The dynamics of the quantum vacuum is one of the major unsolved problems of relativistic quantum field theory and cosmology. The reason is that relativistic quantum field theory and general relativity describe processes well below the Planck energy scale, while the deep ultraviolet quantum vacuum at or above the Planck energy scale remains unknown. Following the condensed matter experience we develop a special macroscopic approach called q-theory, which incorporates the ultraviolet degrees of freedom of the quantum vacuum into an effective theory and allows us to study the dynamics of the quantum vacuum and its influence on the evolution of the Universe.

     The vacuum in our approach is considered as the Lorentz-invariant analog of a condensed-matter system (liquid or solid) which is stable in free space. The variable q is the Lorentz-invariant analog of the particle number density, whose conservation regulates the thermodynamics and dynamics of many-body systems. This approach is universal in the sense that the same results are obtained using different formulations of the q-field. In the paper, we choose the q-field in terms of a 4-form field strength, which has, in particular, been used by Hawking for discussion of the main cosmological constant problem -- why is the observed value of the cosmological constant many orders of magnitude smaller than follows from naive estimates of the vacuum energy as the energy of zero-point motion. In q-theory, the huge zero-point energy is naturally cancelled by the microscopic (trans-Planckian) degrees of freedom, as follows from the Gibbs-Duhem identity, which is applicable to any equilibrium ground state including the one of the physical

vacuum.

            In the paper, we consider a further extension of q-theory. We demonstrate that, in an expanding Universe, the variable  effectively splits into two components. The smooth part of the relaxing vacuum field is responsible for dark energy, while the rapidly oscillating component behaves as cold dark matter. In this way, q-theory provides a combined solution to the missing-mass problem and the cosmological constant problem. If this scenario is correct, the implication would be that direct searches for dark-matter particles remain unsuccessful in the foreseeable future.

F.R. Klinkhamer and G.E. Volovik,

JETP Letters  105, issue 2 (2017)

The ability to detect nonequilibrium spin accumulation (imbalance) by all electrical means is one of the key ingredients in spintronics . Transport detection typically relies on a nonlocal measurement of a contact potential difference induced by the spin imbalance by means of ferromagnetic contacts  or spin resolving detectors . A drawback of these approaches lies in a difficulty to extract the absolute value of the spin imbalance without an independent calibration. An alternative concept of a spin-to-charge conversion via nonequilibrium shot noise was introduced and  investigated in  experiment recently . Here, the basic idea is that a nonequilibrium spin imbalance generates spontaneous current fluctuations, even in the absence of a net electric current. Being a primary approach , the shot noise based detection is potentially suitable for the absolute measurement of the spin imbalance. In addition, the noise measurement can be used for a local non-invasive sensing.

In this letter, we calculate the impact of a spin relaxation on the spin imbalance generated shot noise in the absence of inelastic processes. We find that the spin relaxation increases the noise up to a factor of two, depending on the ratio of the conductor length and the spin relaxation length. The design of the system. A diffusive normal wire of the length L is attached to normal islands on both ends. Nonequilibrium energy distribution on the left hand side of the wire generates the shot noise at a zero net current. The spin imbalance on the left-hand side of the wire is due to the electric current flowing from one ferromagnetic lead (red) to another one with opposite magnetization (blue).

V.S. Khrapai and K.E. Nagaev JETP  Letters 105, №1 (2017)     

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Dryuma V.S.

Institute of Mathematics and Informatics AS of Moldova

valdryum@gmail.com

 The article is devoted to the application of the Inverse Scattering Transform Method (IST)   discovered in 1967 year to exact integration of nonlinear p.d.e.,

\begin{equation}
\left(U_t+UU_x+U_{xxx}\right)_x+\pm U_{yy}=0,
\end{equation}

known  as the Kadomtsev-Petviashvili equation (KP), which describe propagation waves in various problems of the plasma physics and hydrodynamics. By the author was first shown that possibilities of
the IST-method can be essentially extend and it can be used to the integration of multi-dimensional equations having physical interest. The representation of Lax $\hat L_t=[\hat L,\hat A]$), which is the basis of this method and previously was known only for the Korteveg-de Vries equation ($U_t+UU_x+U_{xxx}=0$) and for the nonlinear Schrodinger equation ($\Psi_t+\Psi_{xx}+|\Psi|^2\Psi=0$) allowed to construct sets  of exact solutions of these equations that  has led to the discovery of notion of Soliton, which play an important role in modern mathematics and physics. Multi dimensional generalization of the IST-method present time are used to solving the problems of differential and  algebraic geometry, in the various branches of the field theory and gravitation. As example discovery of the gage
equivalence between the NS-equation $ iv_t+v_{xx}+2|v|^2v=0 $ and the KP equation $ (4v_t + 6vv_x + v_{xxx})_x = 3v_{yy} $ has found application in the theory of the rogue waves, meeting in the
hydrodynamics, dynamics of gases and investigation of their properties can to have practical meanings.

