arXiv subjects

E. Alfinito

Publications and source records attributed to E. Alfinito.

46 records · Page 3Linked to original sources

arXiv1997

Double Universe

We discuss the canonical quantization of non-unitary time evolution in inflating Universe. We consider gravitational wave modes in the FRW metrics in a de Sitter phase and show that the vacuum is a two-mode SU(1,1) squeezed state of thermo field dynamics, thus exhibiting the link between inflationary evolution and thermal properties. In particular we discuss the entropy and the free energy of the system. The state space splits into many unitarily inequivalent representations of the canonical commutation relations parametrized by time $t$ and non-unitary time evolution is described as a trajectory in the space of the representations: the system evolves in time by running over unitarily inequivalent representations. The generator of time evolution is related to the entropy operator. A central ingredient in our discussion is the doubling of the degrees of freedom which turns out to be the bridge to the unified picture of non-unitary time evolution, squeezing and thermal properties in inflating metrics.

hep-th↗

arXiv1996

A class of nonlinear wave equations containing the continuous Toda case

We consider a nonlinear field equation which can be derived from a binomial lattice as a continuous limit. This equation, containing a perturbative friction-like term and a free parameter $γ$, reproduces the Toda case (in absence of the friction-like term) and other equations of physical interest, by choosing particular values of $γ$. We apply the symmetry and the approximate symmetry approach, and the prolongation technique. Our main purpose is to check the limits of validity of different analytical methods in the study of nonlinear field equations. We show that the equation under investigation with the friction-like term is characterized by a finite-dimensional Lie algebra admitting a realization in terms of boson annhilation and creation operators. In absence of the friction-like term, the equation is linearized and connected with equations of the Bessel type. Examples of exact solutions are displayed, and the algebraic structure of the equation is discussed.

hep-th↗

arXiv1996

Algebraic properties of the 1+1 dimensional Heisenberg spin field model

The Estabrook-Wahlquist prolongation method is applied to the (compact and noncompact) continuous isotropic Heisenberg model in 1 + 1 dimensions. Using a special realization (an algebra of the Kac-Moody type) of the arising incomplete prolongation Lie algebra, a whole family of nonlinear field equations containing the original Heisenberg system is generated.

solv-int↗

arXiv1996

The symmetry structure of the heavenly equation

We show that excitations of physical interest of the heavenly equation are generated by symmetry operators which yields two reduced equations with different characteristics. One equation is of the Liouville type and gives rise to gravitational instantons, including those found by Eguchi-Hanson and Gibbons-Hawking. The second equation appears for the first time in the theory of heavenly spaces and provides meron-like configurations endowed with a fractional topological charge. A link is also established between the heavenly equation and the socalled Schr{ö}der equation, which plays a crucial role in the bootstrap model and in the renormalization theory.

hep-th↗

arXiv1996

Neutrino Mixing and Oscillations in Quantum Field Theory

We show that the generator of field mixing transformations in Quantum Field Theory induces a non trivial structure in the vacuum which turns out to be a coherent state, both for bosons and for fermions, although with a different condensate structure. The Fock space for mixed fields is unitarily inequivalent to the Fock space of the massive (free) fields in the infinite volume limit. As a practical application we study neutrino mixing and oscillations. A new oscillation formula is found where the oscillation amplitude is depressed, with respect to the usual one, by a factor which is momentum and mass dependent. In the relativistic limit, the usual formula is recovered. We finally discuss in some detail phenomenological features of the modified oscillation formula.

hep-ph↗

arXiv1995

Properties of equations of the continuous Toda type

We study a modified version of an equation of the continuous Toda type in 1+1 dimensions. This equation contains a friction-like term which can be switched off by annihilating a free parameter $\ep$. We apply the prolongation method, the symmetry and the approximate symmetry approach. This strategy allows us to get insight into both the equations for $\ep =0$ and $\ep \ne 0$, whose properties arising in the above frameworks are mutually compared. For $\ep =0$, the related prolongation equations are solved by means of certain series expansions which lead to an infinite- dimensional Lie algebra. Furthermore, using a realization of the Lie algebra of the Euclidean group $E_{2}$, a connection is shown between the continuous Toda equation and a linear wave equation which resembles a special case of a three-dimensional wave equation that occurs in a generalized Gibbons-Hawking ansatz \cite{lebrun}. Nontrivial solutions to the wave equation expressed in terms of Bessel functions are determined. For $\ep\,\ne\,0,$ we obtain a finite-dimensional Lie algebra with four elements. A matrix representation of this algebra yields solutions of the modified continuous Toda equation associated with a reduced form of a perturbative Liouville equation. This result coincides with that achieved in the context of the approximate symmetry approach. Example of exact solutions are also provided. In particular, the inverse of the exponential-integral function turns out to be defined by the reduced differential equation coming from a linear combination of the time and space translations. Finally, a Lie algebra characterizing the approximate symmetries is discussed.

solv-int↗

arXiv1995

Squeezed Neutrino Oscillations in Quantum Field Theory

By resorting to recent results on fermion mixing which show that the Fock space of definite flavor states is unitarily inequivalent to the Fock space of definite mass states, we discuss the phenomenological implications on the neutrino oscillation formula. For finite momentum the oscillation amplitude is depressed, or "squeezed", by a momentum dependent factor. In the relativistic limit the conventional oscillation formula is recovered.

hep-ph↗

arXiv1995

Integrable nonlinear field equations and loop algebra structures

We apply the (direct and inverse) prolongation method to a couple of nonlinear Schr{ö}dinger equations. These are taken as a laboratory field model for analyzing the existence of a connection between the integrability property and loop algebras. Exploiting a realization of the Kac-Moody type of the incomplete prolongation algebra associated with the system under consideration, we develop a procedure with allows us to generate a new class of integrable nonlinear field equations containing the original ones as a special case.

solv-int↗

arXiv1994

Two Extended Versions of the Continuous 2D-Heisenberg Model

We analyze two extended versions [the Ishimori model (IM) and a related system, which will be called modified Ishimori model (mIM)] of the continuous Heisenberg model in (2+1)-dimensions within the complex Hirota scheme. The IM, proposed in 1984, is an integrable (2+1)-dimensional topological spin field model which has been studied in many theoretical frameworks. The mIM has been introduced quite recently by some of the present authors [Phys. Rev. {\bf B 49}, 12915 (1994)]. Using the same stereographic variable in the Hirota formulation, we build up some new exact solutions both for the IM and the mIM in the compact and noncompact case. For the IM new configurations are a class of static solutions related to a special third Painlevé equation, time-dependent solutions linked to an other kind of the third Painlevé transcendent, and asympotic time-dependent solutions whose energy density behaves as Yukawa potential. For the mIM, new configurations are a class of exact solutions expressed in terms of elliptic functions, and a class of time-dependent solutions related to a particular form of the double sine-Gordon and the double sinh-Gordon equations with variable coefficients. We discuss the new configurations and certain known solutions which clarify the different possible phenomenological role played by the considered topological spin field models.

cond-mat↗

arXiv1994

Exact Solutions for Wave Propagation in Birefringent Optical Fibers

We carry out a group-theoretical study of the pair of nonlinear Schrödinger equations describing the propagation of waves in nonlinear birefringent optical fibers. We exploit the symmetry algebra associated with these equations to provide examples of specific exact solutions. Among them, we obtain the soliton profile, which is related to the coordinate translations and the constant change of phase.

cond-mat↗