Lev Landau

Paradise Lost. Part One

The initiation into Landau School of Thought started with famous Theoretical Minimum Exam. This was a sequence of increasing tests of that rare mix of knowledge, durability and passion, which was necessary to be accepted and survive the School.

I was lucky to be initiated by Landau himself, just one year before the tragic automobile accident, after which Landau never recovered.

My friend Sasha Polyakov and I came to Landau in spring of 1961, with zero combined life experience and infinite combined self-confidence, after some success in Mathematical Olympics where we shared the First Prize.

Landau had that childish expression at his face — a mixture of surprise, impatience and arrogance — as if he was saying: “Let us see if you are as dumb as I think you are.”

Kapitza Institute in Moscow
He placed us in two different offices in “Kapichnik” (Kapitza Institute for Physical Problems), gave us some math problems and started pacing between these offices, looking over our shoulders with curiosity and making nasty remarks at every line we wrote.

I felt as if my Lord came to Earth and crucified me with His own hands. One of my problems was to integrate rational function—textbooks recommend the method of variation of constants — i.e. to represent

P(x)/Q(x) = R(x) + sum c/(x-a),

with a being roots of Q(x), and obtain coefficients c as residues at x=a and similarly for coefficients of polynomial R(x) as residues at x = ∞.

But I have never read those textbooks — in fact I was very bad at reading textbooks all my life — I preferred to do it myself and then ask my educated friends whether my solution was right.

I had just a few minutes to invent my own method before Dau would have run out of his short patience. I do not remember now how I solved that problem — but I remember very well that I did, because I still hear his voice in my head — “Well, you finally got a solution — invented a wheel — should have known such triviality in a first place”.

Sashka had similar experience in his cell, after which we were pulled together in Dau’s office and he looked into our eyes without smiling. “Well, kids — you passed, but you got to really work on your mathematical skills — theoretician cannot live with the skills like that. You got to know Complex Analysis, PDE, Group Theory, all nice and easy stuff — and everything else they will teach you in the University you just flow around (“obtekaite”).”

Arkady Migdal and Sasha Migdal, the early 60s
I came back home totally humiliated. My father Arkady, former student, friend and rival of Landau, was waiting for me. He was initiated in the thirties without even being tested by TheorMinimum.

“Congratulations—you passed the first Landau Exam” — he hugged me, but I pushed back. “What are you talking about? Landau was cursing us, he said that a theoretician cannot live with the technique like that, he was mocking the way we solved problems…”

“He showed his respect to you idiots by treating 15-year old boys as grown-up theoreticians! Do you really think the grown-up theoretician could live with your mathematical technique? Go and learn Group Theory like he suggested, and always take good advice regardless how insulting it may sound! … And by the way, he called me up right after you two left his office and he was very excited. He said that you were so smart, you reminded him of himself when he was young.”

Landau did more than that to help us. He wrote a letter, recommending us to be accepted in the University, which later actually helped that miracle to happen. There were two miracles, in fact. One, young kids were allowed to attend the Physical Technical Institute entrance exams without graduating from high school. Second, Jews were actually accepted into PhysTech, which was next to impossible.

Sasha Polyakov, Vitya Zharinov, Seriozha Gurvitz, and Sasha Migdal in the mid-60s at Military Training.
The Landau letter was so good, that it was never shown to us, until just a few years ago. We lived in tough country at tough times, when kids were not supposed to be spoiled by being praised. I guess now this letter cannot spoil us anymore.

After Landau’s death Isaak Khalatnikov and few other Apostles created the Landau Institute of Theoretical Physics. It was late sixties, when the Stalin’s Fear was starting to fade, and Iron Curtain was starting to rust a little. KGB still ruled the country, but it was already playing more sophisticated games, not necessarily the deadly ones.

Isaak Khalatnikov is truly a remarkable man, whose immense contribution to Theoretical Physics is underestimated in my view. He was involved in seminal work with Landau and Abrikosov, where they first discovered the famous “zero charge” problem, and laid the ground for a modern quest for consistent filed theory. But his life achievement is creation and leadership of Landau Institute, which played such an important role in History of Physics of the 20th Century.

Landau with his Apostles. First row, right to left: E. Lifshitz, L. Landau, I. Khalatnikov, A. Abrikosov
Khalat was a genius of political intrigue. Being married into Inner Circle of the Soviet System (his wife Valya is the daughter of a legendary Revolution hero), he used all his connections and all the means to achieve his secret goal — assemble the best brains and let them Think Freely.

On the surface, his pitch to the Party went as follows.

“The West is attacking us for anti-Semitism. The best way to counter this slander is to create an Institute, where Jews are accepted, allowed to travel abroad and generally look happy. This can be a very small Institute, by standards of Atomic Project, it will have no secret military research, it will cost you very little, but it will help “Rasryadka” (Détente). These Jews will be so happy, they will tell all their Jewish friends in the West how well they live. And if they won’t –it is after all, us who decide which one goes abroad and which one stays home. They are smart kids, they will figure out which side of the toast is buttered.”

As I put it, Khalat sold half of his soul to Devil and used the money to save another half. I truly respect him for that, now once I learned what it takes to create a startup and try to protect it against hostile world.

As many crazy plans before it, this plan really worked. Best brains were assembled in Landau Institute, they were given a chance to happily solve problems without being forced to eat political shit like the whole country and - yes, they sometimes traveled abroad and made friends in the West.

In a way the plan worked too well — we became so worldly and so free that we could no longer be controlled. And, needless to say, our friends in the West became closer to us that our curators in KGB.