1. B.B.Kadomtsev, V.I.Petviashvili, DAN SSSR 192:4, (1970), 753-756.
2. V.S. Dryuma, DAN  SSSR, 268:1 (1983), 15-17.
3. Teoriy solitonov, red.S.P.Novikov, 1982.
4. P. Dubard and V. B, Matveev, "Multi-rogue waves solutions: from the NLS to the KP-I equation", Nonlinearity, v. 26 (2013), R93-R125.

V.E. Adler, Landau Institute for Theoretical Physics

The paper is devoted to applications of the following remarkable transformation. An easy computation proves that if $\psi(x,\lambda)$ is a general solution of the equation
\[ \psi''=(u(x)-\lambda)\psi,\]
and $\psi_0(x)$ is its particular solution corresponding to the value $\lambda=\lambda_0$, then the function
\[ \tilde\psi=\psi'-w\psi,\quad w=\psi'_0/\psi_0\]
satisfies an equation of the same form with a new potential $\tilde u=u-2w'$. For the first time, this observation was made by Darboux [1], and later on it was rediscovered by Schrodinger [2] in the quantum mechanical context. The sequence of the Darboux transformations is defined by operators $H_n=d^2/dx^2-u_n$,
$Q^\pm_n=d/dx\pm w_n$ related by the factorization
\[ H_n+\lambda_n=Q^+_nQ^-_n \quad\mapsto\quad H_{n+1}+\lambda_n=Q^-_nQ^+_n,\]
which is equivalent to the chain of differential-difference equations
\[ u_n=w'_n+w^2_n+\lambda_n,\quad w'_n+w'_{n+1}=w^2_n-w^2_{n+1}+\lambda_n-\lambda_{n+1}.\]
Any solution of these equations gives rise to a family of operators $H_n$ with the $\psi$-functions which can be computed explicitly for all $\lambda=\lambda_n$; the operators $Q^\pm_n$ play the role of the creation-annihilation operators. As it turned out, almost all exactly-solvable models of quantum mechanics (harmonic oscillator, Kepler problem, spherical harmonics, reflectionless potentials, Morse, P\"oschl-Teller potentials and so on) admit an uniform description within this approach [4, 5]. Moreover,

functions $w_n$ corresponding to different $n$ are of the same form and differ only in the values of the parameters.
 

The formulation of this {\em shape-invariance} property is the main result of the Gendenstein's work. This idea was further developed by Shabat, Veselov, Spiridonov [6-8] and others, and new families of exactly solvable potentials were introduced (in contrast to the previously known examples, these potentials were defined in terms of the Painlev\'e transcendents and their generalizations rather than elementary functions).

The Darboux transformation admits generalizations for the non-stationary Scrodinger equation and other spectral problems. It is directly related with the supersymmetry [9-11] and with the Backlund transformations for the nonlinear equations integrable by the inverse scattering method [12,13,7]. In 1970--90, the development of these theories was parallel and the Gendenstein's paper has had a marked impact on these studies.

