Leo P. Kadanoff is John D. MacArthur Distinguished Service Professor
Emeritus, Departments of Physics and Mathematics, University of
Interview recorded in Chicago by PoS collaborators Babak Ashrafi, Karl Hall,
and Sam Schweber.
Topical links within the interview:
I. Biography and training as a physicist
I propose to spend five minutes telling you about my boyhood education,
and we can go on from there. I was born on January 14, 1937, in
New York city. My mother was a schoolteacher, my father an attorney.
They were educated at Day and Night school, at New York University
and Columbia. I went to standard grade schools in New York City,
I grew up on a street which was notable for having many scientists
within shouting distance. Roy Glauber, who eventually became my
thesis adviser, grew up in the same apartment house that I did,
at 110 Seaman Avenue, 204th street, as far west as you can get in
Manhattan Island. Sheldon Glashow (Nobel Laureate,
Harvard) was a half a block down the street. Gordon Baym (my co-author), about
an equal distance.
And you knew all these people as you grew up?
I knew none of the people as a young man. I met them at Harvard
somewhat later. I knew Glauber's family, and Glauber's family was
one of the reasons I went to Harvard. After grade school education
I went to DeWitt High School, an all-boys school about 5 miles away
from home, I think because my mother did not want me to be too close
to girls. There I was a reasonably successful high school student,
went on at age 16 1/2 to Harvard University. By this time my family
was reasonably prosperous, so I went on family money rather than
on Harvard's money.
In high school were you already clearly directed towards physics
I enjoyed physics and math, I took all the courses in many of the
subjects that were available to me. I was a member of what was called,
more or less, the biological setup crew, which set up the biological
experiments. I took a couple of good advanced math courses from
two teachers, both of whom had the last name Grossman, and were
indecorously described as Fatty and Skinny, and I don't remember
their first names. I got medium good grades, I was an excellent
student, I was interested in science. I spent the summer working
in the American Museum of Natural History in New York, writing numbers
on human bones. It was my last non-remunerated summer -- must have
been when I was 15 1/2. I was interested in mathematics, and read
in it and enjoyed it, but didn't get much of a chance to do advanced
What made you pick Harvard?
I suspect it was my parents who picked Harvard. I think everyone
thought it would be good, being an only child, somewhat spoiled,
to be away from home, and it was pretty close, but not close enough
so I could come home every weekend. New Haven would not have been
quite far enough. First year at Harvard, I took math and physics
courses. My parents wanted me to be a doctor. I enjoyed the physics
course. I was not especially good at it, I don't think, but I enjoyed
it enthusiastically and, following what was then the tradition,
went as quickly as I could on to graduate courses
in my second year at Harvard. I found the graduate courses
an awful lot easier than the undergraduate courses.
And this is the fall of 1955?
I graduated from high school class of '53, so this would have been
the fall of 1954 that I started to take an electrodynamics course
from one of my future thesis advisers, Roy Glauber. The further
I got in physics, the easier it got, as far as I could tell. I took
the standard undergraduate courses, physics, mathematics, had a
reasonably broad education at Harvard. Met my future first wife,
decided that moving someplace else was too complicated, and went
on to graduate school at Harvard. I was class of '57 as an undergraduate,
so this brings me to graduate school starting in 1957. One of the
major advantages I had partially because of the family connection,
and partially for reasons that are not totally clear to me, I was
part of the "in" group at Harvard by the time I was beginning graduate
school. I lunched with Schwinger and his post-docs, and some of
the other faculty people, and sat, I suppose, at the very end of
the table, as the most junior person. But listened to what was going
on, and was totally a member of the "in" group.
When did you first meet Paul Martin?
I must have met him in the course of my graduate studies. I do not
remember the occasion. He was a young faculty member. You would
probably be able to fill in the information better if you noted
when he came to Harvard, since I was his third graduate student.
Probably I did not meet him at the beginning of my stays at Harvard
because he was not there.
No, all I was trying to ask is, how did you become the "in" group
with Schwinger, as an undergraduate?
You had taken his courses already as an undergraduate?
I had taken his course already as an undergraduate. I hardly ever
had a conversation with him until the very last year of my graduate
But you go to lunch with him.
I would go to lunch with him, yes.
The "in" group means that you had conversations with his graduate
students and postdocs, and not with him?
