Dreams, deliriums and one-night stands

The story of what I went through in the past two days, would include all the above three words: a one-night's (more precisely two) stand that brought free dreams and deliriums.
It all originated in the wicked desire that I had on Sunday to have pizza. Having seen nobody in the office with whom I could have dinner; and deciding to catch up with the jogging, I decided to order a pizza at night. It was a medium sized pizza from Smokin Joe's, along with an assorted garlic bread and a coke---an amount which I have had before at times, and succeeded admirably.
This time however, it proved to be somewhat heavy--causing me get up at 2 different occasions in Sunday night seeking cold water to quell a parched mouth. Not to speak of the intermittent vampire dreams that I had.
Monday woke up late with an extremely heavy stomach that counseled my reason not to go ahead to the office, but simply sleep more and pass the day.
But just had biscuits and soup only, since the stomach was still heavy and a visit to the loo hadn't helped. By night, I was becoming scared of the apathy to work that was being generated--I felt that that I didn't go to the office for no reason.
If the night before was just dreams, this night deliriums took over. I went to the loo about once every one-and-a-half hour to extreme excretions of foul smelling liquid stuff. By early morning, this had turned to gas and mucus, but it still didn't stop. I couldn't rehydrate myself with water, since that chose to come out as my back-ward excreta with mucus within 5 minutes. And in between these visits to the loo, was trying to sleep, but of course without the least fraction of success. Kept on being in deliriums---punctuated by intervals of watching movies to pass the time. The only respite in all this, was that I online on skype with babun-da and that was doing wonders.
By early morning, I was so weak and faint headed that I'd just toss and turn in my bed relentlessly, sometimes going down to sleep on the floor, until the next wave of stomach pain sent me rushing to the loo.
Hah, what a night! Didn't get a single wink of sleep. In the morning, somehow managed to drag myself to the canteen to have a toast and jam with sweet black tea. Have been safe since then!
What a night's stand!

Miss Marple

What have I been doing all these time? Besides working, that is. Why reading Miss Marple. Why her all of a sudden? Don't exactly know. But the settings, the plots and the characters suddenly seemed so nice and appealing, that I couldn't resist for long. And of course there was the fact that at some point of time, I was really bored with my work, my surroundings and my circumstances.
Anyway, sometime into this period I decided that I will read up all the Miss Marple that Christie ever wrote and that's what I have been doing, sometimes recklessly neglecting my work. Very foolhardy, I suppose.
I have finished most of the books--the only ones that are left are: A Caribbean Mystery, At Bertram's hotel and the Sleeping Murders. The question that naturally rises are which books I have liked and why? So, one of the issues that I realized is that Christie has reused several of her plots from time to time: many of the plots that she has toyed with in the "The Tuesday Murder club" has been reused in her later novels. Nonetheless, I must say that the books that I found to be pure genius are : The Murder at the Vicarage,  The Moving Finger and A Murder is Announced. The plot is considerably more intricate in the first and the last ones than the middle, but the middle one compensates in terms of atmosphere. I shouldn't miss out 4:50 from Paddington--that's sheer brilliance as well. Among the next best are : The Body in the Library, Nemesis, The Mirror Crack'd, A Pocket Full of Rye, and others. I wouldn't put anything in the third rank! :)
In the midst of all this, I also quickly read Ken Follett's Code to Zero. Of course, he was superbly brilliant in his The Eye of the Needle, so much so that I would have compared him with Forsyth, but then Code to Zero is a huge fall from the position. Sure the action is taut, but I find that the plot is terribly weak sometimes. I ask myself again and again if the US were really so lax in their security measures in the 1958 as he describes. I mean, even the events that Forsyth describe take place in London and/or the UK, but they seem more believable. It course remains that Ken Follett tried a romantic quadrangle in the latter book and not in the Eye of the Needle. Nearly the whole plot in Code to Zero is based on the romantic plot 15 years ago from the time when the story takes place and somehow this makes the plot pretty unsteady, according to my opinion.
Anyway--way too much of this! I must go back to working!

