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. 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...
  2. 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...
  3. 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
  4. 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
  5. 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:
  6. 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...
  7. 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...
  8. 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...
  9. 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
  10. 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...
  11. S

    Graduate Student Struggles to Keep Up in Quantum Field Theory

    I just entered graduate school. As an undergraduate I took a graduate course in Quantum Mechanics, mostly for fun and practice because I knew the credits wouldn't transfer to the uni I was applying to for grad school. So, I got accepted there and even though the credit wasn't transferred the...
  12. E

    Relation between quantum computer and quantum field theory?

    I'm a computer science and engineering student, who has recently developed interest about quantum computers. I can understand that quantum computers are totally linked with quantum mechanics. But I would like to learn whether there is any relation between quantum computing and quantum field...
  13. H

    How much mathematics do I need to know to start Quantum Field Theory?

    I plan to study from Peskin and Schroeders book if it helps, I just need to know what topics I need to study and it would be greatly appreciated if someone could tell me what books are good on the subject, I have a limited budget however and if I could get a single or only 2 or 3 books covering...
  14. S

    The Lagrangian formalism of Quantum Field Theory

    Recently i am reading A.Zee's Quantum Field Theory in a Nutshell 2nd Edition. there is a equation that i can not derive by myself. I suspect its correctness. <k1k2|exp(-iHT)|k3k4>=<k1k2|exp(i∫dxL(x))|k3k4>, where the L(x) on the RHS is an operator function of space-time. This equation...
  15. I

    Solving a Quantum Field Theory Recursion Relation Through Self Study

    Hello Everyone! I have a problem I am solving through a self study project from Lowell Brown's book entitled: Quantum Field Theory". It is a math question (basically) on recursion relations. Homework Statement The variational definition gives us the relation: det[1-λK] = exp{tr...
  16. Y

    What would be the pre-requisites to learn Topological Quantum Field Theory?

    Personally, I am interested in Topological Quantum Field Theory. And now I am battling against Quantum Field Theory. I am not sure how much Quantum Field Theory is needed to do Topological Quantum Field Theory. And I am not sure what should be the mathematical pre-requisites of Topological...
  17. J

    Black Holes and Quantum Field Theory

    Now, I must preface this by saying that my understanding of QFT is limited, and my understanding of GR is even more so. Nevertheless, I was reading about the No Hair Theorem, and it seemed to me to be suggestive of the indiscernibility of Quantum Particles. Obviously, for a macroscopic black...
  18. E

    Arising of exp(-ipx) in QM in quantum field theory

    Wave functions and their exp(-ipx) are base of quantum mechanics and QFT. But how to derive them the most simply that we will understand why they are base of QM? It is interesting that Feynman in his book "QED: The Strange Theory of Light and Matter" very simplifies QED, but he did not give a...
  19. Spinnor

    Static electric field in Quantum Field Theory?

    In quantum field theory do we "describe" static electric fields with proper combinations of transvers propagating photons? Is that a basis? Is there a basis using the longitudinal and timelike photons to describe static fields? Thanks for any help!
  20. B

    Quantum Field Theory lecture by Tong (Cambridg)

    I am struggling with equation 1.5 in Tong's QFT course. I try to understand/explain it in strict calculus, i.e. without physics shortcuts like "small variations". I guess in the full blown explanation, \delta S is a total derivative. To be specific, with total derivative I mean the linear map...
  21. A

    A few doubts about quantum field theory and high energy physics.

    1. I read that the picture of gauge bosons as mediators of interaction originates in and is valid in perturbation theory. But how do we know that picture is correct? We do perturbation theory only because we do not know how to study a system in a fully non-perturbative way. If someday we...
  22. N

    Quantum field theory and the renormalization group

    The following statements are from the paper with the above title, recommended in another thread, are from here: http://fds.oup.com/www.oup.co.uk/pdf/0-19-922719-5.pdf An interpretion of these statements would be appreciated: 1. [first paragraph, page 3] What is 'conservation of...
  23. H

    Ideal book to learn Quantum Field Theory

    I'm an undergraduate with interest in theoretical particle physics. No course available in QFT. I have background in particle physics, quantum physics and relativity. Want to start learning it before going for M.Sc I've seen books like Mandl and Shaw, Landau and Lifgarbagez in university...
  24. M

    Requirements on Quantum Field Theory to be correct physical theory?