I certainly listened to the conversations as they occurred. Exactly
how I added to them is not within my recollection. I was a brash,
brash, brash young man, and would probably have said more than a
wise person would have said.
And the "in" group at that stage, Ken Johnson was still there?
Kenny was still there. Paul Martin, Kurt Gottfried. I had heard
discussions of his exile to Europe because he had the wrong kind
of visa, and his return to Harvard. The group met at an Alsatian
restaurant you probably know: Chez Dreyfus. They had a 99 cent special
for lunch, and Schwinger had the $2 steak. You can see that my recollections
are spotty at best.
Who were you talking to a lot?
I spent a lot of time with my fellow students as a graduate student.
I remember a close family friend, Popat Patel, who became a nuclear
physicist and went to McGill. There were other people, unconnected
with physics, who were my acquaintances and friends in graduate
school. Although my recollection is not tremendously good, I was
probably self-sufficient. At some stage I got a problem from Roy
Glauber and went off to work on that, and probably spent a lot of
time with a pad of paper and a pencil.
And it was always clear you were going to be a theorist?
I never could figure out which way to turn a dial to achieve a given
effect. I tell the story which maybe be apocryphal, that my partner,
Jack Sanderson, in the lab course, told me to keep both my hands
on the lab book. (laughter) But although the story might
not be correct in detail, it's right in spirit.
In your first year of graduate school, there's a choice to be taken,
It was never outlined to me that way. Because of the family connection,
I started out with Roy. And Roy was interested in problems in the
fundamentals of what you might describe as low-energy electrodynamics
at the time. That part of my thesis was about an electron in a cavity
and it's interaction with radiation. This was just before the invention
of a coherent wave picture, and we didn't have the full mechanism
that one uses to work on laser problems. But through the earlier
work of [Sinitskii] and Schwinger, and then through the work of
Glauber, we were talking about the non-linear effects in the interaction
of light with electrons in a cavity, and that was the content of
the thesis, although it was somewhat hard slogging. The best stuff
came after, because of inventions and discoveries that come in after
So when you come in to first-year graduate school, which would be
the fall of 1957, Martin has come back, Martin and Schwinger is
being written, or?
Yes, and so you have to visualize we're taking this succession of
core graduate courses from Martin and Schwinger and Glauber and
other people, and I am listening to Schwinger's vision of how quantum
mechanics should be thought about, I'm hearing from Glauber about
his high-energy approximation, the eikonal approximation, and learning
about the local work. However, I'm also noticing that there are
a tremendous number of people who are chasing after a very limited
amount of Julian's time. Whereas Glauber and Martin are more easily
available to me, and it seems natural for me to be involved with
How about your education in statistical physics or thermodynamics?
I have mixed memories. I would have imagined that I'd taken a graduate
course from either Glauber or Martin or both, but I don't remember
that. I remember doing an oral examination on statistical things
as the analogue of a candidacy exam, and I believe that in preparing
that, I read many of the standard books on statistical mechanics,
Tolman, and several of the other standard books. [Note added:] I did take a statistical mechanics graduate course from Glauber. It was excellent.
Do you remember whether you picked up the second edition of Landau
and Lifschitz, which came out in English in 1958?
I'm embarassed to say that I have probably never read through any
one of Landau and Lifschitz's volumes. I've used them, but I have
never read any of them from cover to cover.
But they're reference works, they're not--.
--they're reference works, yes, and the quality of the index is
such that it has cost me much pain (laughter).
And your cohorts in terms of graduate students and talking to one
I remember it was a lively business. On the other hand, the majority
of the graduate students were housed in a room called B12, if my
memory serves me correctly, at that time. I was not part of that,
probably because of my personality, I did not have, as I recall,
enemies among the graduate students, I was not part of it. I did
have good occasional interactions with, for example, Popat Patel,
whom I've already mentioned. I was probably to some reasonable extent
a loner, and to some other reasonable extent absorbing the culture,
not so much through the fellow graduate students, but through my
So your introduction to things like BCS, superconductivity, all
of these things?
