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. N

    Quantum field theory questions?

    In QFM, what does it mean to say that an electron is just an excitation of the electron field? Does this apply to all particles? Does it mean to say that an electron is the quanta of the electron field?
  2. K

    Operator state mapping in Conformal Field Theory

    can anyone suggest any good reading material on operator state mapping in conformal field theory? I know only elementary field theory... So it might be helpful ifsomeone suggest a book where it is done in little detailed way..
  3. Luca_Mantani

    Exercise of Dirac Field Theory

    Homework Statement [/B] This is an excercise that was given by my professor in a previous test: Consider the equation: $$ \displaystyle{\not} p =\gamma^\mu p_\mu= m$$ where the identity matrix has been omitted in the second member. Find its most general solution. Homework Equations The...
  4. T

    Does Compactification Affect the Uncertainty of Field Localization on a Torus?

    Integrating the lagrangian over spacetime in regular field theory (by regular i mean field theories with noncompact dimensions) gives the action. To do this, one integrates over all spacetime , minus infinity to plus infinity in each dimension. For field theories with compactified dimensions...
  5. S

    Normal ordering in an interacting field theory

    I am using Mandl and Shaw and Lahiri to get an introduction to QFT. Something I haven't seen discussed much or at all is whether the commutators or anti-commutators vanish for the normal ordering of a product of different field operators. As a concrete example, let's say that I want to normal...
  6. A

    Which Beginner Book is Best for Learning Quantum Field Theory?

    Hello, I'm looking for a good beginner book about QFT. Thanks!
  7. J

    Spin parity and attractive/repulsive forces

    In most introductory QFT treatments, it's stated early on (and without proof) that particles with even integral spin are always attractive, while those with odd integral spin can be repulsive; sometimes this is even cited as evidence that the graviton must be spin 2 (I think Feynman's...
  8. J

    Normalization of ground state "1/2hw"

    Hello everyone: I didn't have a complete view of the quantum field theory and cannot understand this question. We now there will always be fluctuation field in the universe which corresponds to the ground state energy 1/2hw of harmonic oscillator. In the free space, we will use box...
  9. V

    Total derivative in action of the field theory

    When applying the least action I see that a term is considered total derivative. Two points are not clear to me. We say that first $$\int \partial_\mu (\frac {\partial L}{\partial(\partial_\mu \phi)}\delta \phi) d^4x= \int d(\frac {\partial L}{\partial(\partial_\mu \phi)}\delta \phi)= (\frac...
  10. V

    Upper Energy Limit in Field Theory: Exploring Quantum Gravity

    I see that we use dimensional analysis involving constants of nature to obtain the Planck length and then apply the uncertainty principle to find the corresponding Planck mass-energy. But the energy and length scales were found by invoking a "particle" interpretation of fundamental entities of...
  11. arupel

    Does quantum field theory supersede quantum mechanics?

    In discussing the wave/particle duality, a friend stated basically that the discussion in quantum mechanics is not relevant because quantum mechanics is superseded by quantum field theory. 1. I do not know if this statement is relevant with respect to the wave/particle duality. 2. I am not...
  12. G

    Field Theory: Prove transformations are a symmetry

    Homework Statement Consider the lagrangian L=\delta_\mu \phi \delta^\mu \phi^* - m^2 \phi \phi^* Show that the transformation: \phi \rightarrow \phi + a \,\,\,\,\,\,\,\,\,\, \phi^* \rightarrow \phi^* + a^* is symmetry when m=0. The attempt at a solution Substituting the transformation...
  13. L

    Cross Section: Quark-Gluon vs. Quark-Photon

    This isn't a homework problem. I am preparing for a particle physics exam and although I understand the theoretical side of field theory, I have little idea how to approach practical scattering questions like these. THE PROBLEM: Dark matter might be observed at the LHC with monojet and...
  14. Breo

    An Introduction to Quantum Field Theory (Peskin and Schröder) - Page 22

    Hello, Can someone tell me how to derive: $$ grad\hat{\phi} $$ from: $$ \hat{P}= -:\int \mathrm{d³}x [\pi (x) grad\hat{\phi}(x)]: = \int \mathrm{d³}p [p a⁺(p)a(p)] $$ Are all vectors. Note normal ordering ":" is used. I want to understand well QFT and want to learn to do this calcs...
  15. Richa Sharma

    Studying Reading Quantum field theory by Weinberg books?

