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Aug
29
comment Spinor irreducible reps of the Lorentz group and their algebra
sorry i didn't read it carefully. T(g) is usual vector representation and you are talking about its splitting into two su(2)'s right? By Dirac representation i meant 4d complex spinor representation which is direct sum of right and left Weyl.
Aug
29
comment Spinor irreducible reps of the Lorentz group and their algebra
Is representation T(g) Dirac representation ?
Aug
24
comment superposition of two states with different number of particles
@richard In absence of any mechanism for production or annihilation of particles, time evolution will not be able to mix up the states with different particles numbers and hence you can study them separately too.
Aug
22
comment A curious issue about Dyson-Schwinger equation(DSE): why does it work so well?
@Jia Yiyang I am not sure but i think any derivation of (1) making use of this assumption can't be correct. For a free field we can anyway derive (1) by actually first computing the time ordered expression (using mode expansion of fields) and then verifying that it satisfies (1)
Aug
21
comment A curious issue about Dyson-Schwinger equation(DSE): why does it work so well?
I think correlation function of any product of fields in path integral can be written equal to the expectation value of the corresponding time ordered expression of quantum fields. So in particular equation (4) is correct. But RHS of (4) is still not zero. I guess the rule is that whenever there is an integral or differential operator expression inside time ordering then one should use discretized version of the expression appearing inside time ordering. So the issue is to correctly interpret the time ordering expression, and not the path integral
Aug
20
comment Introduction to spinors in physics, and their relation to representations
There are two different notions of a "vector". First is the definition used by mathematicians according to which any element of a vector space is a vector. Another definition is what is often used by physicists according to which a vector is that which behaves as a vector under rotations. Spinors are of course vectors in mathematical sense however they are not vectors in physics sense.
Aug
17
comment Why is renormalization necessary in finite theories?
By "finite" you mean usual quantum mechanics?
Aug
17
revised Why Weyl invariance is important for consistent string theory
added 38 characters in body
Aug
17
comment Why Weyl invariance is important for consistent string theory
@user26143 I meant its independent of choice of coodinates $\sigma_1,\sigma_2$ on the surface $S$ not of $X^\mu$
Aug
17
comment Why Weyl invariance is important for consistent string theory
@user26143 Coordinates $\sigma_1,\sigma_2$ on the surface are chosen independently of the spacetime coordinates $X^\mu$. We could rather use coordinates $X^\mu$ themselves to denote each point of the surface and also to express its area. For example think of a 2d spherical surface in 3d space and consider a very fine triangulation of this surface. Area of sphere would be sum of the areas of the triangles and area of each triangle can be known by the spacetime coordinates of its vertices. Thus we don't need to introduce any coordinates on the surface itself to measure its area
Aug
17
answered Why Weyl invariance is important for consistent string theory
Aug
16
comment Why Weyl invariance is important for consistent string theory
i too don't understand Polchinski's argument;) May be he wants to say that since the counterterm for the divergence is non Weyl invariant so the divergence itself has to do with non-Weyl invariance and so it should not be there. But whether or not the divergence has anything to do with non-Weyl invariance it should anyway be regularized ! However in any case the idea is that Weyl invariance is necessary to get rid of unphysical metric degrees of freedom and so one demands that the Weyl invariance remain preserved under quantization. May be I will write an answer after understanding it properly
Aug
16
comment Why Weyl invariance is important for consistent string theory
In case of string theory the three components of worldsheet metric tensor are unphysical degrees of freedom. Reparametrization invariance along the two directions on a worldsheet can cancel 2 of them. To cancel the third one you need Weyl invarince. If you don't care about preserving Weyl symmetry then one of three degrees of freedom of the metric will not be canceled. This left out degree of freedom is i think called Liouville mode and corresponding string theories are known as noncritical string theories
Aug
16
comment Massless fields in curved spacetimes
Prahar when answering to someone's comment you should use @ (user name). e.g. @joshphysics
Aug
15
comment Chirality and helicity operators for the massless bispinor rep and their generalisation on arbitrary (tensor, 4-vector etc) cases
let us continue this discussion in chat
Aug
15
comment Chirality and helicity operators for the massless bispinor rep and their generalisation on arbitrary (tensor, 4-vector etc) cases
sorry I still don't understand how absense or presence of helicity values s-1,..., -(s-1) is relevant to the question of relation between chirality and helicity.
Aug
15
comment Chirality and helicity operators for the massless bispinor rep and their generalisation on arbitrary (tensor, 4-vector etc) cases
sorry I didn't understand. Is there anything wrong with above argument?
Aug
15
comment Chirality and helicity operators for the massless bispinor rep and their generalisation on arbitrary (tensor, 4-vector etc) cases
So now if we consider space of eigenstates of helicity operator for a massless particle then since Lorentz transformations do not change the sign of helicity so the eigenstates with positive and negative eigenvalues will separately form a representation of Lorentz group. You may call them two chiral representations if you want.
Aug
15
comment Chirality and helicity operators for the massless bispinor rep and their generalisation on arbitrary (tensor, 4-vector etc) cases
For a massless particle sign of helicity is independent of Lorentz frame. This can be understood by the usual argument that you can't overtake a particle moving at the speed of light and so if projection of its spin in one frame is found to have positive (respectively negative) value, then in any other frame too it will be found to be positive (negative).
Aug
14
comment Heisenberg picture of QM as a result of Hamilton formalism
Using the definition of derivative as ratio of differences you can see that "operator corresponding to the derivative of function" = "derivative of the operator corresponding to the function".