BCS I can tell you about very specifically. Martin was interested
in BCS, and perhaps a year and a half before I got my PhD (in September
of 1960),he described to me what BCS had done, probably roughly
in these terms: if you have this 4-fermion interaction, you factorize
that interaction and then you use the factorization to solve the
problem, replacing one of the products by an average; probably in
those terms. I worked for six weeks and got nowhere. I got an answer,
but it was the Hartree approximation rather than BCS. I came back,
he told me I'd done it the wrong way, probably pushed me towards
doing the factorization in another fashion, and then after that
I understood BCS more or less, although of course there's an awful
lot in BCS. I do not remember as well the actual reading of the
paper. You are learning something about how I do physics. I'm not
proud of it, but I do struggle through for myself, and find it hard
to get it from the literature. It is a very standard thing in my
life for people to tell me you do it thus and so, I will pick up
on what I've been told, and then understand it. It's much less common
for me to get it from the literature.
So the problem that Martin gave you was when?
This would have been a year and a half before the degree.
And that becomes "Martin-Schwinger 2," it's really Kadanoff and
Martin becomes a theoretical many-body problem.
I haven't acquainted myself with the literature on that subject
for a while, but my recollection (which is, after all, probably
of interest here) is that there were Martin-Schwinger 1, 2, and
3. Martin-Schwinger 1 being the great Green's function paper that
Martin and Schwinger did together. Then there was a 2 which is in
fact Kadanoff and Martin, which is a Green's function theory of
superconductivity based upon the BCS ideas plus the ideas of Martin-Schwinger
1. The Russians claimed, I think absolutely correctly, that they
had done the same things or similar things either earlier or in
parallel. I'm certainly not claiming any priority over Russians
on this paper. And then there was so-called Martin-Schwinger 3,
which is Kadanoff and Baym, produced in the postdoctoral period
in Copenhagen largely.
Just for getting clear in terms of background, you certainly know
of everything that goes on in terms of Green's functions, and Martin
and Schwinger and so forth. How much of the Russian literature are
you aware of?
Probably I was entirely innocent of it. I want to also emphasize
that Kurt Gottfried was important to me in this and a little bit
later period, in that he was interested in knowing what I did not
understand, and capable of making me understand it. So he was an
important teacher, although not in any literal sense or formal sense
connected with teaching.
Do you know Ken Wilson from those days?
I met him once or twice. I remember sharing a car journey with him.
My reaction was that he was absolutely brilliant. I thought he was
just marvellously intelligent person, from the brief conversations
we had. Or the brief listening that I had in that period.
I doubt that I would have. I would have heard of it, but I doubt
that I would have known anything about it until somewhat later.
I do not remember whether I studied Kerson Huang's book for this
period when I was learning statistical mechanics. Huang's book may
have been later. I do remember that I learned something about the
Onsager solution from there. I also, I think, learned it from a
paper by Montroll and others. And then I did go back to the
original literature in this case and read the Onsager-Kaufmann work.
This electron in a cavity, is that your work on the Knight shift?
No. My thesis was published in two volumes, one which never saw
the light of other publication. One of them was for the electron
in a cavity, and the other was the Martin-Schwinger 2 paper, in
essence, or part of the Martin-Schwinger 2 paper. The Knight shift
paper was probably produced in a post-doctoral period at Harvard.
There's a brief post-doctoral period after I got my PhD, but before
I went to Copenhagen. This would have been in 1959. That was part
of my graduate work. It was part of work which I will uncharitably
characterize as reworking a whole variety of problems -- some of
them classical problems in solid-state physics, some of them new
problems using Green's function techniques. Just taking the new
tool and applying it to everything at hand, whether you learn something
new from it or not. The Knight shift paper, again, continuing to
be uncharitable, is probably the only paper ever written on the
Knight shift that has no component of truth in it.
Were you familiar with Benedek?
George Benedek, MIT? I became familiar with his work later on. I
do not remember him in this context.
Not on his work on the Knight shift?
No, I do not remember whose experiments we were trying to explain.
And sensitivity to experiments in general? That's part of the training?
I don't know. I believe, as you are nicely implying, that I have
characterized my work by such sensitivity. It may very well have
been a part of the lunchtable conversation, it may have been something
that I picked up from lunchtable conversation. Certainly the people
at lunch were likely to be talking about what came out of the experiments.
But I don't know where it came from.
You go to Copenhagen in the fall of 1961.
No, this would be fall of 1960. I spent a year and a half in Copenhagen,
from fall of 1960 through the winter of 1961-62. In the last eight
weeks or so at Harvard, I met a person who became very important
in my life, Gordon Baym. We discovered we had lots of similar interests.
