DIARY 1997
 by Changhai Lu 
本日记只代表写作之时的观点， 此处重贴纯系纪念， 读者请勿引用或视之为参考资料。 
Jan 1, 1997, Wednesday
These days I have been reading some background materials about monopoles, but
Kimyeong asked me to do a twodimensional field theory in which he wants to
find the SUSY partners of a Qball and its excitations. Contrary to his
expectation, I have shown him that the uniform background charge present
in the theory will destroy SUSY. My calculation also shown that the spectra of
the bosonic and fermionic excitations are not match.
Jan 23, 1997, Thursday
One of the reasons Kimyeong believes there exists SUSY partners of Qballs
is that (in some sense) he treated Qballs as states of quantized
field. His argument is based on the Schrödinger representation of the quantum
field theory.
This argument is not new to me since I have considered the same thing but in the
canonical formalism. The question is: can we really treat a Qball state φ_{b}>
as a state of quantum field? I believe the answer is "no".
(... ... mathematical details omitted ... ...)
Jan 30, 1997, Thurday
Things have changed a lot recently, Kimyeong finally gave up his belief on
the existence of the fermionic zero mode in our original model. He asked me to
generalize our model by adding another neutral scalar field (since our original
model doesn't have large Qballs). When calculations on the new model still
produced asymmetric bosonic and fermionic spectra, he seems no longer strongly
insisted.
We also tried to add a term 1/6Φ^{6} to the superpotential of
the model. In that case something unexpected was found and it finally led us to
a systematic way to compute models with an arbitrary superpotential W(Φ^{2}).
(... ... mathematical details omitted ... ...)
Jan 31, 1997, Friday
Although I'm quite experienced in playing with superfields now, I'm not quite
optimistic on the physical significance of the whole problem. It seems to me that the
expectations we had on this problem was wrong from the very beginning. But I have
to leave it for Kimyeong to make a judgement.
Feb 3, 1997, Monday
Kimyeong finally asked me to go back to the monopole space, I think that
is an alternative way to say goodbye to the Qballs.
Feb 25, 1997, Tuesday
I have been reading several papers on Nahm's equations these days. Those papers are
all very mathematical, but they really provided a nice way to compute multimonopole
solutions and moduli space metrics. Kimyeong asked me to find out the exact moduli space metric
for two identical massive and one distinct massless monopoles in the case
when a gauge group Sp(4) breaks into SU(2)×U(1). Our strategy is to embed the Sp(4)
group into an SU(4) group for which the Nahm's equations are directly applicable.
Mar 9, 1997, Sunday
I have read a short paper of H. J. Schnitzer "The Quantum Field Theory of Physics and
Mathematics". In this paper the main difference between the two types of QFTs is stated as:
QFTs in the mathematical sense is welldefined at any scale while QFTs in physics is only
welldefined up to a certain scale. So far as I know, rigorous QFTs in the mathematical
sense only exist in 1+1 dimensions. On the other hand, I remember that exact
conformal symmetries also exist only in 1+1 dimensions. It seems these two concepts are related to each
other since in some sense the exact conformal symmtry ensures if a theory is welldefined
at some scale, it will be welldefined at any other scale.
It is guessed for a long time that pure YangMills theories might be the candidates of mathematical
QFTs in 3+1 dimensions. Similar to the case of 1+1 dimensional QFTs, this might be related to
the conformal invariance of
such theories. Here the complexity is, the conformal invariance for (3+1)dimensional
YangMills theories is  unlike its 1+1 dimensional analogue 
broken at a quantum level, this probably is why it is so hard to prove
such a conjecture.
Apr 3, 1997, Thurday
Kimyeong thought we have basically obtained everything we want to know about
this Sp(4) monopole system. I will begin to write a draft paper on that.
Apr 9, 1997, Wednesday
I have finished a draft paper on the Sp(4) results and gave it to Kimyeong.
Apr 22, 1997, Tuesday
I'm reading something on differential geometry and twistor thoery.