Had this focaccia bread today. For details look up http://en.wikipedia.org/wiki/Focaccia. Hell, that was wondeful. Might have had this in Italy, but if so don't remember it quite so well. But the one that I got from Theobroma was just heavenly. (The use of contrasting adjectives for the same object is purposeful.) The olives were wonderful and the smell enticing, even though this was cold. I wonder what it will be like when served hot! Mind blowing.
It was nice to go out, even if completely by myself. I still didn't feel like having those there, so I carried them back home. But at least, I would have been more disappointed if I had stayed back at TIFR and did nothing. Anyway, I was expecting the streets to be crowded due to Ganesh Chathurthi and Eid, but thankfully it was rather empty. So no additional troubles! Also, this time didn't go to Muhammed Ali Road. Missed the kababs and the sweets. Damn!
Sometimes, I get tired of this life in TIFR. A fresh beginning somewhere else? but then, --- for how long? and then?

I really wanted to go out today (but did not make any plans) --- to Muhammed Ali Road. Ramadan is going on, remember? Tomorrow is Id. Maybe I could have made it. But in the end what matters is that I didn't. :( Need to something interesting to cheer me up.

Every time I try to cut myself out of the emotional shackles, I end up getting more and more hopelessly entangled in them. Damn, why did I ever start writing my Diary? Do you think that I didn't do that I'd be as I am today? That'll require another lifetime to find out----with the exact same initial conditions. Nah, too much of a bother, forget it!

Yogurts and the Quantum World

Hah! --a bizarre impossible connection you'd say. Not really, hear me out! When I was visiting Les Houches, attending a school devoted to Lattice Quantum Chromodynamics devoted to studying the quantum world in much more detail, there were lots of things that would make our life fun. One of those was the yogurts and diary products from DANONE, some diary brand.
Today, while coming back from the bank, I saw an advertisement of DANONE. Here in India!  India is fast becoming a market to expand into.
Well, what a weak link! But I had to mention this. Why exactly it caused me such an excitement when I saw the ad, I can't exactly express. Maybe my country and its people being courted by foreign companies to sell their product? Pride? Or folly that we have to depend on them, still? I wish I knew!

The Spending Spree in India

Recently, as most people have noticed, the Indian economy has experienced a boom, with a lot of good and bad effects. To sustain this growth, a spending spree seems inevitable. Let me tell you how I actually experienced it.
There is this travel company called Make My Trip, a pretty well known company in India. I had used this to book some air tickets previously. But, suddenly, a month ago they suddenly offered me a package--for which I had to a pay a service charge of about 7000, and in return they gave me several discount vouchers. They did explain all the terms and conditions--or as much of them as they thought would not put me off in accepting the offer. I was a bit sceptical and so were some of the people I consulted with. But it seemed an interesting thing to experiment with. So I have accepted the offer. The entire package gives you a lot of discounts, but it also necessiates that you spend a lot more than you planned to! I knew all this, but the real challenge to me is how to get the most by spending the least. Lets see how it goes--I have about an year.
But this is indeed what goes on all the time--everywhere---the entire credit system based on the Credit and Debit cards promises you more benefits the more you use them. The more you spend. The more debt you incur.
No longer a scary thought; but a reality to deal with!

Do you think if somebody smiled at you, you can make out if the smile was out of genuine pleasure of seeing you, or merely trying to be polite? Can you be sure? Ever?

It was a cloudy day, and we were there in some sort of a huge stadium. Not these modern stadiums you see in the movies, but in a pretty old fashioned one where the benches were made of wood. I don't exactly remember what game was being played, but I remember the moment when everything suddenly stopped and there was a great commotion in the skies. A huge object has started approaching us, the stadium. It was there in a sudden flurry, and before you could start wondering what it was--it revealed itself to be a huge spaceship. Pretty huge, I'd say, but I can't give you the exact dimensions. It was alien. How did I know it? I don't know, but somehow all of us were sure that it was an alien ship, though there was nothing in the make to suggest it to be so. And we didn't panic. We didn't try to run away. We just sat there, in wonder, gaping at the huge shape in front of us, that was slightly wobbling as it was trying to maintain it's height in the sky. And then, from nowhere, this other large ship appeared in the stadium, which was, by now I had realized, was far from being circular. It was like a curved runway, but made of earth. If the Earth was expecting to fight the aliens with this ship then it was going to be a poor job. The Earth-ship was equally unobtrusive as the alien one, but it was smaller in shape and more wobbly on the ground than the alien one was in the sky. But it made up to the sky--and then suddenly a flurry of smaller ships appeared on the runway and started taking off. We all waited and watched in wonder what would happen--what the Earth to offer, more? And then I suddenly asked myself, why do we have to fight? Why can't we ask these people, or however shaped they were, what they wanted?  I imagined that there should be a helicopter in white, waving white flags going to the alien ship. But what if the aliens didn't know the meaning of white? What if they blew the helicopter up thinking it was a sign of aggression? 


