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. J

    Quantum Field Theory - variational principle

    Quantum Field Theory -- variational principle In non-relativistic quantum mechanics, the ground state energy (and wavefunction) can be found via the variational principle, where you take a function of the n particle positions and try to minimize the expectation value of that function with the...
  2. G

    Difference between a classical and quantum field theory?

    This may be a very basic question, but I've had now some background on the quantum theory, and I think I am missing something. Roughly speaking, I feel like the main difference is that quantizing involves going from field amplitudes to counting operators, implying that a quantum process involves...
  3. J

    Kaku, Quantum Field Theory Page 47 (2.68/9)

    Homework Statement Here is equation (2.68) (M^{ij})_{ab} = -i(\delta^i_a\delta^j_b - \delta^j_a\delta^i_b) Here is equation (2.69) (abbreviated) [M^{ij},M^{lm}]_{ab} = +i\delta^{jl}(M^{im})_{ab} +- ... The problem is to show that (2.68) implies (2.69) Homework Equations The...
  4. marcus

    Quantum field theory in a fractal universe (Calcagni)

    At least one of us at this discussion board has expressed an interest in fractal modeling of spacetime, or of dynamics.* This paper by Calcagni may be suggestive of what form such an approach could take. http://arxiv.org/abs/1001.0571 Quantum field theory, gravity and cosmology in a fractal...
  5. K

    Quantum Field Theory and Mereological Nihilism/Atomism

    Research in relativistic quantum mechanics proves, through a series of no-go theorems, that localized three (or four) dimensional particles cannot be the basic elements of reality. It is claimed that a field ontology can explain the appearance of three dimensional particles, but this new idea...
  6. W

    Integrable Quantum Field Theory

    Hi there, I am currently studying Quantum Field Theory (well, for about 3 weeks isch), and it's really interesting and good fun! However, I would like to know how QFT relates Integrable QFT... I don't really know what it is. Can anyone tell me (i) The theoretical background of Integrable...
  7. W

    Integrable Quantum Field Theory

    Hi there, I am currently studying Quantum Field Theory (well, for about 3 weeks isch), and it's really good fun! I would like to know how QFT relates Integrable QFT... I don't really know what it is. Can anyone tell me (i) The theoretical background of Integrable QFT (ii) The...
  8. DarMM

    Rigorous Quantum Field Theory.

    Hey everybody, since the previous thread got locked I thought I would open this thread as a place to discuss rigorous issues in quantum field theory, be it on the constructive or axiomatic side of things. I apologize if one is not supposed to start a discussion with posts from old threads...
  9. L

    From quantum field theory to quantum mechanics

    i need references on the topics. thanx
  10. B

    Questions on Normal Ordering in Quantum Field Theory

    I have a few questions about this. My understanding is this: In the canonical approach to QFT there is an ambiguity in the order in which we write operators when calculating matrix elements. The different choices just correspond to different vacuum energies, which we are free to ignore since...
  11. R

    Which books on quantum field theory are accessible for non-physicists?

    What are some good books for non physicists on quantum field theory?
  12. Peter Morgan

    Quantum Field Theory Observables: Distinguishing Two Types in Free Fields

    For free quantum fields, there are two types of observables indexed by wave-number, \tilde{\hat{\phi}}(k), the Fourier transform of the local field, which can be written as a(-k)+a^\dagger(k), and projection operators such as a(k)^\dagger\left|0\right>\left<0\right|a(k), a(k_1)^\dagger...
  13. J

    Is knowledge of scattering theory necessary for studying Quantum Field Theory?

    Please let me know what lecture I have to previously take. I already took undergraduate level lecture of quantum mechanics and mathematical physics. And I also want to know that perturbation and scattering theory is hardly important on studying QFT..I'm so worry about that I didn't study...
  14. S

    Quantum Field Theory Demystified (David McMahon)

    Hi all, I bought a book recently of this title. I wanted this one to compliment the field theory book I have already (Peskin and Schroeder) because I find the latter a little hard to follow on my own (I am currently taking Relativistic Quantum Mechanics and will be taking QFT course at some...
  15. G

    Quantum Field Theory book suggestions

    I have a fairly good background in mathematics (algebra, analysis, topology, differential geometry)... and a good physics background (till QM, general relativity). I am looking to study Quantum Field Theory on my own. I do not intend to master QFT completely and all its techniques, but want to...
  16. P

    Question About Calculation in Maggiore's Quantum Field Theory

    I have a question about an equation in Maggiore's Modern Introd. to Quantum Field Theory p.52: \delta x^\mu = w^\mu_\nu x^\mu = \sum_{\rho < \sigma} A^\mu_{(\rho \sigma)} w^{\rho \sigma} where the A is defined as A^\mu_{(\rho \sigma)}=\delta^{\mu}_{\rho}x_\sigma - \delta^\mu_\sigma x_\rho...
  17. M

    Quantum Field Theory: Multiparticles and Single Particles

    In quantum field theory a field is described by a multiparticles state? And, a single particle is itself a field?
  18. Fredrik

    Questions about quantum field theory

    I'm not sure if this post should go here or into the quantum physics forum, but I figure this can't be a bad place to put it. I have a few questions about canonical quantization and quantum field theories with interactions that I hope someone can answer. 1. I've been told that in Klein-Gordon...
  19. A

    Quantum Field Theory in Curved Spacetime?

