Field theory Definition and 554 Threads

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. P

    What is the interpretation of a mass term in field theory?

    Hello! I've some problems understanding why in field theory a term (appearing in a Lagrangian) like \propto \phi^{2} is called "mass"-term (whereas \phi denotes a real field). Is there any interpretation? And is this a general expression for a mass term or could it be of any other shape...
  2. A

    String Field Theory and Background Independence?

    Hi all, I've recently been reading about string field theory (note: I'm a novice). As I understand, the string field is an infinite collection of classical fields. But I'm uncertain as to why this formulation leads to background independence? Thanks all.
  3. C

    Fifth International School on Field Theory and Gravitation (BRAZIL)

    http://fisica.ufmt.br/school2/ Some of the invited speakers: Paul Davies, Abhay Ashtekar, Lawrence M. Krauss, James B. Hartle (to be confirmed), etc.
  4. F

    Why is the CFSE for d6 not equal to -24Dq+3p in crystal field theory?

    at crystal field stabilization in strong field case d4 CFSE=-16Dq+p d5 CFSE=-20Dq+2p d6 CFSE=-24Dq+2p d7 CFSE=-18Dq+p d8 CFSE=-12Dq it was shuld be +3P and +4 P why it be +p,2p,2p,p ?
  5. P

    Deriving the Poincare algebra in scalar field theory

    Homework Statement Find the commutators [P^\sigma,J^{\mu \nu}] The answer is part of the Poincare algebra [P^\sigma,J^{\mu \nu}]=i(g^{\mu \sigma}P^\nu-g^{\nu \sigma}P^\mu) If someone can convince me that \partial_i T^{0\mu} = 0, (i.e. the energy-momentum tensor has no explicit spatial...
  6. J

    Learning Conformal Field Theory after QM

    I will be starting a Masters degree in physics next year - 30% of the assessment will be a thesis (review, not research). I have selected CFT as a topic and my future advisor has pointed me to Francesco's 'Conformal Field Theory' as the book to use. Francesco's book is very good but I am...
  7. 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...
  8. A

    I'm frustrated because of Field Theory

    I'm now in my fourth year of physics and taking QFT right now. I always was quite OK gradewise at my german university, had a 1 (=A) in my pre-diploma, was among the best, and thought I can do what I want to do, which is fundamental physics. Right now I'm in the USA. Every teacher I had was...
  9. 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...
  10. Peter Morgan

    Field theory approaches to understanding Quantum Theory

    Why do people who think that quantum theory is great go on and on that classical particle models are impossible? Why do they never mention fields? There are endless articles in Nature on the latest experiment and why classical particle models won't do. Give or take the de Broglie-Bohm approach...
  11. E

    What is the idea behind Group Field Theory by Oriti?

    In plain English, what is the idea behind Group Field Theory by Oriti? How does this involve LQG, SF, and CDT? There is not a popular exposition on the subject nor even a wiki article. thanks
  12. 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.
  13. C

    Thermal masses in particle kinematics - thermal field theory

    Hi, I decided to open a knew thread since I was not sure whether my problem is close enough to the existing thread "FTFT for computing particle scattering". When dealing with Thermal Field Theory in the early universe, some people (eg. Giudice et al. hep-ph/03010123, Weldon...
  14. 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...
  15. S

    Unified Field Theory: Relating Quantum Mechanics & General Relativity

    People say that general relativity and quantum mechanics is not yet combined...i have a doubt,photon is the origin of quantum mechanics and light(photons) is bent by heavy mass and is the origin of general relativity...so this is the relation between quantum mechanics and general relativity..i...
  16. 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...
  17. T

    Lattice field theory in solid state physics

    I've gone through undergrad courses of QFT, Solid State Physics and Quantum Statistical Physics but the first one didn't cross path with second and third so I only got taste in QFT applications in Solid State Physics through reading Zee's "QFT in a nutshell". My first impressions was WOW! Solid...
  18. 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...
  19. E

    String Field Theory: Facts & Grand Unified Theory

    I know about string theory, but have heard that string theory is part of the bigger scheme of string field theory, which I think is part of the bigger scheme of M-theory, which is part of the bigger scheme of the Grand Unified Theory. Are my speculations correct, and how long will the Grand...
  20. 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
  21. J

    Electrical Field Theory and Tension In A String

    Homework Statement A ping-pong ball of mass 3.0 \times 10^{-15} is hanging from a light thread 1.0 m long, between two vertical parallel plates 10 cm apart, as shown. When the potential difference across the plates is 420 V, the ball comes to equilibrium 1.0 cm to one side of its original...
  22. T

    Why Is Fourier Transform Used in Diagonalizing Operators in Mean Field Theory?

