Scalar Field In Two-dimensional Spacetime Research Articles

Connections between kinks with different asymptotics

In this letter, we show how to build bridges between field-theoretic models that have kink solutions with different asymptotic behavior. We study transformational properties of kinks in models with a real scalar field in two-dimensional space-time. We show how to obtain new models with solitons having different asymptotic behavior, using deformations with specific functions. In particular, starting from the well-known model, we obtain kinks with super-exponential, super-super-exponential, power-law, and logarithmic asymptotics. We also comment on how asymptotic behavior of stability potential and zero mode can be obtained for deformed kinks.

Quasi-compact Q-balls

This work deals with charged nontopological solutions that appear in relativistic models described by a single complex scalar field in two-dimensional spacetime. We study a model which supports novel analytical configurations of the Q-ball type, that engender double exponential tails, in this sense being different from both the standard and compact Q-balls. The analytical solutions are also stable, both classically and quantum-mechanically, and the stability follows as in the case of the compact configurations.

Novel connection between lump-like structures and quantum mechanics

This work deals with lump-like structures in models described by a single real scalar field in two-dimensional spacetime. We start with a model that supports lump-like configurations and use the deformation procedure to construct scalar field theories that support both lumps and kinks, with the corresponding stability investigation giving rise to new physical systems. Very interestingly, we find models that support stable topological solutions, with the stability potential being able to support a tower of non-negative bound states, generating distinct families of potentials of current interest to quantum mechanics. We also describe models where the lump-like solutions give rise to stability potentials that have the shape of a double-well.

Analytical study of kinklike structures with polynomial tails

This work deals with models described by a single real scalar field in two-dimensional spacetime. The aim is to propose potentials that support massless minima and investigate the presence of kinklike structures that engender polynomial tails. The results unveil the presence of families of asymmetric solutions with energy density and linear stability that behave adequately, enhancing the importance of the analytical study. We stress that the novel topological structures which we find in this work engender long range interactions that are of current interest to statistical mechanics, dipolar quantum gases and the study of quantum information with Rydberg atoms.

Compact structures in standard field theory

We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential equations and illustrate how to find compact structures in models engendering standard kinematics. In particular, we study linear stability and show that all the static solutions we have found are linearly stable.

From kinks to compactons

This work deals with the presence of localized structures in relativistic systems described by a single real scalar field in two-dimensional spacetime. We concentrate on kinks and compactons in models with standard kinematics, and we develop a procedure that helps us to smoothly go from kinks to compactons in the suggested scenario. We also show how the procedure works in the braneworld scenario, for flat brane in the five-dimensional spacetime with a single extra dimension of infinite extent. The brane unveils a hybrid profile when the kink becomes a compacton, behaving as a thick or thin brane, depending on the extra dimension being inside or outside a compact space.

Quantum complex scalar field in two-dimensional spacetime with closed timelike curves and a time-machine problem

The quantum complex scalar field which obeys the authomorphic condition in the two-dimensional spacetime with closed timelike curves and the chronology horizon is considered. The renormalized stress--energy tensor is obtained. It is shown that the value of the stress--energy tensor is regular at the chronology horizon for specific authomorphic parameters. Thus the particular example of a field configuration is given for which the Hawking's chronology protection conjecture is violated.

Vacuum polarization of a complex automorphic scalar field in two-dimensional spacetime with closed null geodesics and the time-machine problem

A quantized automorphic scalar field in two-dimensional spacetime with closed null geodesics (Cauchy horizon) is considered. The renormalized energy—momentum tensor 〈Tμv〉ren is obtained. It is shown that for specific values of the automorphic parameter 〈Tμv〉ren remains regular on the Cauchy horizon.

Heisenberg fields in the neighborhood of a classical solution

For the example of nonlinear models of a scalar field in two-dimensional space-time a study is made of a method of quantization in the neighborhood of a classical solution based on direct solution by perturbation theory of the Cauchy problem for the Heisenberg field equations. It is shown that, as in the classical Bogolyubov-Krylov method, zero modes and associated secular terms arise because of the perturbation-theory expansion of the Bogolyubov operator argument of the classical component. The Lehmann-Symanzik-Zimmermann procedure is used to make a complete investigation of the asymptotic states of the field in the soliton sector in the lowest orders of perturbation theory.