[1] G. Darboux. Sur une proposition relative aux equations lineaires. Compt. Rend. Acad. Sci. 94 (1882) 1456{1459. [arXiv:physics/9908003]
[2] E. Schrodinger. A method of determining quantum-mechanical eigenvalues and eigenfunctions. Proc. Roy. Irish Acad. A 46 (1940/1941) 9-16.
[3] E. Schrodinger. Further studies on solving eigenvalue problems by factorization. Proc. Roy. Irish Acad. A 46 (1940/1941) 183-206.
[4] L. Infeld, T.E. Hull. The factorization method. Rev. Modern Phys. 23:1 (1951) 21-68.
[5] M.M. Crum. Associated Sturm-Liouville systems. Quart. J. Math. Oxford Ser. 2 6 (1955) 121-127.
[6] A.B. Shabat. The innite-dimensional dressing dynamical system. Inverse Problems 8 (1992) 303-308.
[7] A.P. Veselov, A.B. Shabat. Dressing chains and the spectral theory of the Schrodinger operators. Funct.
Anal. Appl. 27:2 (1993) 81-96.
[8] V. Spiridonov. Exactly solvable potentials and quantum algebras. Phys. Rev. Lett. 69 (1992) 398-401.
[9] E. Witten. Dynamical breaking of supersymmetry. Nucl. Phys. B 188:3 (1981) 513-554.
[10] L.E. Gendenshtein, I.V. Krive. Supersymmetry in quantum mechanics. Sov. Phys. Usp. 28 (1985) 645-666.
[11] V.G. Bagrov, B.F. Samsonov. Darboux transformation, factorization, and supersymmetry in onedimensional quantum mechanics. Theor. Math. Phys. 104:2 1051-1060.
[12] H.D. Wahlquist, F.B. Estabrook. Backlund transformations for solutions of the Korteweg{de Vries equation. Phys. Rev. Let. 31:23 (1973) 1386-1390.
[13] V.B. Matveev. Darboux transformation and explicit solutions of the Kadomtcev-Petviaschvily equation, depending on functional parameters. Lett. Math. Phys. 3:3 (1979) 213-216.
 

I. V. Polyubin

Landau Institute for Theoretical Physics,

Institute of Theoretical and Experimental Physics


 

In 1973 S. Coleman and E. Weinberg investigated the effect of radiative corrections on the possibility of spontaneous symmetry breaking in seminal paper [1]. A. D. Linde studied some
physical consequences of spontaneous breaking of gauge symmetry at one-loop level. The author considered a complex scalar field minimally coupled to U(1) gauge field with potential

$V=\lambda(\varphi^*\varphi)^2-{\mu}^2{\varphi}^*{\varphi}$. Renormalization conditions  for effective potential fixed vacuum expectation value and mass of excitataions to its classical values.
The effective potential has the second minimum at $<\varphi>=0$. The condition $V_{eff}(\sigma)< V_{eff}(0)$ imposed a constraint on self-interaction coupling :

$$\lambda>\frac {3}{32{\pi}^2}g^4$$

Even if classical value of $\lambda$ is very small, due to one-loop correction it becomes equal to $\lambda_{eff}=\lambda+\frac{1}{2{\pi}^2}g^4$.

These inequalities for coupling constant were rewritten in terms of masses of scalar and vector particles. The lower bound on the Higgs mass was estimated as $m_H>5  GeV$. This approach was generalized soon  to non-abelian case by S. Weinberg [2]. In this case the lower bound on Higgs mass is $m_H>7.4 GeV$ taking into account contribution of $W,Z $-bosons to effective potential. This lower bound is known as Weinberg-Linde value [3]. It is worth to mention that fermions propagating in the loop diminish WL value ( due to the opposite statistics). t-quark contribution makes the effective
potential unbounded from below. So one loop approximation is not valid. At two loops [4,5] nonsymmetric vacuum approaches the metastability boundary $V_{eff}(\sigma)\simeq V_{eff}(0)$  at
$m_H\simeq126 GeV$, $m_t\simeq174 GeV$ [6].

[1]  S. R. Coleman, E. J. Weinberg, Phys. Rev. D7 (1973), 1888-1910
[2]  S. Weinberg, Phys. Rev. Lett. 36 (1976), 294-296
[3]  Hung P. Q.  Phys. Rev. Lett. 42 (1979), 873-876
[4]  Casas J. A., Espinosa J. R., Quiros M. and Riotto A.,  Nucl. Phys. B436 (1995)3Ö29
[5] Hambye T. and Riesselmann K.,  Phys. Rev. D55 (1997) 7255-7262
[6] Isidori G., Ridolfi G. and Strumia A., Nucl. Phys. B609 (2001) 387-409




 

V. A. Khodel
Russian Research Center Kurchatov Institute, Moscow, 123182, Russia

McDonnell Center for the Space Sciences & Department of Physics, Washington University, St.Louis, MO 63130, USA

V. R. Shaginyan

National Research Center "Kurchatov Institute", Petersburg Nuclear Physics Institute, Gatchina, 188300, Russia