From the pointview of fiber bundle theory, general relativity and YangMills theories are
fairely similar to each other. Geometrically speaking, the reason that makes their quantizations
so different is the following: in the case of a usual YM theory, the fiber manifolds
are not correlated to the base manifold (which is a fourdimensional pseudoRiemannian
manifold) while in the case of GR, the fiber manifolds are the tangent space of the base manifold,
therefore is closely related to the base manifold. It is this subtle correlation that makes the
quantization of GR so much more difficult.
Jun 2, 1997, Monday
Today is the first day of the TASI97 summer school (hosted by University of Calorado at Boulder).
The first four series of lectures are:
 J. Hewett (The Standard Model)
 P. West (Introduction to Supersymmetry)
 S. Dawson (MSSM)
 J. Gates (Superspace)
P. West and J. Gates are pretty good, but the other two (ladies) are not as good.
Jun 4, 1997, Wednesday
I have learned something about MSSM (Minimal Supersymmetric Standard Model)
through the lectures, I have to say that
I don't like this theory at all, even though it has a fairly good experimental
fit comparable to that of the standard model. What makes it ugly is its introducing
of a huge number of free parameters, what makes me even more unhappy
is the fact that all the SUSY breaking terms in MSSM are the socalled soft
SUSY breaking terms. Those terms are something that break SUSY
explicitly ("soft"
only refers to the fact that they still preserve the cancellations of the quadratic divergence).
This kind of symmetry breaking is way too arbitrary that it is not quite different from
directly throwing SUSY away (breaking a symmetry arbitrarily is not very different from
not introducing it at all). Another aspect that makes MSSM questionable 
in my opinion 
is it predicts the mass of the lightest Higgs to be less than 120 Gev, which is almost
ruled out by experiments (the standard model, on the other hand, wants it to be
heavier than 135 Gev).
The reason that MSSM has a Higgs mass prediction radically different from the
standard model (as an extension to the standard model, one might
expect MSSM be able to reproduce standard model results under certain limit) is
 in my understanding  due of the fact that the couplings (at least some of them) between SUSY
particles and ordinary particles are related to the couplings of the standard model
in a definite way, therefore can't go to the strict weakcoupling limit. On the
other hand, in order to solve the hierarchy problem it is required that the
masses of the SUSY particles be in the region of 1 Tev, therefore no
infinite mass limit can be taken as well.
Jun 5, 1997, Thursday
In today's MSSM lecture I realizeded that the number of the free parameters in
MSSM can be highly reduced by assuming superparticle masses and
coupling constants present in the soft SUSY breaking terms equal at the GUT scale.
This reduced model (called CMSSM  constrained MSSM or supergravity inspired
MSSM) contains only a few extra parameters beyond the standard model and yet
preserves an excellent experimental fit. This slightly improved my feeling
about MSSM.
Jun 9, 1997, Monday
A new week started, the speakers in this week are:
 D. Kaplan (Effective Field Theory)
 L. Randall (Super Cosmology)
 R. Kallosh (Gravity and Supergravity)
Kallosh's lecture is good.
Jun 12, 1997, Thursday
In a quantum theory, should central charges be quantized? In the simplest case of
the N=2 SU(2) SuperYangMills theory we know that central charges represent electric
and magnetic charges, both are quantized. I asked Prof R. Kallosh, but she doesn't
know the answer.
Jun 16, 1997, Monday
This week we have
 D. Pierce (Radiative Corrections in SUSY)
 S. Lammel (Tevatron Searches)
 L. Hall (SUSY Flavor Problem)
 R. Mohapatra (Super GUTs)
 S. Thomas (Dynamic SUSY Breaking)
Thomas' lecture will start tomorrow. Among the four lectures
we had today, Hall's and Mohapatra's are good (especially Mahapatra's).
Jun 17, 1997, Tuesday
Thomas' lecture is also not bad.