Gordon, as you know, is a student of Julian Schwinger. But we were
working on the same kinds of things. I found him to be very intelligent
and continued to work with him at Copenhagen.
In Copenhagen, there was lots of work going on, but none (almost)
in directions that were close to my solid-state, statistical mechanics
interest. There was a lot of nuclear physics, with Bohr and Mottelson
being the leading people in that. There was Cutkowsky, who was
working on dispersion relations, and there were miscellaneous
postdocs from all over the world working on miscellaneous problems.
Among them were Sid Kahane from McGill working on positron annihilation.
Vinay Ambegaokar (I do not remember where he got his PhD) -- he
and I became collaborators after a bit. Dean McCumber, if I'm
not mistaken, but we were never close, so I don't recall very
well. But there was a group of Americans, and there were a group
of people interested in condensed matter problems. Enough of a
group so that Baym and I could lecture on the Green's function
things that we had done. And we started to work on such lectures,
which eventually became our book.
At that time, I had started working on what turned into Martin-Schwinger
3, and a portion of the book, namely, how one uses conservation
laws to derive correlation functions which agreed with the known
conservation laws. This was triggered by the fact that Gordon
Baym and I were calculating precisely the same correlation function,
we got two different answers, with different factors of K and
omega in them. He was satisfied with his calculation. He got the right factors for calculating,
if I remember correctly, the ultrasonic attenuation. I was calculating, if I remember correctly, the conductivity, so we
both got the answers we wanted, but since these were the same
functions we thought we were calculating, we felt rather embarassed
when we discovered this. And we then asked, how could we have
gotten two different answers to the same problem, and that became
a portion of our joint work.
I had done some of the formal stuff. No, that's not the right
way to describe it. I had invented, by dint of a tremendous hard
work, and just plain seat-of-the-pants stuff, a whole bunch of
conserving approximations. Grinding them out slowly. To tell the
story of how this happened, I have to go back a little bit. It
didn't have only the root in the work with Gordon on the correlation
function, it had to do with a difficulty in my thesis. As you
all know, the BCS theory is not gauge-invariant. That has as its
consequence that if you calculate a correlation function, it does
not obey what is called the Ward identity. In my thesis, I calculated
that correlation function, and the Ward identity was that the
left hand side of the equation should equal the right hand side
of the equation. And indeed I calculated left and right, got answers
of the same form, and stopped. Unfortunately, it was the same
form, but there was a minor flaw. The signs were different! And so there
was an inconsistency in my thesis. When this was submitted for
publication, John Bardeen, who was the referee, couldn't find
the error, but did the wise and kind thing and sat on the paper
for eight months.
He noted that there was a discrepancy?
No, just sat on it (laughter). At some point, lightning struck,
and I realized what the difficulty was. The solution to the problem
was given by Phil Anderson in a paper which, at the time, struck
me as unusually incomprehensible, in which he derives the structure
of the excitations in superconductors. I believe this is the famous
paper in which his version of the invention of the Higgs boson occurs.
In any case, I had great troubles with that paper. I read it and
struggled through the correlation function stuff. Using a formalism
which had been derived by Yoshiro Nambu, whom I did not know, but
apparently, I understood that portion of the literature well enough
to dig it out, and ground through the construction of the appropriate
correlation functions, using that Green's function formulation.
I want to emphasize, since we're talking about my vision of myself
to some extent, that I visualize myself, now looking back, and probably
then, too, as someone of boundless enthusiasm for doing problems
that were hard, and involved lots of dull algebraic manipulation.
And this was that sort of problem. Hard, lots of algebraic manipulation,
even when made more elegant by Nambu's technique. So little by little
I was grinding through this and constructing a conserving approximation
Now we're talking Copenhagen?
Since you caught me last time, you're not going to catch me this
time (laughter). I don't know, but probably. And so there
are two things that Gordon and I now have to understand. One day
Gordon wanders into my office, as I tell the story to myself, and
said "Well, you were telling me yesterday about conserving approximations.
Here's how you construct them generally. You take this free-energy
and do variational this and that and the next thing." Well, I had
heard about variational this and that and the next thing from Julian
just like everyone else had, but just like everyone else, I felt
it was, well, "Schwingerish", but not useful for anything. Here
was Gordon deriving with complete insouciance and in practically
no time, stuff that took me absolutely forever to do. And I sort
of said "oh, that's nice. Can you do any more of those?" He did,
maybe, one more, whereupon this became one of the major threads
of our book on Green's functions. And we incorporated it in our
You had a joint paper on it?
