
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