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. Math Amateur

    MHB Field Theory - Nicholson - Section 6.2 - Exercise 31

    In Section 6.2 of Nicholson: Introduction to Abstract Algebra, Exercise 31 reads as follows: Let E \supseteq F be fields and let u \in E be transcendental over F. (a) Show that F(u) = \{ f(u){g(u)}^{-1} \ | \ f,g \in F[x] ; g(x) \ne 0 \} (b) Show that F(u) \cong F(x) where F(x) is the...
  2. P

    Proving Det(A) From Quantum Field Theory Problem

    Homework Statement I was following this book "problem book in quantum field theory by voja radovanovic" and I got stuck in the following problem Prove...
  3. Math Amateur

    MHB Field Theory - Basic Theory - D&F Section 13.1

    I am reading Dummit and Foote (D&F) Section 13.1 Basic Theory of Field Extensions. I have a question regarding the nature of extension fields. Theorem 4 (D&F Section 13.1, page 513) states the following (see attachment)...
  4. Radarithm

    What is quantum field theory trying to explain?

    The title says it all. I'm sorry if you get annoyed because of my "noobishness", but I'm still a physicist in training (taking undergrad Classical Mechs). I'm really interested in Quantum Theory and I keep hearing about Quantum Field Theory, but not a single website accurately explains what it...
  5. Math Amateur

    MHB Field Theory - Algebraic Extensions - D&F - Section 13.2 - Exercise 7, page 530

    ------------------------------------------------------------------------------------------------ 7. Prove that \mathbb{Q} ( \sqrt{2} + \sqrt{3} ) = \mathbb{Q} ( \sqrt{2} , \sqrt{3} ). Conclude that [\mathbb{Q} ( \sqrt{2} + \sqrt{3} ) \ : \ \mathbb{Q} ] = 4 . Find an irreducible...
  6. Math Amateur

    MHB Field Theory - Algebrais Extensions - D&F - Section 13.2 - Exercise 4, page 530

    Can someone help me get started on the following problem. Determine the degree over \mathbb{Q} of \ 2 + \sqrt{3} and of 1 + \sqrt[3]{2} + \sqrt[3]{2} Peter [This has also been posted on MHF]
  7. Math Amateur

    MHB Field Theory - Algebrais Extensions - D&F - Section 13.2 - Exercise 2, page 529

    Dummit and Foote Exercise 2, Section 13.2, page 529 reads as follows: ------------------------------------------------------------------------------------------------------------------ 2. Let g(x) = x^2 + x -1 and let h(x) = x^3 - x + 1 . Obtain fields of 4, 8, 9 and 27 elements by...
  8. Math Amateur

    MHB Algebraic Extensions: Dummit & Foote Section 13.2, Example 2 pg 526 - Help!

    I am reading Dummit and Foote on algebraic extensions. I am having some issues understanding Example 2 on page 526 - see attachment. Example 2 on page 526 reads as follows...
  9. Math Amateur

    MHB Field Theory - Algebrais Extensions - Dummit and Foote Section 13.2

    I am trying to clarify my understanding of Proposition 11 of Dummit and Foote Ch13 Field Theory concerning the degree of \alpha over F. Proposition 11 reads as follows...
  10. Math Amateur

    MHB Field Theory - Dummit and Foote Ch 13 - Exercise 1, page 519

    I am studying Dummit and Foote Chapter 13: Field Theory. Exercise 1 on page 519 reads as follows: =============================================================================== "Show that p(x) = x^3 + 9x + 6 is irreducible in \mathbb{Q}[x] . Let \theta be a root of p(x). Find the...
  11. sas3

    New geometric version of quantum field theory

    The new geometric version of quantum field theory could also facilitate the search for a theory of quantum gravity that would seamlessly connect the large- and small-scale pictures of the universe https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/ I...
  12. D

    Many-Body Quantum Field Theory

    What kind of background do I need to study many-body quantum field theory?
  13. S

    Unitary in quantum field theory

    In QFT, which have infinite degree of freedom, there exlst infinite unitary nonequvilent representation. Expecially after phase transition, the two representation are unitary nonequvilent. So can we say that unitary are broken in QFT? Or a pure state can evolved to a mixed state which is a...
  14. C

    Why Is a Given State an Eigenstate of Field Operators in Quantum Field Theory?

