Introduction to conformal field theory, Lecture 1
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- čas přidán 6. 07. 2024
- In this seminar I will, over some 10 lectures, introduce the basics of conformal field theory. The emphasis will be on the physical content, however, there will be reference to mathematical formulations throughout.
The course is based on a mixture of Ginsparg's "Applied Conformal Field Theory", hep-th/9108028 and Schottenloher's "A mathematical introduction to conformal field theory".
Prerequisites for the course comprise: advanced QM, QFT, advanced QFT, and some familiarity with symplectic methods, which you can cover by watching my previous videos.
In the first lecture I introduce the conformal group, and its classification via infinitesimal actions.
Dear Prof. your lectures in CFT is extremely helpful for students. I had a lot of trouble when I learned CFT by myself. Thank you so much for sharing your videos.
Do really thanks for giving such a nice precious comprehensive resource, the videos, which means a lot for the students like me.
Great video, I like how you try to give a flavor of what is to come in the next lectures, and I think more teachers should do the same.
Great lecture. Very accessible and concise.
@18:33, 24:07, 30:28, 39:08, 43:55, 47:15, 53:16, 58:32, 1:01:56, 1:07:26, 1:14:05 oddly satisfying! Amazing lecture.
😂
Excellent! Feeling very at-home with the language and setup, especially after going through QFT and Advanced QFT.
A. S. Yeah right
This series is very well done, thank you.
Thanks so much!
Yay
Thanks for sharing the excellent lecture! But I have a small question. At about 41:30 when you write down the infinitesimal transformation of the metric, should it be g_{\mu
u} - (\partial_\mu \epsilon_
u + \partial_
u\epsilon_\mu)? I just mean may be the sign should be minus but not plus since we take \frac{\partial x}{\partial x^\prime}. Thanks a lot ！: )
Wonderful Lecture .. I watched just first lecture. I request please have a lecture series on Chern Simons theory
unfortunately I don't know about Chern Simons theory to give a lecture course on it...
Sincerely,
Tobias Osborne
aka as the "Phone Book"
I don't understand a point:
when you take trace of \eta_{\mu
u} why isn't the answer p-q but p+q=d?
Because the trace is calculated by contracting the \eta_{\mu
u} with g_{\mu
u}, which in flat space is just \eta_{\mu
u} (i.e. just changing the sign of the -1 in the 00 component and summing over the d entries in the diagonal)
Dear Tobias, why do we say that a theory has conformal symmetry if there exists a unitary representation of the conformal group? Surely the fact that we have a unitary representation isn't telling us anything about the physical states of the system. For example, we can define a unitary representation of the group of translations by exponentiating the momentum operator whether our system has translational symmetry or not, i.e. whether translations commute with the Hamiltonian or not. Thank you
Many thanks for your comment. What I am referring to here is the "non Wick rotated" conformal group of R^{1,1}. Here one of the generators then corresponds to time translation, i.e., the hamiltonian. So the hamiltonian itself is a required part of the unitary representation. Scaling and translations then intermix with the hamiltonian. For example, a lorentz boost mixes the momentum operator and the hamiltonian operator. Thus the hamiltonian is highly constrained and requiring conformal symmetry has a profound effect on all the eigenstates.
I hope this helps; sincerely,
Tobias Osborne
How are CFT and effective field theory (EFT) related? CFT is an infrared limit of QFT, and EFT obtains from QFT by integrating out the ultraviolet scale. So, CFT is EFT in this case?
I also see people discuss about relevant operator in both CFT and EFT
I would rather broadly define an effective theory as an approximation of an underlying microscopic model. So, in this sense I do think that CFTs can give EFTs (when applied to approximating, e.g., statistical physics models). CFTs can also arise as fundamental theories (i.e., as a building block of the standard model).
Sincerely,
Tobias Osborne
@@tobiasjosborne Thank you. Please correct me if I am wrong, I am not an expert in this subject. From what I read online, any QFT at extreme UV or IR limit can be described by CFT, not only at extreme UV. Let say that we have Lagrangian that is 1 massive and 1 massless.
At an extreme UV limit ( really high E), The massless field is definitely a CFT one. The massive field has particles that energy is mostly kinetics and behaves like massless particles, so the field becomes CFT. I think this one is the idea that you mention above.
At an extreme IR limit (really low E), the massless field is a nontrivial CFT. The massive field doesn't have enough energy to excite particles, so it becomes an empty or trivial CFT, so it is better to be described by TQFT, and QCD and the condensed matter is falling into this category.