    In some class notes I found those conditions interpreted as a "five requirements on Hamiltonian of physical system": 1. Unitarity -> Hamiltonian has to be hermitian operator 2. Claster decomposition (microcausality and locality) -> (? missing part) 3. Poincare invariance -> Hamiltonian...
  25. alemsalem

    Symmetry breaking and the ground state of a quantum field theory.

    when a continuous symmetry is broken, we say that the ground state is just one of the possible ground states, and there is no energy cost in moving from one to the other.. why doesn't the state keep changing with the slightest perturbation (production of goldstone boson). why don't we have a...
  26. N

    The state space in quantum field theory

    I'm a grad student in math, and I've been trying to learn some physics on the side by taking some classes and reading books. I took a class on quantum field theory last semester that was taught out of Srednicki; the class was very good, but I found myself at the end with a conceptual question...
  27. B

    What are the required mathematics for studying Quantum Field Theory?

    Hello everyone! I want to study QFT and I want to know all of the required mathematics for it. I know most of quantum mechanics topics -wave function -schrodinger equation -state, operator -perturbation theory I know some of special relativity. And I almost familiar with einstein's...
  28. D

    Is Dark Matter actually a gravitational byproduct of quantum field theory?

    Hi All, I don't know whether to post this in quantum field theory or in cosmology. Maybe this stuff is one subject, not two. Hajdukovic published some papers recently which seem very intriguing even to an amateur like me who doesn't understand it. Here's the latest one...
  29. P

    Electric charge in quantum field theory

    I have a question concerning the notion of electric charge in QFT. What value of charge for electron should I use if I want to compute the force acting on electron in some external electric field. Of course in first approximation it is just elementary charge which value might be found in...
  30. E

    What does it mean if something Transforms Covariantly ? (Quantum Field Theory)

    What does it mean if something "Transforms Covariantly"? (Quantum Field Theory) Referring to an isospinor, \psi which transforms as \psi(x)→ \psi'(x)=S(x) \psi(x) (S(x) being an n by n matrix) I'm told that it is clear that ∂_{μ}\psi does not transform covariantly. Now, correct me if I'm...
  31. sujoykroy

    Is Quantum Field Theory and General Relativity Theory mutually exclusive?

    Does Quantum Field Theory and General Relativity Theory predict anything which is mutually exclusive? This question came up to me as i was thinking about why there was/is apparent rivalry/debate between the proponents of these two theories. As far as i understood, Universe(or Multiverse) is...
  32. R

    Quantum field theory and string theory

    What is the relationship between quantum field theory and string theory?
  33. L

    Is quantum field theory the return of the ether?

    Hi, My question is about why quantum fields are used. Are quantum fields just a reinvention of the ether? It seems like something superimposed on spacetime (from which theoretically spacetime should emerge in the case of gravity) from which particles can pop in and out of. How wrong is...
  34. 6

    What is the best Quantum Field Theory book for self-study?

    Hi, I'd like to ask recommendation for a QFT book. I have seen several other recommendations on this forum, but hopefully I'll provide enough info so you guys can have more specific advice. Background: QM (Griffiths, some parts of Sakurai), GR (Carroll), some residue...
  35. M

    Virtual particles in rigorous quantum field theory

    "virtual particles" in rigorous quantum field theory If I am not mistaken "virtual particles" are just a name someone put to some integrals that we use to calculate different things, and those integrals depends on the perturbation scheme and on the gauge selected, and they don't even exist in...
  36. L

    Quantum Field Theory Exam Q3: Draw Feynman Diagram | Advice Needed

    Consider q3 in this exam: http://www.maths.cam.ac.uk/postgrad/mathiii/pastpapers/2006/Paper48.pdf I reckon I can manage a good part of the rest of the question. Unfortunately, I cannot manage the very first bit (drawing the Feynman diagram) and this is preventing me from continuing! I...
  37. L

    Quantum Field Theory: Stationary Point of the Effective Action

    We have the effective action which obeys \frac{\delta \Gamma[\varphi]}{\delta \varphi(x)}=J(x) where and we are told the stationary point, \varphi_0, of this action, \frac{\delta \Gamma[\varphi_0]}{\delta \varphi(x)}=0, corresponds to the vacuum expectation value. (This is out of my notes -...
  38. E