    Hi, I am studying Peskin's An Introduction To Quantum Field Theory. On the beginning of page 284, the authors say We can turn the field \phi_S(x_1)|\phi_1\rangle=\phi_1(x_1)|\phi_1\rangle. I tried hard to prove this relation but still can't get it right. Could anyone give me some hints? Thanks.
  15. Math Amateur

    MHB Field Theory - Dummit and Foote - Chapter 13 - Theorem 6

    I am trying to understand the proof of Theorem 6 in Chapter 13 of Dummit and Foote. Theorem 6 states the following: (see attachment) ===================================================================================== Theorem 6. Let F be a field and let p(x) \in F[x] be an irreducible...
  16. S

    Is Quantum Field Theory currently used in engineering?

    Hey all, I'm not sure if this belonged in the physics or engineering forum, but here's the question: has quantum field theory been applied to any engineering disciplines yet? I know quantum mechanics has been used extensively in electrical engineering and materials science/engineering. I also...
  17. P

    Book/PDF # Field Theory / Langrangians / Variations

    Hey, I am looking for a book / paper / pdf which covers things like -maxwell EM field theory -gravitational field theory -variational calculus / principle of least action -lagrangian mechanics -basic scalar fields / wave equations -field equations out of lagrangians -maybe some basic...
  18. S

    Determinism, causality and field theory

    hi i read some text about causality and determinism, but i can't exactly distinguish between them. what's really difference between them? does not quantum mechanics respect one of them? i read this phrase in article of S.Carlip about quantum gravity "Quantum field theory includes...
  19. jtbell

    Quantum Student Friendly Quantum Field Theory by Klauber

    Author: Robert D. Klauber Title: Student Friendly Quantum Field Theory Amazon Link: https://www.amazon.com/dp/0984513922/?tag=pfamazon01-20 (submitted by elfmotat)
  20. shounakbhatta

    Strong interaction and unified field theory

    Hello All, I am quiet new to the subject, so if anybody can help me. The four fundamental forces of nature, gravity, strong, weak,electromagnetism. Through weak force, all the electrons, protons and neutrons interact with each other. An attempt was made late in the 20th.century to unify...
  21. atyy

    Effective field theory, black hole evaporation, firewalls

    Arkani-Hamed, Dubovsky, Nicolis, Trincherini, and Villadoro argue in section 2.2 of A Measure of de Sitter Entropy and Eternal Inflation that the effective field theory description of black hole evaporation fails after a time tev, even though the curvatures are small. Almheiri, Marolf...
  22. QuantumCurt

    Is Special Relativity a field theory?

    Hey everyone, I've got a question. I've been doing a lot of reading about Quantum Field Theories lately, and watching a lot of lectures about field theories in general, and I'm wondering, is Special Relativity a field theory? For instance, in this article and the lecture accompanying...
  23. N

    Can we consider string theory as a special type of field theory?

    The notion field of Quantum Field Theory is deduced from the combination of Quantum Mechanics and Special Relativity.The local characteristic of field is led from Cluster Decomposition Principle. String Theory is also a combination between Quantum Mechanics and Relativity Theory.Then I wonder...
  24. C

    Functional or regular (partial) taylor series in Field theory

    When expanding a function (for example the determinant of the space-time metric g) as a functional of a perturbation from the flat metric ##h_{\mu \nu}##, i.e. ##g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} ## i would think that the thing to do is to recognize that ##g_{\mu \nu}## and thus also...
  25. R