In the paper submitted in April of 1990, a new type of phase transition is introduced [1]. This phase transition occurs as the effective mass of quasiparticles diverges, $M^*\to\infty$, that is the fermions get very heavy. Beyond the point of the phase transition a fermion condensate (FC) arises in new phase: The energy $\varepsilon(p)$ of quasiparticles with momenta $p_i<p<p_f$ are equal to the chemical potential $\mu$, becoming flat or dispersionless, with $p_i<p_F<p_f$ and $p_F$ is the Fermi momentum [1]. Thus, the foundation of a new theory of strongly correlated Fermi-systems has been laid and the FC theory has emerged, while the Landau theory ceases to operate in that case [1]. The main novelty is that the quasiparticle distribution $n(p)$ in the region $p_i<p<p_f$ does
not coincide with that of ideal Fermi gas, and is given by the variation condition $\delta E(n)/\delta n(p)=\mu$, where $E(n)$ is the Landau functional. Analysis of the FC state, carried out by G. E. Volovik, has shown that systems with FC represent a new class of Fermi liquid characterized by their own topological structure, and can be viewed as topological protected [2-4]. It has been shown that FC emerges in 1D fermions located in the core of quantized vortices, e.g. in $\rm ^3He$ superfluid, and leads to room-temperature superconductivity [3, 4]. Nonetheless, the FC state has been evaluated and criticized by P. Nozi\`eres, who have suggested that the lifetime $\tau$ of quasiparticles hopelessly small making the observations of FC state problematic \cite{noz}. On the other hand, P. Nozi\`eres has taught us how one can transport the FC behavior to finite temperatures $T$; and a careful study has demonstrated that $\tau\propto 1/T$ [6, 7]. Further investigations has also shown that properties of systems with FC, or located near the phase transition, are sharply different from those of common Fermi-systems.

As a result, the FC theory has proposed explanations of numerous important experimental facts and paved the way for much subsequent research in the condensed matter physics of strongly correlated Fermi-systems represented by heavy-fermion (HF) metals and high-temperature superconductors [4, 8, 9], quantum spin liquids [10], quasicrystals [11], and two-dimensional Fermi-systems [12, 13].
With regard to experimental facts observed in the physics of strongly correlated systems, it is necessary to revise many sections of the traditional physics of solid state and liquids. At the same time there are effects that are absent in the physics of solid state. For example, violation of the particle-hole symmetry, the asymmetry in the tunneling conductivity measured on HF metals, violation of the Wiedemann-Franz law, etc. The most various strongly correlated Fermi-systems have the identical universal scaling behavior other than the observed behavior of common metals and
Fermi-liquids. Such behavior, explained within the FC theory, signals that a new state of matter, possessing unique properties, may be realized by these systems. Thus, it turns out that the FC theory offers an unexpectedly simple and complete description of strongly correlated Fermi-systems [1-14].

[1] V. A. Khodel and V. R. Shaginyan, JETP Lett. 51, 553 (1990).
[2] G. E. Volovik, JETP Lett. 53, 222 (1991).
[3] G. E. Volovik, JETP Lett. 59, 830 (1994).
[4] G. E. Volovik, Phys. Scr. T 164, 014014 (2015).
[5] P. Nozieres, J. Phys. I France 2, 443 (1992).
[б] V. A. Khodel, V. R. Shaginyan, and P. Shuck, JETP Lett. 63, 752 (1996).
[7] J. W. Clark, V. A. Khodel, and M. V. Zverev, Phys. Rev. B 71, 012401 (2005).
[8] V. A. Khodel, V. R. Shaginyan, and V. V. Khodel, Phys. Rep. 249, 1 (1994).
[9] V. R. Shaginyan, M. Ya. Amusia, A. Z. Msezane, and K. G. Popov, Phys. Rep. 492, 31 (2010).
[10] V. R. Shaginyan, A. Z. Msezane, and K. G. Popov, Phys. Rev. B 84, 060401(R) (2011).
[11] V. R. Shaginyan, A. Z. Msezane, and K. G. Popov, G. S. Japaridze, and V. A. Khodel, Phys. Rev. B 87, 245122 (2013).
[12] V. R. Shaginyan, A. Z. Msezane, K. G. Popov, and V. A. Stephanovich, Phys. Rev. Lett. 100, 096406 (2008).
[13] A. A. Shashkin, V. T. Dolgopolov, J. W. Clark, V. R. Shaginyan, M.V. Zverev, and V. A. Khodel, Phys. Rev. Lett. 112, 186402 (2014).
[14] M. Ya. Amusia, K. G. Popov, V. R. Shaginyan, and V. A. Stephanovich, Theory of Heavy-Fermion Compounds — Theory of Strongly Correlated Fermi-Systems, Springer Series in Solid-State Sciences 182, (2014).

