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Apr
14
comment Is it possible to define a notion of temperature in a microcanonical ensemble?
@V.Moretti Well - the question is - whether this mathematical definition makes physical sense. A system in a microcanonical ensemble is an isolated system which can't exchange energy or particles or volume with anything else. Then how is the system equilibrating to a temperature? Can a system spontaneously determine its temperature without an infinite heat-bath? Isn't this the notion of temperature that leads to freaky things like negative temperature a finite system of spins? [...think of black-hole thermodynamics - isn't that a microcanonical ensemble?...]
Apr
14
comment canonical and microcanonical ensemble
In a microcanonical ensemble isn't it true that all microstates are equally probable and hence the probability distribution is just flat?
Apr
14
asked Is it possible to define a notion of temperature in a microcanonical ensemble?
Apr
11
comment About the recent discovery of 4-quark boundstates.
So to make a bound-state colour neutral we would need a notion of "anti-colour" for the anti-quarks - right?
Apr
11
comment About the recent discovery of 4-quark boundstates.
So even in a bound-state we can say that the quark and an anti-quark are distinguishable? So problem would start if you had more than 3 quarks in the bound-state?
Apr
11
asked About the recent discovery of 4-quark boundstates.
Mar
18
comment What does it mean to “wrap” a D-brane around some manifold?
Bruinner I have been reading that book - anything specific you can point out there - where this is explained? - as to how wrapping happens "on its own"? What is the dynamics of it?
Mar
16
comment What does it mean to “wrap” a D-brane around some manifold?
Brunner Thanks for the answer. Can you give some reference where this analysis is done? I mean is anywhere it is explained how Dp branes can take arbitrary shapes? I mean - what is the mechanism for them to attain some shape? The T-duality argument doesn't seem to lead to any shape information?
Mar
14
asked What does it mean to “wrap” a D-brane around some manifold?
Mar
11
accepted CFT and the conformal group
Mar
9
revised Large-N critical NLSM (equation 13.115 of Peskin and Schroeder)
added 474 characters in body; edited title
Mar
7
asked Large-N critical NLSM (equation 13.115 of Peskin and Schroeder)
Mar
4
comment CFT and the conformal group
I think you are missing my point - You are right that "the Hilbert space of a theory with a symmetry, that is some group of transformations that leave the generating functional of correlation functions invariant, decomposes as representations of that symmetry" - BUT - if an action is invariant under conformal diffeomorphisms then $SO(2,d+1)$ is NOT the full symmetry group of transformations (its only so locally!) - then why does the Hilbert space still split under its representations? (...and this happens irrespective of the topology of the locally $d+1$-Minkowskian space-time - right?...)
Mar
4
comment CFT and the conformal group
(3) Do you have a reference where this is proven that all states in a CFT Hilbert space will be eigenoperators under the dilation generator? I have never seen such a proof! (...all arguments begin by assuming that such an eigenspace of dilation exists for a CFT and then one looks for the lowest among them and thats the one which commutes with $K$ and gets called the primary..)
Mar
4
comment CFT and the conformal group
(2) See the issue with Weyl resacalings is quite serious to my mind - because classically when thinking of a CFT in $(d>1)+1$ thats what we always do - we write down a Weyl invariant Lagrangian - and then as a QFT we think its Hilbert space to split under $SO(2,d+1)$ - one needs to know that this indeed follows!
Mar
4
comment CFT and the conformal group
Thanks for the reply! (1) So if SO(d+1,2) is only a local model for whatever one wants to call as the "conformal group" (the group of all conformal diffeomorphisms - diffeomorphisms which keep the metric invariant upto a Weyl rescaling) then why should the Hlbert space of the CFT split under its representations? QFTs are supposed to see the full space-time and not just a local symmetry group - right? SO we are saying that no matter how complicated is the space-time topology a CFT on it will have its Hilbert space split under $SO(2,d+1)$!
Mar
3
comment CFT and the conformal group
Also is it true that in a CFT Hilbert space all operators will be eigenoperators under commutation with the dilatation operator? (...because when one argues what is the highest-weight sate in a conformal module one looks for that operator among only such operators which commutes with the $K$ - and that is the primary...)
Mar
3
comment CFT and the conformal group
Here are my 2 questions rephrased better, (1) Isn't it true that the conformal group in $(d>1)+1$ Minkowski manifold is only locally isomorphic to $SO(d+1,2)$ and not globally? (2) Is there a proof for $(d>1)+1$ Minskowskian space-time that demand of the classical Lagrangian being invariant under Weyl rescalings of the metric implies that the Hilbert space of the corresponding QFT will split into $SO(d+1,2)$ representations? [...AFAI have seen this crucial link between the classical and the quantum picture is provable only on Riemann surfaces with a fixed metric...]
Mar
1
asked CFT and the conformal group
Feb
23
asked A question about particle scattering