By this fact, I think that CFT (both trivial and nontrivial) is EFT or QFT at an extreme IR limit while EFT, in general, is just QFT at some IR scale, not need to be at extreme IR.
Also, CFT is also QFT at fixed points or critical points.
@@khoanguyen5321 this sounds good to me. Sincerely,
Tobias Osborne
So why the conformal symmetry is show near only the critical point, not order phase or disorder phase?
because in these cases there is a lengthscale in the problem, e.g., the localisation length for disordered phases or the correlation length for ordered phases. Conformal symmetry contains scale symmetry which is incompatible with a lengthscale. I hope this helps.
Sincerely,
Tobias Osborne
Achha padha rahe bhau
Hi, should denominator of the angle be \sqrt{g_\mu
u u^\mu u^
u * g_\mu
u v^\mu v^
u }?
Many thanks for your comment. Indeed yes: my board writing is not so good. There is actually a squared symbol hidden there. (See bottom of page 4 of Ginsparg arxiv.org/pdf/hep-th/9108028.pdf)
Sincerely,
Tobias
shut up and calculate
What university is this from?
DdDark energy exsist as a FIELD INVARIANCE of Space configuration "PHASALITY" using a form of Spatial automorphism to auto regulate (gauge) ( ENGAGE) or Break Symmetry , the amount of energy , time , Velocity ( NEWTONIAN MECHANICS) plus {frequency) , and Volume required to Continuous Transform Any particle matter of that SPACE TIME "Configuration" ( FIELD, TENSOR, PARTICLE WAVE ENERGY PAIRING ) (LANGRAININ MECHANIC ) at that specific location ,` or at any future location in that Space Time, Ex. photons or light like particles Traveling in a straight line at a Fraction of speed of light (ECLUDIEAN SPACETIME DILATION) gives rise to Baryonic mass and (RADIOACTIVE DECAY ) through Quasi-Local Fields INTERACTION SCALAR FIELD "PHASING" like (HIGGS BOSON) particles fields , Extending into like matter electron proton ect. thru When ( Riemann space) gravity, electromagnetic, nuclear Strong force is engaged thru Baryionic Field Boson interaction the electromagnetic Photon Particle enters and engages Curvatured Space. Reaching infinite mass (NEAR INFINITE PHASALITY) for that particle wave location causing a curved Deceleration we call gravity.and Electromagnetism
Entanglement happens by Shears TRANSFORMATION of this Baryonic mass/particle/ when Space itself shears and Rotates , Like a Automorphism mapping of Space, So all FIELD in that Space becomes INVARIANT Orients itself, to a common point enabling one PARTICLES (like the MUON) to exist as a COLLAPSING Wave Function in Two Different Non-Local SPACES or fields. (PHASE) or thru a local Field SYMMETRY ,and Because Information travels in a Linear fashion in 3 Dimension Space , We olny become Aware of this Spacetime Information by attempting to Communicate outside our everyday 4 Dimensional Spacetime . and Not Seeing ,or Receiving anything back then we say mass is missing,
Entangled particles don't need this Same Time information to Communicate
because it Exists at every point in the Entangled PARTICLES BARYONIC MASS WAVE function . The SpaceTime Coordinates has Shared Merging at a Every Point in the field .So Field Entaganelment is (BOTH)a Attractive Force Within a mutual , Baryonic LEPTON MUON MESON Field space is a Repulsive Force where the Wave Particle are Running Away from Itself as a non local non mutual (RELATIVISTIC )field, So when you observe or try to measure the Particle the Wave function does not Collapses because the wave and Particle exsist as non mutual independent Quasi local Field OVER A DISTANCE WAVE or a Gauge less field for Relativistic and Quantum Field Entanglement the Field Symmetry Collapse of breaks from a ( DIALATED SCALAR Field
So Dark Matter Could be a Non-Localized Spacetime like a Black Hole with Equally distributed gravitational mass and inertial mass .Analysis of high velocity Nuetrino burst from Gamma rays as Observed from our 4 Dimensional Spacetime Frame of Reference might confirm this. Were the Nuetrino ACT as a SYMMETRY break of ENTROPY (Gauge Field) breaks and lose its Orientation.and this ROTATIONAL SYMMETRY break can be Non-Local or Quasi-Local Field when all Particle waves FIELD and SPACES becomes INVARIANT UNDER A mutual FLAT MANIFOLD
☝️This is what happens when you train an AI on a physics textbook and generate random text.