 M.A. Shifman

School of Physics and Astronomy, University of Minnesota, Minneapolis, MN

55455, USA
 William I. Fine Theoretical Physics Institute, University of Minnesota,

Minneapolis, MN 55455, USA

            The penguin mechanism or penguin graphs present a class of Feynman diagrams which turned out of paramount importance for understanding weak flavor changing decays. While in the original paper in which they were introduced [1] only strange particle decays were considered, the idea was generalized to a large range of other applications, for instance, CP violating processes in B-meson decays, electroweak penguins, and many others. (The term penguin graphs was suggested by John Ellis later, see below.) The first developments were reported by the authors in [2]. The B-physics “penguins” are sensitive to new physics, especially those rare decays that are dominated by “penguin diagrams.” They were directly observed in 1991 and 1994 by the CLEO collaboration.

 “Penguins started to fly” [3] in high-energy physics in 1974. It was the very beginning of the quantum chromodynamics (QCD) era. We started to study interplay between the weak and strong interactions in 1973. The most perplexing issue in the strange particle decays was a seemingly unexplainable enhancement of the ∆I = 1/2 amplitudes in the kaon and baryon decays compared to the ∆I = 3/2 amplitudes. This mystery known under the name of “∆I = 1/2 rule” had been discussed by J. Schwinger as early as in 1964. The advent of QCD gave a new hope for explanation of this phenomenon. The publication [4] of Gaillard and Lee, which reached ITEP in a preprint form, provided us with a stimulating impetus. These authors noted that gluons act differently on the ∆I = 1/2 and ∆I = 3/2 amplitudes, with a tendency to enhance the former and suppress the latter [5]. This tendency was not enough, however, to explain the effect. When we discovered the penguin graphs and realized that they can appear only in the ∆I = 1/2 part of the strange quark decay amplitudes we understood that we were on the right track. Special chiral features inherent only to penguins led to the successful completion of the ∆I = 1/2 rule derivation (for a review see [3]). This result was reported in summer of 1974 at an international conference.

 In four decades that elapsed the march of the penguin diagrams in various flavor-changing processes was quite remarkable. Certainly, we could not anticipate this when we submitted the first paper to JETP Letters. At that time the newly discovered (SVZ) diagrams did not look like penguins. They

were distorted to look penguin-like by John Ellis.

The SVZ graph in John Ellis’ “penguin” rendition.

Here is John’s story which travels from one website to another (originally published in [6]): “Mary K. [Gaillard], Dimitri [Nanopoulos] and I first got interested in what are now called penguin diagrams while we were studying CP violation in the Standard Model in 1976. The penguin name came in 1977, as follows. In the spring of 1977, Mike Chanowitz, Mary K. and I wrote a paper on GUTs predicting the b quark mass before it was found. When it was found a few weeks later, Mary K, Dimitri, Serge Rudaz and I immediately started working on its phenomenology. That summer, there was a student at CERN, Melissa Franklin who is now an experimentalist at Harvard. One evening, she, I and Serge went to a pub, and she and I started a game of darts. We made a bet that if I lost I had to put the word penguin into my next paper. She actually left the darts game before the end, and was replaced by Serge, who beat me. Nevertheless, I felt obligated to carry out the conditions of the bet. For some time, it was not clear to me how to get the word into this b quark paper that we were writing at the time. Then, one evening, after working at CERN, I stopped on my way back to my apartment to visit some friends living in Meyrin, where I smoked some illegal substance. Later, when I got back to my apartment and continued working on our paper, I had a sudden flash that the famous diagrams look like penguins. So we put the name into our paper, and the rest, as they say, is history.”

References

[1]  A.I. Vainshtein, V.I. Zakharov, M.A. Shifman, Pisma ZhETF 22​​, 123 (1975) [JETP Lett. 22, 55  (1975)].

[2] M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B120  316 (1977) Non-leptonic decays of K-mesons and hyperons. ZhETF 72  1275  (1977) [JETP 45  670 (1977)].

[3] A. I. Vainshtein, Int. J. Mod. Phys. A 14, 4705 (1999) [hep-ph/9906263].

[4] M.K. Gaillard and B. Lee, Phys. Rev. Lett. 33, 108 (1974).

[5] Mary K. Gaillard, A Singularly Unfeminine Professions, (World Scientific, Singapore, 2015), p. 59.

[6] M. Shifman, ITEP Lectures in Particle Physics, (World Scientific, Singapore, 1999), Vol. 1, p. x [hep-ph/9510397].