    Question about quantum field theory

    Hi there! I'm attending an introduction to elementary particle physics and I came into this statement about the Dirac equation: "When an interaction is added (using the gauge principle) in a field theory, then some terms appear like: gBj where, g is the coupling constants, B is a bosonic...
  39. G

    Introduction to Quantum Field Theory: A Relaxed Approach

    Sometimes I find useful and more interesting to read a less rigorous textbook before tackling a reference textbook of a given subject. Having said that, I am looking for a book that introduces the ideas of quantum field theory in a relaxed way. This allows to grab the ideas and then formalize...
  40. R

    Quantum Field Theory and Perturbation Approximation

    Pls. answer in the simplest and the most intuitive way. 1. What is the reason our quantum field theory needs perturbative approach. Is it because in the concept of fields, there is an infinite number of freedom in the oscillations of the virtual particles, or is it because the field is...
  41. Simfish

    What % of Physics students ultimately learn quantum field theory?

    It's not a requirement at my school's Physics PhD program (it's a graduate-level pass/fail course), so I'm curious as to whether or not other schools have the requirement, and how many students ultimately opt to take it.
  42. StevieTNZ

    Exploring Quantum Field Theory: From Entanglement to Superposition and Beyond"

    From a previous post, I now know that the 'qualities' of QM such as entanglement, superposition of states, decoherence, measurement problem, are still with us in QFT. 1. Is the Dirac equation the primary equation in QFT? 2. What equation governs the evolution of a macroscopic object in QFT...
  43. N

    Why quantum field theory is not called quantum mechanics of changeable number particl

    Please teach me this: Why we do not call the quantum field theory the quantum mechanics of a changeable number particles.Why we must use the term ''field''.I think that the indistinguish of identical particles,the dual particle-wave and changeable in number of particles mean the ''expansion''...
  44. A. Neumaier

    What is observable in a relativistic quantum field theory?

    Steven Weinberg wrote: ''In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the universe, and particles are just bundles of energy and momentum of the fields.'' (see p.2 of his essay, ''What is Quantum Field Theory, and What Did We Think It...
  45. C

    Mark Srednicki's Quantum Field Theory

    Mark Srednicki's "Quantum Field Theory" I just wanted to know what level the book QFT by Mark Srednicki is, that is... Is it considered first year Masters, second year masters... Low PhD..?? I know it's not upper year undergrad, that's for sure. Just wondering. thanks!
  46. A

    Quantum Field Theory Purly in Momentum Space?

    Quantum Field Theory Purly in Momentum Space? Hello, I have a complicated nonlinear-nonlocal-nonrelativistic-effective action in momentum space and would like to do perturbation theory with that. I need to find propagator and Feynman rules. I can not go to x-space and follow the standard...
  47. L

    Quantum Field Theory: Understanding Path Integrals and Limit Trick

    I'm trying to understand path integrals as described in my lecture notes (which are reinforced by Peskin &Schroeder). Anyway on p284 of P&S, there is a formula inbetween eqns (9.17) and (9.18) that reads: e^{-iHT} | \phi_a \rangle = \sum_n e^{-i E_n T} | n \rangle \langle n | \phi_a \rangle...
  48. N

    Can we demontrate the convergence of perturbation quantum field theory?

    Please teach me this: Can we demontrate the convergence of perturbation series of quantum field theory(Feymann diagrams) after making the renormalizing procedure? If we can't demontrate that,why we still consider the perturbative method using in quantum field theory being useful and believable...
  49. S

    Exploring the Strange Result of Equation 8.9 in Quantum Field Theory

    Dear all, I am taking 'field theory' course this semster and I am reading 'quantum field theory' by mandl and shaw. In chapter 8, equation (8.9) we see: E_1 E_2 v_rel=〖[(p_1 p_2 )^2-m_1^2 m_2^2]〗^(1/2) and we know that as p is a four vector: p=(E,P)=m so p_1 p_2 = m_1 m_2 ! Isn't...
  50. C

    A Beginner's Guide to Quantum Field Theory

    What is a good to book to start reading about quantum field theory?
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