Yes. It was just such a wonderful moment. I I had the problem and
Gordon had the elegant method of solution and we just put them together,
and it was really very nice.
So should we think of your work at Copenhagen as a continuation
of your work at Harvard, or were there new inputs into what you
were doing because of being at Copenhagen?
Martin and Schwinger had developed this wonderful technique. They
went on to use it for other things. We were probably the only people
in the world who were interested in using this technique to understand
transport phenomena, non-equilibrium stuff at long wavelength. What
we had to do was to find ourselves a bubble, and hide in that bubble.
Sort of semi-isolated, but stimulated by people who cared about
physics. And we found that in the post-doctoral period. That's not
entirely true. For example, Ambegaokar and I wrote a paper on just
exactly the subject in that period, but mostly the two of us lived
our lives in this problem. Again, Gordon did other things then,
but as I see it, we lived our lives in this problem in the environment
of good physics, international people, people from all over the
world, and leisure to think that was provided by Copenhagen.
Would it be fair to say that at this point you conceive of a description
of the microscopic world in terms of Green's functions, rather than,
say, the field theory behind it? I'm interested in the mode of description,
the language employed in trying to understand a work.
What you say probably would be true, were this the high point of
my career. These were the best toys of my youth, but this was not
my mature scientific career. I have a world in which I live, but
it is a world of critical phenomena. It's a world of self-consistent
behavior, and not a world, I don't think, of Green's functions.
I may be mistaken, but I think Green's functions are a toy that
I've put away or a tool that I have in my closet to take out from
time to time, but they're not a crucial part of my world view. On
the other hand, just to follow you where you're taking me, I would
say that my view of the world is conditioned on correlations. And
if you push me a little further, that's correlation functions, and
if you push me a little further, that's Green's functions. But worrying
about how the frequency comes in, and doing frequency sums, I haven't
done that in recent years. That was then, this is now.
No, I meant more in terms of what constitutes your toolkit in addressing
the problems as you face the world. That's all, really.
Well, amusingly enough, the major portion of my toolkit was brought
to me by Gordon. It's the free energy, the thing I didn't think
I had absorbed from Schwinger. It's the idea that you have a generating
function. Now that was part of my thesis with Glauber, too, generating
functions were there, and for all I know it may have been part of
my work with Martin. I think the free energy, the generating function,
has provided a very major portion of my toolkit.
What's in the back of my mind in asking is how do you formulate
it, and how do you get to the problem of Kadanoff and Martin hydrodynamics
Green's function and that connection -- going from the macroscopic
to the microscopic rather than the other way around?
There were two discrepancies, and we see now that they come out
two different ways. The two discrepancies that I mentioned to you
were the gauge invariance in BCS, and the behavior of the correlation
function in transport phenomena, as Baym and I saw it. Now, this
requires two things. I said I only had a few conversations with
Schwinger. Schwinger was the great mind of Harvard at that day.
The Nobelist, an amazingly intelligent man who was a little inaccessible.
Despite the fact that I ate lunch with him every day for years and
years and years, three times a week, for years -- a little inaccessible.
But we brought these discrepancies to Julian; I remember just sitting
in a classroom with him and Martin explaining the discrepancies.
And he produced words roughly to the effect that what you need is
a physical understanding of what's going on, plus a method of calculating
that includes that physical understanding. I'm not remembering very
well, but despite the fact that I don't remember, it was an important
event in my life.
Continue reading part II of the interview.
Now part of it was then the development of the formalism via
the Green's functions. Part was something that Martin and I picked
up on after the Copenhagen period, I think, in which we looked
at physical behavior, and asked what was the implication for
the behavior of correlation functions. And we did some,
in my view, excellent work on this subject, important paper in
my opinion, not made less important by the fact that Landau and
Placzek had done work with similar content. And published in some,
I believe, rather obscure place. I do not know whether I ever
saw the Landau-Placzek paper, but it is said to have similar content,
and that is easy to believe. In any case, Martin and I put together
this paper, I think in the period just after Copenhagen, but I'm
not remembering very well. And it, then, was the other great achievement
of this series of things which begins at Harvard and ends in Green's
functions and correlation functions. And then there is a major
breaking point in my scientific life as I see it. (break)