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Nov
27
revised Error in books of conformal field theory?
added 19 characters in body
Nov
27
answered Error in books of conformal field theory?
Nov
27
comment Proof that eigenvalues of Fermionic creation/annihilation operators are Grassman numbers
"It's stated probably in all textbooks.." Can you give some particular reference which states this ?
Nov
26
revised Is Einstein-Hilbert action the unique action whose variation gives Einstein's field equations?
added 12 characters in body; edited title
Nov
26
asked Is Einstein-Hilbert action the unique action whose variation gives Einstein's field equations?
Nov
24
comment C, T, P transformation mistakes in ``Peskin&Schroeder's QFT''?
I guess the reason that both the ways of transformation are valid is the following. $C,P,T$ are discrete operators. Moreover $C^2$~$I$,$P^2$~$I$,$T^2$~$I$. So even if (e.g.) you use $C^{-1}$ instead of $C$ to transform a state (and hence $COC$ to transform an operator) the result would differ only by a phase and hence physically be the same.
Nov
13
comment How many bits are encoded on the surface of the smallest black hole?
"Perhaps $r$ is defined so as to make this so" Yeah, $r$ is defined to be square root of surface area/$4\pi$. In a curved geometry it need not be equal to the distance from the center.
Nov
12
comment If space and time are equivalent, what's Spin in time dimension
Boost transformation correspond to rotation of time into space; so, in principle, their generators can be taken as analog of spin in time direction. However generators of boosts satisfy very different algebra from the spin algebra. This is because space and time aren't fully "equivalent" as can be seen from the signature of the metric (-1,1,1,1).
Oct
7
comment Definition of phase transitions in statistical mechanics
For a finite (quantum) system with #microstates <<Avogadro's number, partition function loses its thermodynamical interpretation. So even though the partition function of your system has discontinuity in limit of large $\lambda$, this discontinuity can not be interpreted to mean any "physical" phase transition in the system. Statistical mechanical formulation works well only for "large" systems.
Sep
30
comment How to derive the form of the parity operator acting on Lorentz spinors?
@Stephen I am not sure if it would help but look at Osborne's lecture notes on SM (in particular sections 2 and 3.5)
Sep
29
comment How to derive the form of the parity operator acting on Lorentz spinors?
I guess Stephen wants to ask why the matrices are $iI$ when, according to his calculations, they could be of more general form.
Sep
25
comment AdS/CFT seminal papers?
Also see the answer by Genneth to this question: physics.stackexchange.com/q/8162
Sep
24
comment Renormalizability of the Polyakov Action
Yes, 1 means $\eta_{\mu\nu}$. Similarly $aX$ means $af^{(1)}_{\mu\nu\rho}X^{\rho}$ for some 'tensor' $f^{(1)}$, $(aX)^2$ means $a^2 f^{(2)}_{\mu\nu\rho\sigma}X^{\rho}X^{\sigma}$ for some 'tensor' $f^{(2)}$ and so on. Sign of kinetic term for $X^0$ would be wrong. This gives rise to negative normed (unphysical) states in the spectrum which are then eliminated by applying constraints (which come from the equation of motion of the worldsheet metric h ).
Sep
21
revised From quantization under external classical gauge field to a fully quantized theory
added 326 characters in body
Sep
20
comment When Eigenfunctions/Wavefunctions are real?
Sorry, now i understand that the question is not that trivial since you are asking about reality of wavefunctions (i.e. position representation of eigenstates) and not the eigenstates.
Sep
20
comment When Eigenfunctions/Wavefunctions are real?
The answer to 1 actually depends upon how you define reality structure on the complex space of states. One can always choose a basis of eigenstates of the Hamiltonian and call them real.
Sep
18
comment Motivation to introduce von Neumann algebras in addition to $C^*$algebras?
Just a personal view. In matters of relevance to physics one is usually concerned with studying a particular observable ( like momentum, energy etc) or at most a finite algebra of observables (like spin algebra). I personally haven't seen any physics question whose answer is to be found in studying the set of all operators at once. For a physicist the statement "an observable should be Hermitian" is more useful than the statement "set of all operators form Von Neumann algebra (or whatever)"
Sep
16
comment Scale-invariant differential operator
There is no need to make any operator or expression dimensionless unless you have to (say) take its exponential or log etc. $\nabla^2$ is dimensionful and to make it dimensionless you'll have to multiply it with some constant having dimensions of length^2. Mathematically a constant of course won't make any difference. Anyway, I am telling you only very rough and personal view. I hope someone would give a better answer:)
Sep
16
comment Scale-invariant differential operator
Yes, dimensionless quantities whose definition doesn't involve choice of any scale are scale invariant; e.g. (length of stick A)/ (length of stick B). { reply to comment2: Mass=inverse length in natural units ($\hbar=c=1$)}
Sep
16
comment Scale-invariant differential operator
Scale invariance (roughly) means invariance of a quantity independent of the scale used to measure it (e.g. meter or cm scale used for measuring length). The given operator has dimension of mass^2 and hence is not scale invariant. In general dimensionful quantities can never be scale invariant (e.g. lenth. A 1 meter long stick is 100 cm long on cm scale). There are some dimensionless quantities too whose definition itself depends upon choice of some scale and hence which are not scale invariant. One example is charge of an electron. It depends upon from how close you look at it.