I was kept wondering. I don't know what happened next, since I think I woke up at that point. If you want to know what happened next, you could try going to sleep after watching the movie, "Race to the witch mountain", and maybe you'll get the same dream I had, or a much more interesting one. Anyway, that's one of the reasons I have trouble in getting up once I fall asleep. So many dreams, so many stories. I yet have to upload my photos and/or tell you about the trip to Lattice and Extreme QCD.

A tryst with VISA

There, there--hello again! Tryst with VISA-s can be very irritating; as I am sure people who apply to the US already know. But even then small countries, trying to cook up austerity drives to reduce their national deficits, can be so nettling at times! Anyway I am not trying to make general statements here about big things; but I am trying to point out a small case which exemplifies some general features on a much puny scale. Okay so here's my story.

I am going to travel to Italy and Germany for some conferences and both organizers have graciously provided me with all possible documents to help me get my VISA. But of course, the problem with the Italian consulate was that the person sitting with the phone (who was unfortunately an Indian) thought it was too much to listen to what I had to say--all he could happily say was---Go the the VFS and get rid of us. Okay, I decided, that is probably the best instead of wasting my time. But then it turned out that the great VFS, whose job is to provide information on what type of VISA to provide drew a complete bank look at my covering letter. "Sorry sir",---they very politely told me,"we have to send your application to the Consulate to decide on the type of VISA"--etc etc. You cannot imagine the feelings I had after I had travelled to that place wasting so much of my time and money and in the unbearable heat. So what do I do? Nothing, but meekly go back again the next day! And what do they do then---accept the form as it is--and now all because the Consulate has told them. What a big fallacy! And why, because some stupid Indian guy at the Consulate had thought it was beneath his status to talk to the ordinary public. Maybe, I should write a proper letter of complaint to the Consul General.
But anyway---sometimes I wonder whats the point--in today's world, it is the first of the many VISA related frustrations that I am  probably going to have! :( !

24+15

This was an interesting week for me..and extremely intense. There have been only several stints in my life when I have been so intensively involved. One thing was to make the SU3 program running; which I guess I already have described before. The other thing was finishing the rewriting of the draft of the paper on the screening masses. I managed to polish the paper quite a bit and also managed to write quite a few somethings on the introduction, and modify nearly all the figures. On the whole I think it looks quite nice! :) But let us see how much of the modifications I still have to do. The 24 + 15 in the title refers to the 24 hours of work it took on the paper followed by the 15 hours of sleep I needed to refresh myself.

Links and more

Yes, links and more...that was that was keeping my time occupied for the last few days. I did the upgrading for SU2 to SU3 and with some occasional help. But it was as rewarding as it was hectic! It really was ecstatic feeling that I had when I got correct results. Now I feel nice: I have experiencing in programming from scratch all scalar theories (Z2, O(N) models) and gauge theories (SU2,SU3) with a host of updating procedures! To me, quite an expeirence and expertise.
But this is only the beginning of the things that I have to finish before the month is over. Yes, let me go back...

Hunting for treasure

This is the first time I am trying to put some topic into my post. This essentially meant to focus something important that happened to me during the time in between the posts and doesn't necessarily mean that the post will be about the topic exclusively.

Well anyway, although the treasure hunt was important for me, since I was playing this time with a lot of friends, we lost by about a minute. It might be of interest that the winning team took about 40 minutes to decide that the sequence 3 14 15 ... has anything at all to do with the fabled $\pi$. But it was fun and it was tiring.

Back, I have a lot of catch up to do despite the fact that I worked pretty hard yesterday. The SU3 prog is coming up from the SU2 one; and am trying to think the correct tuning for the multilevel process. I was told that the optimum no of sublattice averaging in the latter case might go up to thousands but I didn't appreciate it properly until I saw the Koma et al paper that does the same. That does bring up the question where are we going to get so much time? Another thing that was pointed out, was that could we do any calculation in the strong coupling limit of the theory? Well, it is time I tried to understand the Laine et al paper much more seriously.