Free massless scalar field in two-dimensional space-time: Revisited

The indefinite-metric quantum field theory of the two-dimensional free massless scalar field proposed previously is reinvestigated. In order to reply to various criticisms of it, subtle points are discused in detail, and it is shown that the formalism is free from contradictions. In particular, its is emphasized that the non-uniqueness of the translationally invariant states is consistent with the irreducibility of the field algebra in the theory with indefinite metric.

The solitons in some geometrical field theories

Using the methods of differential geometry it is shown that the Born-Infeld scalar field in two-dimensional space-time and the relativistic string in three dimensions are described by the same non-linear Liouville equation utt-uxx=R eu. This equation admits soliton solutions which may be stable or unstable, and there are periodical solutions among the stable ones. In the quantum case the solitons can be interpreted as massive particles either stable or unstable with respect to the stability of the corresponding classical solution. The periodical soliton generates a series of resonances which have the equidistant mass spectrum. This result appears to be well suited to the theory of the closed relativistic string. In four dimensions the relativistic string is described by the same Liouville equation, but for the complex-valued function u.

Solitons in some geometrical field theories

Using the methods of differential geometry it is shown that the Born-Infeld scalar field in two-dimensional space-time and the relativistic string in three dimensions are described by the same non-linear Liouville equation utt-uxx=R eu. This equation admits soliton solutions which may be stable or unstable, and there are periodical solutions among the stable ones. In the quantum case the solitons can be interpreted as massive particles either stable or unstable with respect to the stability of the corresponding classical solution. The periodical soliton generates a series of resonances which have the equidistant mass spectrum. This result appears to be well suited to the theory of the closed relativistic string. In four dimensions the relativistic string is described by the same Liouville equation, but for the complex-valued function u.

Strong-coupling theory of a point particle and a neutral scalar field in two-dimensional spacetime

We formulate the strong-coupling theory for a system of a point particle interacting with a neutral scalar field in two-dimensional spacetime, treating the degree of freedom of the point particle rigorously. It is shown that the strong-coupling expansion (1/g expansion) becomes possible if the mass of the point particle is of order g/sup 2/. Higher-order corrections to the energy and the elastic point-particle--meson scattering amplitude are obtained to leading order.

Two-dimensional quantum field theories containing a massless scalar field

The following new findings are briefly reported: (a) A consistent quantum theory can be formulated for a free massless scalar field in two-dimensional spacetime. (b) Satisfactory operator solutions in terms of asymptotic fields can be constructed in the Thirring and Schwinger models. (c) Gauge invariance is spontaneously broken in the Thirring model as well as in the Schwinger model.

Free Massless Scalar Field in Two-Dimensional Space-Time

It is known that because of infrared divergence a free massless scalar field in two-dimensional space-time cannot be consistently quantized in a positive-difinite Hilbert space. It is shown that this difficulty can be overcome in the framework of the indefinite-metric quantum field theory. The positivity condition is recovered in a relativistically invariant physical subspace. Various properties of the free massless scalar field are studied in detail as the preliminaries for the investigation of the Thirring and Schwinger models.

Fermion states of a boson field

We construct certain non-Fock representations of the canonical commutation relations for the zero-mass scalar field in two-dimensional space-time. These are obtained from the free-field representation by applying localised automorphisms, are strongly locally Fock, and have a positive energy-momentum spectrum. The model is suggested by an early paper of Skyrme, and provides a concrete example of the algebraic theory of observables and charges. It satisfies some, but not all, of the postulates of Doplicher, Haag and Roberts. The Bose-Fermi alternative does not hold: instead, we find a continuum of representations which interpolates between the Bose and Fermi sectors. We are able to construct the local field algebra, which provides a unitary multiplier representation of a gauge group of the second kind.