Jun 23, 1997, Monday
This is the last week of TASI, we have
 P. Nilles (Superstring Phenomenology)
 D. Nemeschansky (Duality in Supersymmetric YangMills Theory)
and two other series of lectures on experimental topics.
In Nemeschansky's lecture, I asked him about the relation between t'HooftPolyakov
quantization condition and Dirac quantization condition. To my surprise, he was
totally lost on this problem.
Sep 3, 1997, Wednesday
Kimyeong and I found that our previous idea of embedding G_{2}
into Sp(6) is wrong. The reason is fwofold:
(... ... mathematical details omitted ... ...)
It seems the simplest group meets our need is SO(7) which has the same
Dynkin diagram as Sp(6) except that γ is the short root rather than the long root.
Sep 5, 1997, Friday
I've made some progress on the G_{2} case. It is a lot more difficult
to determine the parameters directly from the boundary conditions for G_{2}
than for Sp(4). (... details omitted ...) But it turned out that without getting through those
complications we are already able to determine all the parameters except one.
Sep 9, 1997, Tuesday
So far all the efforts to fix the final parameter failed. We believe the metric of the
fourdimensional hyperKähler quotient space M_{4}(ζ = 0) is
(at least asymptotically) a TaubNUT metric with a positive mass parameter.
Sep 19, 1997, Friday
Today in Brian Greene's quantum field theory lecture, a little question occured to my
mind: usually when people demonstrate how the path integral formalism approaches a classical result
they say when the Planck constant
h approaches zero, contributions from all paths except the classical
one  the one that stablizes the action 
are cancelled. Now what if there are more than one paths that stablize the action? It seems we
will always have interference between those paths therefore no classical limit can be reached. Brian
said usually we assume the uniqueness of such a path. In case when there are more than one,
superselection rules will be applied to pick up a unique path.
A typical example is a particle moving on a sphere, a unique path is selected by specifying the energy,
the direction of the initial motion, etc. These conditions will correspond to a set of superselection rules
in the path integral formalism.
Oct 8, 1997, Wednesday
As we know, spontaneous symmetry breaking (SSB) happens only in quantum field
theory with an infinite volumn. This has a direct consequence on cosmology: if the universe is
closed, there won't be any strict electroweak and GUT
transitions! In other words, so long as we believe in SSB, the universe can't be too small
(at the time SSB happened)!
Oct 17, 1997, Friday
As we are still not able to make definite progress on both the MSB (Maximal Symmetry Breaking)
Sp(4) problem and the G_{2} problem, Kimyeong asked me to do something on calorons
(calorons are periodic instantons or  equivalently  instantons on S^{1} × R^{3},
the name "caloron" came from the word "calorie" since they appear in finite temperature gauge
theories).
Oct 28, 1997, Tuesday
These days we have been discussing a problem in our paper pointed out by a referee. The problem is: when we
constructed the hyperKähler quotient space M_{4}(ζ), we have used a U(1) action that turned out to be
nonfree (it has the spherically symmetric configuration as its fixed point). After discussion, we now realized
a few subtleties about the boundary condition and the U(1) action. (... details omitted ...) The main
results of our paper, however, is unaffected by these subtleties.
Dec 3, 1997, Wednesday
The building blocks of the standard model are combined together in a way that no piece can be
missing. For instance the crosssection of νν
→ W^{+}W^{} scattering will grow with s
therefore violate unitarity in
absence of the ZWW coupling term. This is usually stated as: unitarity requires ZWW coupling. There
are many similar unitaritybased arguments in the standard model.
But it seems to me unitarity is a very general feature of quantum theories as long as the
Hamiltonian of the theory is Hermitian (therefore the evolution operator  in Schrödinger
picture  is unitary). In the example mentioned above, if there is no ZWW coupling, one can
still have a theory with a Hermitian Hamiltonian therefore still have unitarity. If the
tree level perturbation theory violates unitarity, it only means such a perturbative calculation
is not applicable (in high energy). So in my opinion those unitarity arguments
in the standard model are not quite convincing.
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