    Hi all, I have a question about the formulation of quantum field theories in curved spacetime. I'm still learning, and so I might not articulate this very well, but I'm wondering: If a region of spacetime can warp and curve, dynamically changing its shape in response to changes in energy...
  20. N

    Exploring the Mysteries of Quantum Field Theory

    Hello Physics Forum I will be taking a quantum field theory course next semester. I bought Mandl's book and Zee's book and looked them a bit. I have also been talking to others that have taken the class in previous semesters. I have a general idea of the failings of nonrelativistic...
  21. K

    Calculating $\frac{1}{x-i\epsilon}$ in Quantum Field Theory

    \frac{1}{x-i\epsilon}=\frac{x}{x²+a²}+\frac{ia}{x²+a²}= P \frac{1}{x}+i pi \delta(x) P means the principal value, a is possibly infinitesimal (?), i is the imaginary unit Where does the pi, Dirac delta come from? What principal value? It is from a quantum field theory book.
  22. K

    Quantum Field Theory - Charged Field

    The question is as follows; 'A free quantum field theory is related to an infinite number of quantum mechanical harmonic oscillators as unit mass particles on springs with spring constants k, where k takes all values. Now imagine the following scenario: these particles also have non-zero...
  23. JasonJo

    Schools Constructive Quantum Field Theory and Euro grad school

    I will be applying for grad school this Winter, but from January 2009-September 2009, I will be done with any course work and will not have any money to commute to my school to continue to do research. So I figured it would be a good opportunity to go further in my mathematics and physics...
  24. M

    Exploring Micro Black Holes and Entropy in Quantum Field Theory

    When I read the security report from Cern (not that I am too worried), I came to something, which I do not fully understand: As we all know, we are save from micro black holes created at the LHC because of Hawking radiation (for one of many reasons). The Cern people push this argument further...
  25. malawi_glenn

    Quantum field theory of condensed matter

    Hi I was wondering if anyone has a good introductory article about QFT applied to condensed matter physics. I know a bit about condensed matter physics, and a bit of QFT applied to particle physics. thanx
  26. C

    Application of quantum field theory to condensed matter physics

    i've read that quantum field theory can be applied to condensed matter physics but i don't understand how: quantum field theory is the union of SR with QM but how is SR related to condensed matter physics? i understand that quantum field theory would be useful because it can describe...
  27. T

    Who introduced group theory into quantum field theory?

    I am trying to search for the first person who introduced group theory into quantum field theory.
  28. malawi_glenn

    Quantum Field Theory online book, 885pages

    "FIELDS" by: WARREN SIEGEL C. N. Yang Institute for Theoretical Physics State University of New York at Stony Brook Stony Brook, New York 11794-3840 USA http://insti.physics.sunysb.edu/~siegel/Fields3.pdf
  29. F

    Quantum Field Theory: Field Operators and Lorentz invariance

    [SOLVED] Quantum Field Theory: Field Operators and Lorentz invariance Hi there, I am currently working my way through a book an QFT (Aitchison/Hey) and am a bit stuck on an important step in the derivation of the Feynman Propagator. My problem is obviously that I am not a hard core expert...
  30. F

    Non Commutative Quantum Field Theory

    Non Commutative Cross-Section hello, this is my first post here, i have searched the web but i didnt find what i am looking for,so i hope i find it here. i am looking for the formula of the cross section of compton scattring in the non commutative space-time .
  31. S

    Good introductions to quantum field theory and vacuum

    I am to produce a research presentation for a class of Masters' physics students on the casimir force, going via a detailed treatment of the vacuum effects in conducting cavities, going on to explain some real phenomena and applications. What I am after is a good introductory text on quantum...
  32. J

    Exploring Zee's Quantum Field Theory: Unraveling p. 31

    Homework Statement A. Zee Quantum Field theory in a nutshell, p. 31. There is painfully little explanation on this page. I'm okay with the action: S(A) = \int d^4 x \mathcal{L} = \int d^4 x\{ \frac{1}{2}A_\mu [(\partial^2 +m^2)g^{\mu \nu}-\partial^\mu\partial^\nu]A_\nu + A_\mu J^\mu \}...
  33. Q

    Quantum field theory or particle physics what first?