Have been away to Kolkata last week. On work. Therefore no time for play. Yes. Honestly, I mean it. But on the whole it was pretty enjoyable! Of course, the absence of Internet was pretty frustrating and the experience of getting absolutely drenched in the local storm "kalbaisakhi" was superb. However was anxious all the time because the tickets had not been bought, neither the registration not the hotel booking was done. By the way all this is for the LATTICE conference, to which I will be most probably going this time. South Calcutta seemed pretty much changed:beautification projects all around! The South City mall was big and nice, but not as great as some of the malls you can see in Bombay.
And yes, got to see a lot of wonderful sights from the plane. The sight of Bombay, as the plane was taking off----that of the Worli sea link was particularly wonderful. The roads were tubelights of light! So was Calcutta while getting down. It seemed so "cute"! While coming back, the most remarkable were that of the Western Ghats: you can make out where the ranges start, grow taller, some parts of the plateau sandwiched in between the mountains, and finally the mountains giving way to the narrow valley and finally the sea----mesmerising. You could see deep gorges when the river is in the mountain and ox-bow lakes as it is moving on a flat land: geography should be taught on the air like this!
Working hard on the Diffusion coefficient. Need to see how much the multilevel improves over the standard result.

A very tiring set of three days: you wont even imagine what we have to put up through at times! Want to attend the lattice conference and am breaking my head over getting the funds. Have written so many e-mails and have looked up so many different schedules; that if this thing doesnt come off in one piece, I'll probably blow up!
No physics for so many days. No physics posts till now. Very frustrating, indeed!

Last night was worth its weight in gold. Finally managed to finish a first draft of the paper on screening masses. It looked quite good to me. I was able to tie up quite a number of points. It remains to be seen, how much of it will be okay-ed by my guide.

Never realised till now that writing blogs could be so much fun,...and so much useful.
Am writing the first draft of the screeningmass paper. Has been a long day today; but not yet ended!

Electric Dipole Moment

Definition of Electric Dipole Moment

The Energy of a system of charges is defined as:

ε=∫ρΦ dV
where ρ is the charge density and Φ the potential both functions of coordinates.Choosing a particular origin and expanding the potential in a Taylor series about the origin:

ε=∫ρ{Φ(r₀)+x_i&part_i&Phi(r₀)+½ x_ix_j&part_i&part_j&Phi(r₀)+...}

ε=∫ρΦ(r₀)+d_iE_i+d_ijE_iE_j+...

where d_i is the Electric Dipole Moment and d_ij is the Induced Dipole Moment and E the electric field.

For discrete charges the dipole moment is

d=&Sigma_ir_ie_i

where i denotes the sum over the charges.

EDM for a system
Let P is the Parity operator.If P is conserved then the energy eigenstates are also
parity eigenstates.Under a parity transformation

&lang m|P⁺PdP⁺P|m &rang =-&lang m|d|m &rang
.
So the dipole moment must vanish.A non-vanishing dipole moment signals violation of parity.


Let us consider non-degenerate energy eigenstates characterised by only by its angular momentum operator J.

Under the action of time reversal,

T d T^-1 =d

T J T^-1 =-J

implying the EDM has to vanish.

So, the presense of an electric dipole moment would violate both time reversal and parity.

However, a system possessing non-degenerate eigenstates which are parity eigenstates as well can have a non vanishing dipole moment.This is because the energy shift is quadratic in &Delta² where &Delta is &lang+|zE_z|- &rang and therefore quadratic in E.So it is an induced dipole moment and doesnt imply the violation of time reversal.


When the system is in a degenerate state ( for example the ground state of a water molecule), the energy shift can be linear in E, but then it does not imply violation of time reversal invariance.This is usually called the permanent dipole moment.

Projection Operators

Permutation Operator: The Permutation Operator is defined by its action on a N-particle wavefunction as follows:
p_ijψ(...,i,...,j,...)= ψ(...,j,...,i,...) ( 1)
In general, p_ij²= e^2iφ
The order of the permutation group of order N is N!.Further, if the hilbert space of each single particle state is d,dimension of the total hilbert space formed is d^N.The particles are assumed to be indistinguishable.

