1,308 reputation
1515
bio website
location
age
visits member for 2 years, 5 months
seen 1 hour ago

Jun
20
awarded  Yearling
Jun
20
comment Are there massless bosons at scales above electroweak scale?
I am bit confused about your comment about the difference between early universe and LHC. Do you mean following - "We are stuck in a vacuum where the higgs field has a specific vacuum expectation value. We can't come out of this vacuum by feeding energy into electroweak fields only in a local region of spacetime. However if we do so globally at each point of space, then above the electroweak scale the gauge fields will be exactly massless".
Jun
17
comment Intersecting Wilson loops in 2D Yang-Mills
@ACuriousMind Use formula 3.30 for an intersecting loop in the notes by Moore-Cordes-Ramgoolam, and try to do the group integrations using equation (7) in the above answer. I think it should give 6j symbol at the vertex. I too will try to do this calculations if I get time.
Jun
17
answered Intersecting Wilson loops in 2D Yang-Mills
Jun
16
comment Why didn't electroweak symmetry breaking happen earlier than it did?
"The electroweak transition is a phase transition" - But not in the usual sense. Elecroweak theory is a quantum field theory in Minkowski space and its statistical interpretation makes sense in 4D Euclidean space rather than in 3D space as for ordinary transitions. We can say that initially electroweak fields carried a very high energy and hence SU(2) gauge symmetry was manifest, but after a while the system lost its energy to other fields and fell into a particular choice of vacuum out of infinitely many choices. This is what is called electroweak symmetry breaking.
Jun
12
comment What does it mean that there is no mathematical proof for confinement?
Yes, but I don't understand how the existence of mass gap can imply non-existence of such states.
Jun
12
comment What does it mean that there is no mathematical proof for confinement?
I mean a bound state which is not in singlet representation of global SU(3). Can't such states exist ?
Jun
12
comment What does it mean that there is no mathematical proof for confinement?
Why a non-singlet bound state imply free gluons?
Jun
12
comment What does it mean that there is no mathematical proof for confinement?
If we assume that finite energy states are global-SU(3) singlets then it would imply that there is a mass gap. However, I don't understand how the converse is true. There may be a mass gap but, in principle, there may still exist finite energy states which are not global-SU(3) singlets. No?
Jun
7
comment Decoupling of Holomorphic and Anti-holomorphic parts in 2D CFT
To understand the physical meaning consider a gas of particle on a circle. Assume that the particles which are moving clockwise do not interact with the particle moving anticlockwise, so that these two subsystems are decoupled from each other. If we want to compute (say) the partition function of the whole system, we can calculate it independently for both right and left moving parts and then take their product. Thus decoupling simplifies things a lot.
Jun
7
comment Decoupling of Holomorphic and Anti-holomorphic parts in 2D CFT
As far as I understand, the decoupling of holomorphic and antiholomorphic parts may not hold always. However, many of the important examples of 2d conformal field theories have this property. For these theories, holomorphic and antiholomorphic parts can be studied independently and later combined to give the full theory.
May
30
comment Problem understanding sign of volume integral in Minkowski space
@Josh Thanks to you too; I never cared much about $i\epsilon$ Now I understand that its not just important but really necessary:)
May
30
comment Problem understanding sign of volume integral in Minkowski space
@Josh I am not sure but I think the $i\epsilon$ contour can always be rotated to y-axis contour i.e. to Euclidean space. Anyway, all I was saying is that the integrals on Minkowski space itself are ill defined, and in order to make sense of them one needs to choose a different p0 contour in complex p0 plane other than the real axis.
May
30
comment Problem understanding sign of volume integral in Minkowski space
@Josh Yeah that seems to resolve this paradox. More generally, it appears that the integrals of Lorentz covariant real integrands can never be finite on Minkowski space {in particular, integrals of the form $\int d^4 p f(p^2)^2 p^\mu p^\nu$ can not be finite}, and we necessarily have to go to Euclidean space to make sense of these integrals by assuming p0 to be a complex variable and making use of Wick rotation. The reason that they are not finite is may be because any function of the form f(p^2) doesn't go to zero at infinty on Minkowski space.
May
30
comment Problem understanding sign of volume integral in Minkowski space
Your reasoning is perfectly fine but there is still a paradox here that I am not able to understand. From the OP's integral we can see that for $m_1=m_2$ the integral is positive for all $\mu=\nu$, simply because the integrand is positive and also the measure $d^4 k =dk^0 dk^1 dk^2 dk^3$ is positive; whereas if the value of integral were equal to $g^{\mu\nu} B_2$ then the sign of integral for $\mu=\nu=0$ will be opposite to that for $\mu=\nu=i,\: i=1,2,3$!
May
13
comment Astronomical Constant in Astronomical units?
You forgot a factor of $10^{-11}$ in expression for $G$.
May
12
comment Self-dual Maxwell equations, the second homology group, and topological invariants of a four manifold
Now, since on a 4-manifold **=1 on 2-forms, so the space of 2-forms (and hence in particular space of harmonic 2-forms) itself can be written as a direct sum of the space of self dual and anti self dual forms. So we can say that the second cohomology class of a 4-manifold is the space of solutions of self dual and anti self dual Maxwell equations.
May
12
comment Self-dual Maxwell equations, the second homology group, and topological invariants of a four manifold
Not sure about the "intersection form", but i think the relation with second cohomology (and hence also with homology by Poincare duality) follows from the Hodge theorem. From Hodge theory it follows that the second cohomology class (which is usually defined as the quotient of closed 2-forms by exact 2-forms) of a four manifold is same as the space of harmonic 2-forms i.e. 2-forms $X$ which satisfy $dX=0$ and $d^{*}X=0$, where $*$ is the Hodge dual operation wrt a fixed metric. These are precisely the Maxwell's equations.
May
4
comment The properity of $\mathbb{R}^4$ that has infinitely many differential structures is related to Yang-Mills field?
Relevant : 1. Donaldson theory 2. Seiberg-Witten invariants
Apr
2
comment Why do we use functional integration in QFT?
@AlexNelson Its true that we choose a time coordinate but in all the expressions time and spatial coordinates appear on equal footing. There are no expressions such as Exp(itH) in which time 'appears' to be different from spatial coordinates.