    Hi... I hope somebody can help me... Studying mean field theory in a passage it was necessary to calcolate the inverse of this operator defined on Z^2: $A(I,K)=-J\sum_e \delta(I,K-e)+1/(\beta)*\delta(I,K)$ where I,K pass all ZxZ and the sum on $e$ is a sum on the for basis vectors...
  23. A

    Obtaining BPS States in Interacting Field Theory

    What is meant by BPS state in an interacting field theory? Suppose I have the action for some theory. Now how do I obtain the BPS states for the theory? I am looking for clear steps for calculations. Also I need to know what is special about these states. You may give reference to some review...
  24. 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...
  25. 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.
  26. 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
  27. 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...
  28. P

    Can the Variational Principle Explain the Laws of Nature for Classic Fields?

    I'm trying to understand why you can get away with using the variational principle on classic fields at all. The variational principle says minimize some value of a function the action. This idea is for point particles and is also motivated by the fact that Newton's laws can be derived via...
  29. E

    Solved: Field Theory Problem: Z_p in Algebraic Closure of F

    [SOLVED] field theory problem Homework Statement If F is a field that has characteristic p, it must contain a copy of Z_p. Is it true that F must sit inside of the algebraic closure of Z_p? My book assumes that it does and I do not understand why? Homework Equations The Attempt at...
  30. E

    Subfield of Reals: Q(pi^(1/3))

    [SOLVED] field theory Homework Statement Assume pi is transcendental over Q. Find a subfield F of the reals such that pi is algebraic of degree 3 over F.Homework Equations The Attempt at a Solution Umm...the only subfield I know of the reals is the rationals. Is the answer Q(pi^(1/3))? Do...
  31. B

    Ferromagnetism, electrodynamics and field theory

    Hi all, I'm a bit confused about ferromagnetism (and I've come to realize that I'm not the only one)! I'm currently studying electrodynamics and field theory in general to solidify my understanding of such, but permanent magnets and ferromagnetic materials seem to be often ignored in the...
  32. 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 .
  33. S

    Mean Field Theory: Get Book Recommendations

    I have just started reading up on mean field theory. Any book you could refer??
  34. 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...
  35. 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 \}...
  36. 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 ?
  37. 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...
  38. C

    Reading Quantum Field Theory 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.
  39. A

    Exploring the SU(2)_L x U(1)_Y Gauge Field Theory of Electroweak Interaction

    What does it mean to say to say that the electroweak interaction is described by a gauge field theory based on the SU(2)_{L}\timesU(1)_Y symmetry group? I know that SU(2) is a group of unitary matrices and U(1) is the circle group but I don't really see what the sentence means. I haven't taken...
  40. L

    Algorithmic information theory and the existence of a Unified Field Theory

    I have recently been studying Gregory Chaitin's "algorithmic information theory" for a school project. It describes the complexity of mathematical objects by the size of the smallest Turing machine program capable of computing them (in bits). It also defines a "random" object as one with an...
  41. 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...
  42. 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...
  43. 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?
  44. S

    Prosaic discussion of basic lagrangian field theory

    I'm currently trying to pre-familiarise myself with the course on lagrangian dynamics I'll be taking in the upcoming year, by reading the course notes supplied. I'm somewhat getting the hang of it, but I could really do with some more indepth discussion about the whys and wherefores. Could...
  45. 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...
  46. samalkhaiat

    Conformal group, Conformal algebra and Conformal invariance in field theory

    I have noticed that questions about this subject get either ignored or receive some confusing answers. So I decided to write a "brief" but self-contained introduction to the subject. I'm sure you will find it useful. It is going to take about 13 or 14 post to complete the work. Be patient with...
  47. 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...
  48. N

    Commutative Ring with Unique Ideals: Solution Using \mathbb{Z}_4

    Homework Statement I'm trying to find a commutative ring, not a field, who's only ideals are {0} and itself. Homework Equations Definition: A subset of a ring R is an ideal if it is a subring of R and is closed under multiplication by elements of R. The Attempt at a Solution I...
  49. A

    Crystal Field Theory: Understanding d_{xy}, d_{x^{2}-y^{2}} Orbitals

    Does anyone here know of a good site explaining d_{xy}, d_{x^{2}-y^{2}}, etc. orbitals?
  50. 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...
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