50 research outputs found
Energy Density of Non-Minimally Coupled Scalar Field Cosmologies
Scalar fields coupled to gravity via in arbitrary
Friedmann-Robertson-Walker backgrounds can be represented by an effective flat
space field theory. We derive an expression for the scalar energy density where
the effective scalar mass becomes an explicit function of and the scale
factor. The scalar quartic self-coupling gets shifted and can vanish for a
particular choice of . Gravitationally induced symmetry breaking and
de-stabilization are possible in this theory.Comment: 18 pages in standard Late
Divergent Perturbation Series
Various perturbation series are factorially divergent. The behavior of their
high-order terms can be found by Lipatov's method, according to which they are
determined by the saddle-point configurations (instantons) of appropriate
functional integrals. When the Lipatov asymptotics is known and several lowest
order terms of the perturbation series are found by direct calculation of
diagrams, one can gain insight into the behavior of the remaining terms of the
series. Summing it, one can solve (in a certain approximation) various
strong-coupling problems. This approach is demonstrated by determining the
Gell-Mann - Low functions in \phi^4 theory, QED, and QCD for arbitrary coupling
constants. An overview of the mathematical theory of divergent series is
presented, and interpretation of perturbation series is discussed. Explicit
derivations of the Lipatov asymptotic forms are presented for some basic
problems in theoretical physics. A solution is proposed to the problem of
renormalon contributions, which hampered progress in this field in the late
1970s. Practical schemes for summation of perturbation series are described for
a coupling constant of order unity and in the strong-coupling limit. An
interpretation of the Borel integral is given for 'non-Borel-summable' series.
High-order corrections to the Lipatov asymptotics are discussed.Comment: Review article, 45 pages, PD
Renormalization Group Functions of the \phi^4 Theory in the Strong Coupling Limit: Analytical Results
The previous attempts of reconstructing the Gell-Mann-Low function \beta(g)
of the \phi^4 theory by summing perturbation series give the asymptotic
behavior \beta(g) = \beta_\infty g^\alpha in the limit g\to \infty, where
\alpha \approx 1 for the space dimensions d = 2,3,4. It can be hypothesized
that the asymptotic behavior is \beta(g) ~ g for all values of d. The
consideration of the zero-dimensional case supports this hypothesis and reveals
the mechanism of its appearance: it is associated with a zero of one of the
functional integrals. The generalization of the analysis confirms the
asymptotic behavior \beta(g)=\beta_\infty g in the general d-dimensional case.
The asymptotic behavior of other renormalization group functions is constant.
The connection with the zero-charge problem and triviality of the \phi^4 theory
is discussed.Comment: PDF, 17 page
On the Theory of Vibronic Superradiance
The Dicke superradiance on vibronic transitions of impurity crystals is
considered. It is shown that parameters of the superradiance (duration and
intensity of the superradiance pulse and delay times) on each vibronic
transition depend on the strength of coupling of electronic states with the
intramolecular impurity vibration (responsible for the vibronic structure of
the optical spectrum in the form of vibrational replicas of the pure electronic
line) and on the crystal temperature through the Debye-Waller factor of the
lattice vibrations. Theoretical estimates of the ratios of the time delays, as
well as of the superradiance pulse intensities for different vibronic
transitions well agree with the results of experimental observations of
two-color superradiance in the polar dielectric KCl:O2-. In addition, the
theory describes qualitatively correctly the critical temperature dependence of
the superradiance effect.Comment: 8 pages, 1 figur
Asymptotic Behavior of the \Beta Function in the \Phi^4 Theory: A Scheme Without Complex Parameters
The previously obtained analytical asymptotic expressions for the Gell-Mann -
Low function \beta(g) and anomalous dimensions of \phi^4 theory in the limit
g\to\infty are based on the parametric representation of the form g = f(t),
\beta(g) = f1(t) (where t\sim g_0^{-1/2} is the running parameter related to
the bare charge g_0), which is simplified in the complex t plane near a zero of
one of the functional integrals. In the present paper, it is shown that the
parametric representation has a singularity at t\to 0; for this reason, similar
results can be obtained for real values of g_0. The problem of the correct
transition to the strong coupling regime is simultaneously solved; in
particular, the constancy of the bare or renormalized mass is not a correct
condition of this transition. A partial proof is given for the theorem of the
renormalizability in the strong coupling region.Comment: PDF, 16 page
Three-dimensional quantum solitons with parametric coupling
We consider the quantum field theory of two bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium, this corresponds to the process of second-harmonic generation (via chi((2)) nonlinearity) modified by the chi((3)) nonlinearity. The quantum solitons or energy eigenstates (bound-state solutions) are obtained exactly in the simplest case of two-particle binding, in one, two, and three space dimensions. We also investigate three-particle binding in one space dimension. The results indicate that the exact quantum solitons of this field theory have a singular, pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. To estimate the physically accessible radii and binding energies of the bound states, we impose a momentum cutoff on the nonlinear couplings. In the case of nonlinear optical interactions, the resulting radii and binding energies of these photonic particlelike excitations in highly nonlinear parametric media appear to be close to physically observable values
Introduction to quantum statistical mechanics
Introduction to Quantum Statistical Mechanics (Second Edition) may be used as an advanced textbook by graduate students, even ambitious undergraduates in physics. It is also suitable for non experts in physics who wish to have an overview of some of the classic and fundamental quantum models in the subject. The explanation in the book is detailed enough to capture the interest of the reader, and complete enough to provide the necessary background material needed to dwell further into the subject and explore the research literature