To some extent, KGB played similar games in other areas of Soviet Culture as well. Soviet Union improved its image in the eyes of the West, but at the same time the whole country, starting with KGB, got spoiled and seduced by Western influence. The Cold War was lost by USSR not just because of economical burden of arms race, but also because of loss of fighting spirit as a result of careless flirting with the West.

Political games and Cold War was the least of our worries in the 60s and 70s. I joined Landau Institute in 1969, a year after its inception, after defending the PHD on the scale invariant Reggeon Field Theory. When I look back at that time, it turns out to be the time of great discoveries in Solid State Physics (main specialty of Landau Institute) as well as in the Elementary Particle Physics.

Both streams of discoveries were fed by realization of remarkable analogy between these two fields, allowing for cross-fertilization. This analogy was foreseen by great Julian Schwinger, who noted that inverse temperature β= 1/T in statistical mechanics is equivalent to imaginary time in quantum theory, as it follows from the comparison of partition function

Z = Trace(exp(-β H)) in statistics and
Z = Trace(exp(-í t H)) in quantum theory.

At the time I entered the field in the sixties, the analogy was barely noted, but its full implications were not known. I learned about this analogy from remarkable Physicist Tolya Larkin, who pioneered it in USSR with Valya Vaks. The whole discipline of Euclidean Field Theory, which makes no distinction between quantum and statistical applications and uses notions from both — was yet to be born.

I guess the missing link was a realization that this “statistical” imaginary time is the same as Minkovski imaginary time of special relativity. This is the same observation that drove Steven Hawking to interpret the imaginary time of the black hole as inverse temperature. Good ideas are so scarce they come back again and again in different disguise.

Moreover, the Field Theory was pronounced dead by Heisenberg and Landau. As Landau put it “The Lagrangean Field Theory is dead and should be buried, with all the proper honors of course”. The Landau’s motivation was the “zero charge”, which, indeed, indicated inconsistency of all known field theories except one, which was in its infancy and could not yet stand and defend itself. That one was, of course, the Yang-Mills Theory, born in the fifties, and never taken seriously until the seventies, when it was finally quantized and shown to be free of “zero charge” problem. Now it is The Theory of all elementary forces except Gravity.

Werner Heisenberg
Heisenberg’s motivation was even more ambitious. This is an example how one great leader can block the way to the whole army by falling down at a narrow pass. He dared to go one step further from his celebrated uncertainty principle and declare that Physics must only study observable quantities. His own approach was to study so called S-Matrix — collection of transition amplitudes between various observable incoming states, such as anti-proton flying towards the hydrogen atom and the observable out-coming states, such as beams of electrons, positrons, photons and mesons.

Pretty much like medieval Scholastic Magisters were extremely inventive in defending the Church Dogmas and blocking the way to experimental science, some great minds in the sixties developed the S-Matrix dogma with great perfection and skill before it was buried down in the seventies after discovery of quarks and asymptotic freedom.

It turned out — quite unfortunately for Physics — that one could deduce a lot about S-Matrix on purely phenomenological grounds without ever asking heretical questions “what is inside”. One could not, of course, even attempt to compute proton mass or its magnetic moment or explain anything about properties of so-called resonances — short living subatomic particles. Scattering amplitudes were the only numbers to be considered and computed.

In a way, this reactionary idea was a truly revolutionary one. For the first time since Galileo the quest for the structure of matter was stopped on philosophical grounds. There is nothing inside — total nuclear democracy! Everything consists of everything else — do not ask whether there was the rabbit inside the hat — you are only allowed to compute how far it will jump and in what direction.

Left to right: Arkady Migdal, Sidney Drell, Vladimir Gribov, Sasha Migdal, Leonid Strickman, Leonid Frankfurt, Lev Okun,unknown. The late 70s. We are playing push-game (forcing opponent to lose balance).
It is a bitter irony of History, that such a restriction on a free thought was imposed by a German Scientist and so widely accepted in Russia in the second half of 20th century. My Physics teachers Gribov and Okun were respected as liberals and free thinkers, followers of great Landau, but still they would not even talk to me about Yang-Mills Theory because it was “unobservable”.

For the whole two years 1964 to 1966 JETP refused to publish our work with Sasha Polyakov “Spontaneous Symmetry Breaking of Strong Interaction and Absence of Massless Particles” where we (correctly!) argued that vector mesons of the Yang-Mills Theory must acquire mass by absorbing zero mass Goldstone particles. We were stomped to the ground at every seminar we tried to present this work at. The most disturbing thing was that nobody would even argue with us on the subject — the mere mention of “Spontaneous Symmetry Breaking” caused healthy laughter, which ended the conversation. Independently this effect was discovered and published by Higgs and rightfully is called Higgs Phenomenon.

This was the first and very useful lesson of the danger of independent thinking. There were much more, every one of them proving the same point: “ne visovivaisya” — do not stick out.

I eventually realized that I was born dissident and maverick, never to be part of any crowd or achieve any social success. I cannot be satisfied when I reach some harmony with the world — I have to abandon everything and go further.

I am defending my Doctor Degree in Landau Institute, 1973, talking Euclidean Field Theory to the bald head of Khalatnikov.
As for the Lagrangean Field Theory, so respectfully buried by Heisenberg and Landau, my good friend Sasha Zamolodchikov (another Sasha from Landau Institute) summarized it like that: “They buried the Lagrangean Field Theory, but forgot to drive the stake through the heart”.

Another example — the early 70s when we were developing Conformal Field Theory. We were very excited by grandiose perspectives we saw in that theory (it eventually became one of the basic ingredients of the modern Mathematical Physics), so we kept trying to discuss it with our colleagues.