    Is it a good choice to read these books first or there's a better way. My professor recommended me these books but as I started them they had bulk of maths and really matter was not that understandable on my first try. I am an engineer. I read physics in free time I can get , so shall I go ahead...
  16. M

    Lorentz transformation, quantum field theory

    Hello, I was reading and trying to follow up with Pierre Ramond's "Field theory: A modern primer" and got stuck in his step to step jumping. Kindly, see attachment and note that Eq (1.2.6) = g_{ρσ}=g_{μ\upsilon}\Lambda^{μ}_{ρ}\Lambda^{\upsilon}_{σ}. My question is what do I need from tensor...
  17. G

    Step from Mass Point Mechanics to Field Theory

    At the moment I am trying to understand classical field theory and there's a conceptual problem I encountered, which bothers me a lot and I don't seem to be able to resolve the issue. When making the step to classical field theory, many texts start as follows: First they recall the/a action in...
  18. C

    Group and Quantum Field Theory

    Good afternoon : I now what I've written here : https://www.physicsforums.com/showthread.php?t=763322 in the first message. I've made the Clebsh Cordon theorem with the components. Which can be represented by the Young tableau. There also the SU(3) and the su(3) representation of dimension...
  19. G

    Electromagnetic Field Theory: A Problem Solving Approach

    I stumbled on it while searching for electrodynamics textbooks for undergrads but this seems more advanced than Griffiths. Has anyone else used this book by Marcus Zahn? Is it a worthwhile read for an electrical engineer about to start sophomore year?
  20. F

    Basic question about equations of Quantum field theory (QFT)

    Hello Forum, The electromagnetic field EM must be treated relativistically because it travels at the speed of light in a vacuum. However, the idea of quantization forces us to treat the field as a quantum mechanical field. QFT is the answer to that. QFT is quantum mechanics with...
  21. Math Amateur

    MHB Field Theory _ Dummit and Foote - Example 4 - page 516 - Simple Computation

    I am reading Dummit and Foote, Chapter 13 - Field Theory. I am currently studying Example 4 [pages 515 - 516] I need some help with what D&F call a simple computation. Example 4 on pages 515-516 reads as follows: Now in the above example, D&F write the following: " ... ... In this case, a...
  22. Math Amateur

    MHB Field Theory _ Dummit and Foote - Theorem 3

    I am reading Dummit and Foote, Chapter 13 - Field Theory. I am currently studying Theorem 3 [pages 512 - 513] I need some help with an aspect of the proof of Theorem 3 concerning congruence or residue classes of polynomials. D&F, Chapter 13, Theorem 3 and its proof read as...
  23. R

    EM Field Theory (Action Symmetries)

    Homework Statement I uploaded a picture with the question Homework Equations my problem is : How should I find all the symmetries of the action ? Is there an easy way to recognize those symmetries or should I try all the symmetries I know and see if the action doesn't change...
  24. M

    Understanding Entropy and Gravity in Quantum Field Theory: A Beginner's Guide

    I read a sentence that says if a spherical volume in placed in a quantized space then the maximum entropy of the system can be calculated and it after simple steps found to be: S~V where V is the volume of the spherical volume. "Then the author said: Each local quantum field theory(with UV...
  25. M

    Magnetic Field Theory Contradiction? - Repost

    I've been thinking about Magnetic Fields, and I think that I've found a contradiction in conventional physics theory. While comparing the Left-Hand-Rule for Motors (LHR) and the Right-Hand-Rule for Generators (RHR), I found this contradiction: The Left-Hand-Rule states that if the Magnetic...
  26. C