    Gravitation as curvature of space vs field theory

    Gravitation is described on one hand as curvature of space in the presence of matter. It is also described as a field acting through gravitons on matter. How can the two views be reconciled?
  26. U

    Field Theory Partition Function

    The 'partition function' in QFT is written as Z=\langle 0 | e^{-i\hat H T} |0\rangle, but I'm having a difficult time really understanding this. I'm assuming that |0\rangle represents the vacuum state with no particles present. If that's the case, and the Hamiltonian acting on such a state would...
  27. Demystifier

    Other Modern Quantum Field Theory: A Concise Introduction

    We usually talk about good books, but we rarely talk about bad books. And that is good. But sometimes, we find that some book is so bad, so really bad, that we strongly want to tell this to the others. So I open this thread to inform others about science books which you find so bad that it...
  28. S

    What is an effective field theory?

    What is an effective field theory?? Yeah, there is many information on Internet, but it is a complicated level, they speak about cut-off, top-down, series development without justify limit the coefficients of ignored terms in the development. Aren´t there a simple (but rigurous) explanation...
  29. S

    What is an effective field theory?

    What is an effective field theory?? Yeah, there is many information on Internet, but it is a complicated level, they speak about cut-off, top-down, series development without justify limit the coefficients of ignored terms in the development. Aren´t there a simple (but rigurous) explanation...
  30. L

    Ligand field theory and f orbitals in magnetism

    I've been introduced to ligand-field theory lately and was then wondering what roles f orbitals play in the magnetic properties of elements and alloys. Apparently f orbitals behave oddly in that they hybridize in weird ways because they're so large and that the crystal field actually affects the...
  31. D

    Status and proofs on Superstring Unified Field Theory ?

    So yet we have the Standard Model which tries to explain and unify the 4 fundamental forces or atleast 3 for now since the gravity is not quite well understood in particle physics.So people search for a theory of everything which unifies all forces and yet we didn't found any good theory as...
  32. C

    Physical mass in a quantum field theory

    In special relativity we have the relation that for a free particle E^2 = \vec p^2 + m_0^2 and that also hold in relativistic free field theories (free Klein-Gordon etc) where one can show that we have a completeness relation 1 = \int \frac{d^3 \vec p}{(2\pi)^3} \frac{1}{2E_{\vec...
  33. C

    Book or notes for 'Quantum Field Theory II' by Francois David (PSI)

    Hi! I'm trying to follow the video lectures of the course 'Quantum Field Theory II' by Francois David given at the Perimeter Institute PSI programme, but it would be nice to have some notes or a book which were similar to the lectures. I am especially interested in the part on Wilsonian...
  34. S

    Unified Field Theory - Consciousness

    "Mysticism in Quantum Mechanics": the forgotten controversy by Juan Miguel Marin, Harvard, Eur. J. Phys. 30 (2009) 807 - 822. How's that Mr. Mentor? Or are you going to censor this post also? Small-minded world physicists, like the 'flatlander-earth-centric' astronomers of old better take...
  35. S

    Unified Field Theory - Consciousness

    Is there a discussion on this board of the possibility that consciousness is the missing link in a true unified field theory? Or is this considered heresy, not mainstream, a homework question, too out of the box or just a confounding question as everyone with an open mind here knows that it's...
  36. T

    Quantum Field Theory - Places to study

    Hi! I'm in a master course in theoretical physics and enjoying a lot to learn about Quantum Field Theory (QFT)! So I was thinking doing a PhD related do QFT. What are the best places to work on QFT? Thanks a lot!
  37. Spinnor

    Quantum field theory, photons, and polarization.

    A circularly polarized electromagnetic wave can be thought of proper combinations of orthogonal linear polarized waves, and a linear polarized wave can be thought of proper combinations of left and right circularly polarized waves. It seems one type of wave is no more fundamental then the other...
  38. E

    Quantum mechanics and quantum field theory application ideas?

