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Speeches by the participants of the general meeting of the RAS members

In this concluding talk at the last pre-LHC ICHEP event, a personal view of what is happening in theory, experiment and to some extent cosmology is given.

We present a simple model in which the weak energy condition is violated for spatially homogeneous, slowly evolving fields. The excitations in Minkowski space in an external field with violation of the Lorentz invariance do not contain ghosts, tachyons, or superluminal modes at spatial momenta ranging from some low scale e to the ultraviolet cutoff scale, while tachyons and possibly ghosts do exist for three-dimensional momenta less than e. We show that in the absence of other matter, a slow-roll cosmological regime is possible. In this regime, the weak energy condition is violated, and yet homogeneity and isotropy are not completely spoiled (at the cost of fine tuning), because for a given conformal momentum, the tachyon mode increases during a sufficiently short time.

We suggest a technique that explicitly accounts for the structure of an initial state of quantum field in the semiclassical calculations of path integral in curved space-time, and consider decay of metastable state (conformal vacuum of scalar particles above false classical vacuum) in background de Sitter space-time as an example. Making use of this technique, we justify the Coleman-De Luccia approach to the calculation of the decay probability. We propose an interpretation of the Hawking-Moss instanton as a limiting case of constrained instantons. We find that an inverse process of the transition from true vacuum to false one is allowed in de Sitter space-time, and calculate the corresponding probability., 26 pages,10 figures

The electroweak baryon number violation is expected to be rapid at high temperatures. This implies that at least some multiparticle processes with B-violation are rapid at high energies. We discuss recent attempts to study the two-particle cross sections of instanton-like processes, which show that at energies below 10 TeV, the cross sections increase exponentially, and might even become large at about 10 TeV.

The creation of scalar bosons is studied in background fields which make the effective mass of the scalar field imaginary in a finite region of space-time. The number of created particles in the semiclassical approximation is shown to be exp(- S E inst ) is the euclidean action evaluated at the instanton-like-solution in the theory of a relativistic point particle with the proper time rotated to the euclidean domain, τ → -⇔ τ . The instanton action is negative, so that the number of created particles is exponentially large. The most probable trajectory of created particles is shown to be the analytical continuation of the instanton trajectory back to real proper time.

The cosmological constant problem is one of the most intriguing problems of modern physics (for a review see, e.g., ref.[1]). A proposal for its solution due to Baum [2] and Hawking [3], and its modification by Coleman [4], have attracted much attention. The arguments of refs.[2–4] have essentially two crucial ingredients: i) One assumes that the observable value of the cosmological constant, Λ, is not an absolutely fundamental c-number parameter of the theory; rather, one has to consider universes with different values of Λ which are distributed according to some distribution function P(Λ). In this sense Λ is a dynamical (quantum) variable. This assumption has been supported by the recent study of topological changes (baby universes, wormholes) [5–7] which has finally led to the observation [8–10] that all coupling constants, including Λ, are dynamical variables in the above sense. ii) It is assumed that the probability distribution, P(Λ), is calculable. Furthermore, it is assumed that P(Λ) is saturated by the contribution of the De Sitter instanton (4-sphere) into the euclidean functional integral in quantum gravity. This instanton exists at Λ > 0 and has negative action, I inst = −3πM PI/Λ. Thus, Baum [2] and Hawking [3] argued that (1.1) i.e., P(Λ) is strongly peaked at Λ = 0, as desired. Coleman [4] proposed to sum up the multi-instanton contributions and obtained even stronger peak, (1.2)

The problems associated with multiparticle production in model scalar theories are discussed. When the number of emitted particles is comparable to the inverse coupling constant, ordinary perturbation theory is inapplicable. The possibility of using semiclassical methods to calculate the multiparticle cross sections taking into account all important loop corrections is studied.

We discuss the perturbations around the O(4)-invariant bounce describing the tunneling process leading to the materialization of a bubble of a new phase in metastable vacuum. We find that for some range of parameters, the gravitational effects lead to the existence of a huge number of negative modes. We argue that this implies the breakdown of the quasiclassical approximation and speculate on a possible alternative to the quasiclassical tunneling. We point out that the possibility of non-quasiclassical tunneling makes the quasiclassical description of tunneling questionable even in models with stable classical euclidean configurations.

The possibility is considered that changes of spatial topology occur as tunneling events in quantum gravity. Creation of scalar and spinor particles during these tunneling transitions is studied. The relevant formalism based on the euclidean Schrodinger equation and coherent state representation is developed. This formalism is illustrated in a two-dimensional example. It is argued that the particle creation during the topological changes induces the loss of quantum coherence. The particle creation is calculated in the case of O(4)-invariant background euclidean four-dimensional metrics. This calculation is used for estimating the loss of quantum coherence. An upper limit on the rate of the topological changes, A ⪅10 −17 M Pl 4 , is derived from the observation of K 0 − K 0 oscillations.

We present a toy model for the third quantization theory of topological changes. We find that the natural choice of the “Heisenberg” state vector of the system with one large universe and an arbitrary number of small universes gives rise to the loss of quantum coherence.

A study is made of the production of fermion pairs associated with the tunneling process that leads to decay of a metastable vacuum in field theory. The technique of nonunitary Bogolyubov transformations is developed. Expressions are obtained for the spectrum of the produced fermions. The spectrum of fermion pairs produced when there is homogeneous decay of a metastable vacuum is found as an example.

Linearized theory of gravity is quantized both in a naive way and as a proper limit of the Dirac-Wheeler-De Witt approach to the quantization of the full theory. The equivalence between the two approaches is established. The problem of scattering in the canonically quantized theory of gravitation is investigated. The concept of the background metric naturally appears in the canonical formalism for this case. The equivalence between canonical and path-integral approaches is established for the problem of scattering. Some kinematical properties of functionals in Wheeler superspace are studied in an appendix.

In the context of the Grand Unified MSSM, we investigate the fermion mass matrices at GUT scale. We note that from the experimental mass pattern the determinants of the Yukawa matrices at this scale can be unified with good precision. Taking the unification o determinants as an hypothesis, it gives two model independent predictions that in the MSSM turns out to determine an appropriate value for the product m_d m_s and tan(beta)~7-10 in the favored range. We then review a predictive model of SU(3) flavour in the context of supersymmetric SO(10) that nicely implements this mechanism, while explaining all fermion masses and mixings at 1 sigma level, including neutrino data., Comment: to Appear in the proceedings of "QUARKS-2006"

The basic problem of quantum cosmology is the definition of the quantum state of the universe, with appropriate boundary conditions on Riemannian three-geometries. This paper describes recent progress in the corresponding analysis of quantum amplitudes for Euclidean Maxwell theory and linearized gravity. Within the framework of Faddeev-Popov formalism and zeta-function regularization, various choices of mixed boundary conditions lead to a deeper understanding of quantized gauge fields and quantum gravity in the presence of boundaries., Comment: 14 pages, plain TEX, to appear in Proceedings of the Moscow Quantum Gravity Seminar, Moscow, June 12 - June 19, 1995