    Expanding delta in Field Theory Derivation of Euler-Lagrange Equations

    Every time I try to read Peskin & Schroeder I run into a brick wall on page 15 (section 2.2) when they quickly derive the Euler-Lagrange Equations in classical field theory. The relevant step is this: \frac{∂L}{∂(∂_{μ}\phi)} δ(∂_{μ}\phi) = -∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) + ∂_{μ}...
  27. C

    Expanding delta in Field Theory Derivation of Euler-Lagrange Equations

    Every time I try to read Peskin & Schroeder I run into a brick wall on page 15 (section 2.2) when they quickly derive the Euler-Lagrange Equations in classical field theory. The relevant step is this: \frac{∂L}{∂(∂_{μ}\phi)} δ(∂_{μ}\phi) = -∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) + ∂_{μ}...
  28. A

    Landau classical field theory question

    One page 24 of his book on classical field theory (4th edition), Landau derives the relativistic equation of motion for a uniformly accelarated particle. How does he get the differential equation that leads him to his result?
  29. S

    Is Quantum Field Theory Still Relevant in Modern Physics?

    What ever happened with QFT? Heard so much about it years ago now only once in a while will a past Nobel laureate state it is real. I know string is the thing now. Any thoughts? Sussan
  30. F

    How Do Charge Distributions Affect a Spherical Dielectric Shell?

    Homework Statement Consider a spherical dielectric shell so that ε = ε_0ε_r for a < r < b and ε = ε_0 for 0 < r < a. If a charge Q is placed at the center of the shell, find a) P for a < r < b b) ρ_pv for a < r b c) ρ_ps at r = a and r = b Homework Equations ρ_pv = -div(P) ρ_ps = P...
  31. C

    Troubles learning Quantum field theory.

    Hi everyone, I'm having a lot of troubles learning QFT, personally I find it very challenging, besides that my professor has a very difficult accent and given that I'm not an English native speaker it is really hard for me to follow him. I would like to hear your experience learning QFT, Was it...
  32. N

    Why do we know the particle/quantum field theory is phys of symmetries

    Why do we know that particle physics/quantum field theory is a physics of symmetries?What leads we to the gauge symmetries of all interactions?.Why we can not assume a physics without symmetry?
  33. M

    Supplement problems to Landau's Classical Field Theory?

    There's very few problems in Landau's books. I'm the kind of guy that properly learns material by doing tons of problems. Of course I can pull from other textbooks but there's the issue of different notation, extra material within chapters, etc... Does anyone know of a good resource that can...
  34. N

    Field theory: Requirement for change in perspective.

    I am pursuing electrical engineering and I am currently in my 3rd semester. I have field theory or Engineering electromagnetics as a subject. It seems very interesting but I am not able to figure how to approach the subject to enjoy it. Hence I need to change my perspective from just...
  35. B

    Non-holonomic constraints in field theory

    My question is the following: In field theory, if I have a constraint \chi(q_a, p_a, \partial_i q_a) that depends on the generalised coordinates q_a, momenta p_a and spatial derivatives only of the q_a \partial_i q_a does this count as a non-holonomic constraint? Or is it only...
  36. shounakbhatta

    Lagrangian and quantum field theory

    Hello, I understand the classical Lagrangian which follows the Principle of Least Action(A) A=∫L dt But what is Lagrangian density? Is it a new concept? A=∫Lagrangian density dx^4 Here 4 is the four vector? One time-like and 3 space-like co-ordinates? QFT uses Lagrangian to...
  37. K

    Ligand field theory and CuCl2 colors

    Copper (ii) chloride is a light brown solid, which slowly absorbs moisture to form a blue-green dihydrate. According to ligand field theory, water is a stronger field ligand than chloride. As a result, the dihydrate form should have a larger d orbital splitting than the anhydrous form. Thus...
  38. TrickyDicky

    Quantum field theory basic concepts

    Would it be right to say that QFT tries to bring together the many-particles(many-body) discrete systems of quantum mechanics and the relativistic fields that are basically continuous systems? Of course the discrete particle of classical mechanics that when found in big numbers must be dealt...
  39. M

    Crystal Field Theory: Exploring Octahedral Complexes & Their Bonding

    I have recently been learning CTF and energy differences and orbital splitting is starting to make sense to me a bit more. I have not seen any definitive answers yet so any help would be great. In CTF, octahedral complexes are most common and there are 5 d orbitals that participate. Whether it...
  40. S

    Do we have a quantum field theory of monopoles?