    First of all sorry for my off-topic question here. I'm a computer science student, who has a high interest in mathematics (especially algebraic geometry), and physics (especially quantum mechanics, quantum field theory). For this semester I'm supposed to create to applications, from which one of...
  39. Astronuc

    Field Theory of Guided Waves by Robert E. Collin

    Author: Robert E. Collin Title: Field Theory of Guided Waves (IEEE Press Series on Electromagnetic Wave Theory) Amazon Link: https://www.amazon.com/dp/0879422378/?tag=pfamazon01-20 Prerequisities: Calculus/Engineering Mathematics (introductory complex analysis and linear analysis)...
  40. micromass

    Quantum A Modern Introduction to Quantum Field Theory by Maggiore

    Author: Michele Maggiore Title: A Modern Introduction to Quantum Field Theory Amazon Link: https://www.amazon.com/dp/0198520743/?tag=pfamazon01-20
  41. micromass

    Quantum Quantum Field Theory in a Nutshell by Zee

    Author: A. Zee Title: Quantum Field Theory in a Nutshell Amazon Link: https://www.amazon.com/dp/0691140340/?tag=pfamazon01-20
  42. bcrowell

    Classical electroweak field theory

    A question I'm sure I've seen asked here and/or elsewhere is why there doesn't seem to be any classical force corresponding to the weak interaction. I came up with the following, and am wondering whether this seems correct and satisfying to others. Basically, being able to write down a...
  43. bcrowell

    Classical Electromagnetic Field Theory by Bo Thide

    Author: Bo Thide Title: Electromagnetic Field Theory Download Link: http://www.plasma.uu.se/CED/Book/ Prerequisities: Contents:
  44. Greg Bernhardt

    Quantum An Introduction to Quantum Field Theory by Michael E. Peskin

    Author: Michael E. Peskin (Author), Dan V. Schroeder (Author) Title: An Introduction to Quantum Field Theory Amazon Link: https://www.amazon.com/dp/0201503972/?tag=pfamazon01-20 Prerequisities: Contents:
  45. R

    A (apparently?) non-local quantum field theory

    I need to derive the euler-lagrange equations for the following non-local lagrangian density for a complex scalar field ψ \mathcal{L} = \partial_{\mu}\psi^* \partial_{\mu}\psi - \lambda \int dy\, f(x,y) \psi^*(y) \psi(y) where λ is the coupling constant, f is a certain real-positive valued...
  46. H

    Defeated by quantum field theory yet again

    I haven't taken a course in qft yet, just looking ahead to see what's to come, and so far things are not looking good, I read the firet few chapters of qft in a nutshell, and jesus christ what is this stuff, where are the postulates? The equations of motion? How do I even do these crazy path...
  47. A

    Suggestions for sources with detailed calculations in quantum field theory.

    Can you suggest any source available on internet which may be particularly helpful for those studying/brushing up knowledge of classical or quantum field theory without help of any teacher or friend? Some calculations are at first not so straightforward and there are many types of calculations...
  48. C

    Origin of Spin 1/2: Exploring Quantum Field Theory

    Dear Forum, I would like to understand what the origin of spin 1/2 is. I read in Feynman's lectures that the origin is related to quantum field theory. I know nothing about quantum field theory. Is there an easy explanation? Thanks Cabrera
  49. nukeman

    Is relating Quantum field theory to the brain and how the brain works silly?

    Hey everyone, I would like to first point out I am not a biology major in any way...I am a physics major, with a ever increasing interest in neuroscience. I am trying my best right now to find ways that I can incorporate my physics knowledge to the brain. Right now I am trying to...
  50. maverick280857

    Learning Dynamical Mean Field Theory

    Hi, I'm a masters student trying to apply DMFT to problems involving transport in strongly correlated systems. I have a cursory understanding of the physics behind the Hubbard model, which is to say, I have spent some time with it in a quantum many body theory course. However, I now want to...
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