M.A. Shifman

School of Physics and Astronomy, University of Minnesota, Minneapolis, MN

55455, USA
 William I. Fine Theoretical Physics Institute, University of Minnesota,

Minneapolis, MN 55455, USA

The paper [1] laid the foundation for the so-called SVZ sum ruled method (sometimes also referred to as QCD sum rules) allowing one to calculate properties of a huge variety of low-lying hadronic states basing on average characteristics of the QCD vacuum, such as quark and gluon condensates (the latter was first introduced in [1]). The main conceptual component of the method is the Wilson operator product expansion (OPE). The focus of Wilsons original work was on statistical physics, where the program is also known as the block-spin approach. Surprisingly, in high-energy physics of the early-to-mid 1970s the framework of OPE was narrowed down to perturbation theory. The authors of [1] and the subsequent publications [2] were the first to adapt the general Wilsonian construction to QCD. Their goal was to systematically include power-suppressed effects (condensate corrections), thus bridging the gap between short and large distance dynamics.

 This “bridging” did not lose its significance till this day. This route – matching between the short distance expansion and long distance (hadronic) representation – led to remarkable successes. The SVZ method was tested, and proved to be fruitful in analyzing practically every static property of all established low-lying hadronic states, both mesons and baryons. (For a review see [3].) Later, the very same OPE and the same ideas that were developed in [1, 2], was applied with triumph in heavy quark expansions blossomed in the 1990s in the framework of the heavy quark theory (reviewed in [4]).

The question we asked ourselves in 1977, which eventually led to the idea of deriving properties of matter from the vacuum condensates, was as follows (see also [5]).

What if we start from short distances, where the quark-gluon dynamics was under theoretical control, and extrapolate to larger distances using general features of QCD? What maximal information on hadronic properties could we obtain?

 Surprisingly, we started getting interesting results for charmonium almost immediately. A certain success came, however, after V. Novikov, L. Okun, and M. Voloshin joined us. It turned out that a whole variety of the charmonium parameters could be (and were) predicted. A curious episode is worth mentioning. At this time, according to experiment, the only candidate for the psuedoscalar charmonim was the so-called X(2.83). Its mass seemed to be too low for this interpretation; still, with some tension it could fit potential model predictions which were widespread at that time. In [6] it was unambiguously shown from the analysis of the QCD sum rules X(2.83) could not be the psuedoscalar charmonim. The mass of the latter should have lied at 3.01±0.01 GeV. Later the experimental data regarding X(2.83) were indeed retracted. The current data give 2.983±0.0007 GeV.

 For about a year, we played the game of getting  cc coupling constants and masses from simple numbers. In 1977, we submitted a review report [7]. At about that time, it became clear that our success was limited; and could not be generalized to the most common light-quark mesons and baryons without new ideas. It was a hot summer, just before vacation. Our big collaboration ceased to exist. We were leisurely discussing something when the first hints appeared. The conjecture was that the vacuum is actually something like a gluon medium, and all particle properties are due to the quark interaction with this medium which can be conveniently parametrized by certain quark and gluon condensates. We worked out the first implications of the gluon condensate in fall 1977. At first, we were discouraged by a wrong sign for one of the most important particles (ρ meson). Then we suddenly understood that this sign could be compensated by the four-quark condensate – a real breakthrough. The accuracy of our predictions turned out to be much higher than anyone could expect a priori. Inspired, we worked at a feverish pace for the whole academic year. When the final paper was ready (a short one had been sent to JETP Letters in the beginning [1]), it contained more than 300 typewritten pages. We could not make a preprint out of it because, according to Soviet bureaucratic rules, preprints could have no more than 40 pages or so. So, we divided it artificially into seven or eight parts, trying to do it in such a way that it would not be immediately obvious to the censor. It appeared as three papers occupying the whole issue of Nuclear Physics B.

References

[1]  A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, Pis'ma ZhETF 27 , 60 (1978) [JETP Lett. 27, 55 (1978)] .

[2] M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B 147, 385 (1979), and Nucl. Phys. B 147, 448 (1979).

[3] M. A. Shifman, Prog. Theor. Phys. Suppl. 131,  1 (1998)  [hep-ph/9802214].

[4] I. I. Y. Bigi, M. A. Shifman and N. Uraltsev, Ann. Rev. Nucl. Part. Sci. 47, 591 (1997) [hep-ph/9703290].

[5] M. Shifman, Current Contents, 32,  9 (1992).

[6] V. A. Novikov et al., Phys. Rept. 41, 1 (1978).