Completely Symmetric & Completely Antisymmetric States and Projection Operators:
Notation: |i1,...,iα,...,iN> is a multiparticle state which means that particle no α is in a state denoted by |iα>.If the |i>'s form a complete orthonormal system in the space of N-particle system,the completely symmetric and completely antisymmetric basis states is defined by:
S_±|i1,...,iα,...,iN>=(1/√ N!) Σ_p(±)^pp|i1,...,iα,...,iN> (2)
By definition,it is clear that S_± are 1-dimensional subspaces.This we can also prove by writing down the projection operators onto these states.The trace of the projection perators is equal to the dimensionality of the hilbert space onto which they project as can be seen from the example of a three dimensional vector.From this elementary consideration, the following properties of the projection operators can be formulated:
1.Tr P < D,where D is the dimensionality of the hilbert space.
2.Tr P is always integral.
3.If Tr P =0 then it projects on to the null space.
4.If P_iP_j=&delta_ij and Tr P_i=1, then i can lie between 1 and D.
5.Iff 1 ≤ i ≤ D, then Σ _i P_i=I

Now, let us give some theorems and their proofs.
Theorem 1: The trace of a projection operator is equal to the dimension of the Hilbert space over which it projects.
Proof:Let the basis of an d dimensional Hilbert space be denoted as {|i 〉 }.The projection operator P_r which projects over a r dimensional subspace can then be written as Σ _k=1 ^r |k 〉 〈 k|.Then Tr P= Σ_l=1 ^D 〈 l| P |l 〉 = Σ_l=1 ^D 〈l Σ_k=1 ^r |k 〉 〈 k|l 〉 =Σ_k=1 ^r Σ_l=1 ^D 〈 l|k 〉〈 k|l 〉=Σ_k=1 ^r1 = r, since
〈 k|l 〉=δ_kl.

Theorem 2:The Projection Operator on to the completely symmetric and the completely antisymmetric states are given by
P_±=(1/√ N!)S_± (2)
Proof:From our definition of the S_± operators we know that there can only be a single symmetric or anti-symmetric state.So let us write
P₊=c₊ S₊.We need to find c₊ such that P₊²=P₊
Now, P₊²|i1,...,iα,...,iN&rang =(1/N!)c₊²&Sigma_qpqp|i1,...,iα,...,iN&rang
=(1/N!)c₊²&Sigma_phh|i1,...,iα,...,iN&rang
=c₊²&Sigma_hh|i1,...,iα,...,iN&rang
(since if pq=h, then p=hq^(-1) and has N! distinct elements.)
=c₊²(√ N!)S₊|i1,...,iα,...,iN&rang
=c₊(√ N!)P₊|i1,...,iα,...,iN&rang
which implies c₊=(1/√ N!)
Thus:
P_±=(1/N!) &Sigma _p(±)^pp|i1,...,iα,...,iN&rang

Theorem 3:Tr P_±=1
Proof: We shall prove this theorem only for the case of P₊.The other one involves more complicated algebra, but gives the same result.
Tr P₊=&Sigma{|i 〉 } &lang i1,...,iα,...,iN|(1/N!)&Sigma_pp|i1,...,iα,...,iN&rang
Only p=1 gives non zero contribution and there are N! such identities are generated due to the sum on p and hence we have the result Tr P₊=1

noethers theorem

1. we proved the noether's theorem( for every continuous symmetry with end points fixed characterized by m parameters, there are exactly m conserved quantities characterised by Q_k, where Q_k=(delta L /delta q_dot)*(delta q / delta alpha_k), alpha ks are parameters.) this we did by writing the transformed q_i's as functions of q_j and alpha_k, effecting the variation of the action,setting it to zero for a symmetry and using the lagrange equations.
2.next, we also considered the cases where the end points vary and noted that such a variation of end points causes the lagrangian to remain otherwise unchanged.this variation causes a variation of the coordiantes at the boundary, but along the trajectory.the limits of integration change.for the action to remain unchanged, the change of lagrangian due to this must equal the change of lagrangian due to the coordinate variation.a short calcualtion then yielded the conservation of energy.
3.we also saw that the alpha_k 's form a lie algebra
4.we derived the energy momentum tensor of the field.we noted that the tensor was not unique and so certain tensors(anti-symmetric in the last two indices) can be added to it to symmetrize it.
5.we derived its form for the classical electromagnetic field, checked that the tensor was symmetric and traceless.
6.it was also noted that this tensor cannot always be diagonalised; since under such a transformation the metric (which is not an identity metric, it is a minkowski metric) must also be preserved.