    Quantum field theory or particle physics what first? Hi at present I am confused whether i should try obtining a firm conceptual understanding of QFT before jumping to particle physics or whether aa very brief overview of QFT is enough ?
  34. S

    General Relativity and Quantum field theory

    Since I'm very interested in General Relativity and Quantum field theory, I'd like to start a doctoral program abroad after my master study (I'm studying in Switzerland and will get my master degree in approximately 1.5 years). I was surfing around in the internet and found for example the...
  35. C

    Reading Quantum Field Theory: A Guide to Books

    I was wondering what to read for quantum field theory and in what order if applicable: I have "qft in a nutshell" by zee, "intro to qft" by peskin, "qft" by rydern, and "advanced qft" by sakurai.
  36. U

    General relativity vs quantum field theory

    Hi, I am curious about the following and I aim these questions to the people who do general relativity and uantum field theory over there. What is the difference between field theory of general relativity and field theory of quantum field theory? Is the former only for study of gravitation...
  37. C

    What are some good books for understanding quantum field theory?

    I was wondering if anybody knew any good books that give an easy to understand quantum field theory. I am talking from a view point of a person who has read the third volume of the feynman lectures and quantum mechanics demystified. if this is not enough to even start a easy to understand...
  38. E

    Vacuum in Quantum Field theory is not empty

    I know that the vacuum in Quantum Field theory is not empty, but sometimes I find some people say that the particles are created from nothing because they are created from the vacuum , are those people expression a misleading?
  39. Demystifier

    Quantum field theory vs particle physics

    On this forum, quantum field theory (QFT) is a part of this subforum (Quantum Physics), while particle physics is a subject of another forum. These two topics - QFT and particle physics - are clearly separated. On the other hand, most textbooks on QFT are also textbooks on particle physics...
  40. Demystifier

    Is quantum field theory a genuine quantum theory?

    In my recent paper http://xxx.lanl.gov/abs/0705.3542 entitled "Is quantum field theory a genuine quantum theory? Foundational insights on particles and strings" I argue the following: Practically measurable quantities resulting from quantum field theory are not described by hermitian...
  41. E

    Introduction to Quantum Field Theory in curved spacetime

    http://sites.google.com/site/winitzki/" a draft of an introductory textbook on quantum field theory in curved spacetime - free quantum fields in expanding universe, Unruh effect, Hawking radiation, also Casimir effect and some basic stuff on path integrals and effective action. The book is not...
  42. T

    Quantum Field Theory: Evaluating Integrals on Page 27

    I don't understand how Peskin & Schroeder can evaluate the integral on page 27 by having the real axis wrapping around branch cuts just like that. The picture of the contours are on page 28.
  43. R

    The Best QFT Books for Learning Quantum Field Theory

    hi everyone, There are so many books about QFT, but what is in your oppinion the best book to learn quantum field theory?
  44. G

    Is Quantum Field the Fundamental Structure of the Universe?

    Hi all. I'm running a thread in the Philosophy section about rules of the universe etc but I'm stuck on a fundamental question which probably only a current quantum mechanics expert can answer. In essence do the most current iterations of QF theory maintain that the ultimate and irreducible...
  45. N

    Books for Quantum field theory?

    Hi,there! I want to study Quantum Field Theory but I don't know what book to use! I have a rather good background in quantum mechanics and electrodynamics, and I probably can gain access on the following books: Brown L.S. : "Quantum Field Theory" Peskin and Schroeder : "Introduction to Quantum...
  46. J

    Self-taught Quantum Field Theory

    I'm interested in teaching myself QFT. My BSc is in Mathematics and Physics, so I probably have a stronger mathematical background than the average physics graduate. However, I'm assuming it's almost certainly not good enough. What I am looking for is a way of sensibly teaching myself the...
  47. M

    From Simple Groups to Quantum Field Theory

    U = e^{\frac{1}{2} B} = \cos(\frac{1}{2} \theta) + b \sin(\frac{1}{2} \theta) we can then write: U = e^{\frac{1}{2} \theta b} = \cos(\frac{1}{2} \theta) + b \sin(\frac{1}{2} \theta) And if we rely on Joe's expression, r=\frac{\theta}{2} (rotor angle is always half the rotation): U = e^{br}...
  48. E

    Variatonal principles in quantum Field Theory

    Let be the nuclear reaction: ee \rightarrow e+e+ (if not possible a similar one) Of course we have 2 states |A> with 2 electrons and |B> with two "positrons"..if we wished to compute the transition probability we should know: <B|S|A> where "S" is the S-Matrix..my question is..is...
  49. R

    Exploring Delta Function in Quantum Mechanics and Quantum Field Theory

    As I read in my quantum mechanics book the delta function is sometimes called the sampling function because it samples the value of the function at one point. \int {\delta (x - x')} f(x')dx' = f(x) But then I opened a quantum field book and I found equations like that: \phi (x) =...
  50. E

    Divergent series in perturbation theory of quantum field theory

    if we know that the divergent series in perturbation theory of quantum field theory goes in the form: \sum_{n=0}^{\infty}a(n)g^{n}\epsilon^{-n} with \epsilon\rightarrow{0} then ..how would we apply the renormalization procedure to eliminate the divergences and obtain finite...
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