    Recently, I read a review on magnetic monopole published in late 1970s, wherein some conjectures of properties possibly possessed by a longingly desired quantum field theory of monopoles are stated. My question is what our contemporary understanding of the quantum field theory of monopoles...
  41. G

    Not understanding cosmological constant in field theory

    The bare cosmological constant in field theory is needed to cancel the infinite vacuum zero-point energy. Then you get a renormalized cosmological constant. There are three quantites at play, Ω=E+Ω0, where E is the infinite vacuum zero-point energy, and Ω is the renormalized cosmological...
  42. A

    Do I need to know Solid State Physics for Field Theory?

    Solid State Physics Quantum mechanics and quantum nature of solids, properties of materials. Band theory in metals and semiconductors. Conduction processes, the p-n junction, transistors and other solid state devices. Field Theory Review of vector analysis and coordinate systems...
  43. Math Amateur

    MHB Field Theory - Nicholson - Splitting Fields - Section 6.3 - Example 1

    I am reading Nicholson: Introduction to Abstract Algebra, Section 6.3 Splitting Fields. Example 1 reads as follows: (see attachment) -------------------------------------------------------------------------------------------------- Example 1. Find an extension E \supseteq \mathbb{Z}_2 in...
  44. Math Amateur

    MHB Field Theory - General Question

    I am studying field theory. A general question I have is the following: Let E \supseteq F be fields and let u \in E . Now, if I determine an irreducible polynomial f in F[x] such that f(u) = 0 in E, can I conclude that I have found the minimal polynomial of u over F. Can someone...
  45. Math Amateur

    MHB Field Theory - Nicholson - Algebraic Extensions - Section 6.2 - Example 15

    I am reading Nicholson: Introduction to Abstract Algebra, Section 6.2 - Algebraic Extensions. Example 15 on page 282 (see attachment) reads as follows: --------------------------------------------------------------------------------------------------------------------------------- Example 15...
  46. Math Amateur

    MHB Field Theory - Nicholson - Algebraic Extensions - Section 6.2 - Example 13

    xample 13 from Nicholson: Introduction to Abstract Algebra, Section 6.2, page 282 reads as follows: (see attachment) ------------------------------------------------------------------------------------------------------------------ Example 13: If u = \sqrt[3]{2} show that \mathbb{Q}(u) =...
  47. Math Amateur

    MHB Field Theory: Nicholson, 6.2 Algebraic Extensions - Example 14 (p. 282) Solution

    I am reading Nicholson: Introduction to Abstract Algebra, Section 6.2 Algebraic Extensions. Example 14 on page 282 (see attachment) reads as follows: ------------------------------------------------------------------------------------------- Example 14. Let E \supseteq F be fields and let...
  48. Math Amateur

    MHB Field Theory: Nicholson Alg Ext, Sec 6.2 Ex 13 Pg 282 Explained

    I am reading Nicholson: Introduction to Abstract Algebra, Section 6.2 Algebraic Extensions. Example 13 on page 282 (see attachment) reads as follows: "If u = \sqrt[3]{2} show that \mathbb{Q}(u) = \mathbb{Q}(u^2) " In the third line of the explanation - see page 282 of attachment - we...
  49. Math Amateur

    MHB Field Theory - Nicholson - Algebraic Extensions - Section 6.2 - pages 281-282

    I am reading Nicholson: Introduction to Abstract Algebra Section 6.2 Algebraic Extensions. On page 282 the Corollary to Theorem 5 states the following: (see attachment for Theorem 5 and the Corollary)...
  50. Math Amateur

    MHB Field Theory - Element u transcendental of F

    Field Theory - Element u transcendental over F In Section 10.2 Algebraic Extensions in Papantonopoulou: Algebra - Pure and Applied, Proposition 10.2.2 on page 309 (see attachment) reads as follows...
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