Two-dimensional Scalar Field Theory Research Articles

Self-gravitating kinks in two-dimensional pseudo-Riemannian universes

Two-dimensional scalar field theories with spontaneous symmetry breaking subject to the action of Jackiw-Teitelboim gravity are studied. Solutions for the $\phi^4$ and sine-Gordon self-gravitating kinks are presented, both for general gravitational coupling and in the perturbative regime. The analysis is extended to deal with a hierarchy of kinks related to transparent P\"{o}schl-Teller potentials

Cooling stochastic quantization with colored noise

Smoothing of field configurations is highly important for precision calculations of physical quantities on the lattice. We present a cooling method based on Stochastic Quantization with a built-in UV momentum cutoff. The latter is implemented via a UV-regularized, hence colored, noise term. Our method is tested in a two-dimensional scalar field theory. We show, that UV modes can be removed systematically without altering the physics content of the theory. The approach has an interpretation in terms of the non-perturbative (Wilsonian) renormalization group that facilitates the physics interpretation of the cutoff procedure. It also can be used to define the maximal colored cooling applicable without changing the theory.

Highly nonlinear wave solutions in a dual to the chiral model

We consider a two-dimensional scalar field theory with a nilpotent current algebra, which is dual to the Principal Chiral Model. The quantum theory is renormalizable and not asymptotically free: the theory is strongly coupled at short distances (encountering a Landau pole). We suggest it can serve as a toy model for $\lambda\phi^{4}$ theory in four dimensions, just as the principal chiral model is a useful toy model for Yang-Mills theory. We find some classical wave solutions that survive the strong coupling limit and quantize them by the collective variable method. They describe excitations with an unusual dispersion relation $\omega\propto|k|^{\frac{2}{3}}$ . Perhaps they are the "preons" at strong coupling, whose bound states form massless particles over long distances.

Kink-boundary collisions in a two-dimensional scalar field theory

In a two-dimensional toy model, motivated from five-dimensional heterotic M-theory, we study the collision of scalar field kinks with boundaries. By numerical simulation of the full two-dimensional theory, we find that the kink is always inelastically reflected with a model-independent fraction of its kinetic energy converted into radiation. We show that the reflection can be analytically understood as a fluctuation around the scalar field vacuum. This picture suggests the possibility of spontaneous emission of kinks from the boundary due to small perturbations in the bulk. We verify this picture numerically by showing that the radiation emitted from the collision of an initial single kink eventually leads to a bulk populated by many kinks. Consequently, processes changing the boundary charges are practically unavoidable in this system. We speculate that the system has a universal final state consisting of a stack of kinks, their number being determined by the initial energy.

Low-energy expansion of the one-loop type-II superstring amplitude

The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s^4 log s R^4, where R^4 denotes a specific contraction of four linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the two-dimensional scalar field theory propagator over the toroidal world-sheet as well as the moduli of the torus. The values of these coefficients match expectations based on duality relations between string theory and eleven-dimensional supergravity.

Tricritical behavior of two-dimensional scalar field theories.

We compute by Monte Carlo numerical simulations the critical exponents of two-dimensional scalar field theories at the $\lambda\phi^6$ tricritical point. The results are in agreement with the Zamolodchikov conjecture based on conformal invariance.

COMPLEX q-ANALYSIS AND SCALAR FIELD THEORY ON A q-LATTICE

We develop the basic formalism of complex q-analysis to study the solutions of second order q-difference equations which reduce, in the q → 1 limit, to the ordinary Laplace equation in Euclidean and Minkowski space. After defining an inner product on the function space we construct and study the properties of the solutions, and then apply this formalism to the Schrödinger equation and two-dimensional scalar field theory.

Tunneling at finite temperature

In a two-dimensional scalar field theory the rate of the metastable vacuum decay at finite temperature is calculated.

Partition function for two-dimensional solitons

The partition function for two-dimensional scalar field theories which possess soliton states, is constructed in the semi-classical approximation. Divergences are handled by using zeta-function methods. The result is naturally interpretated after the appropriate mass renormalisations, as being that due to a massive particle confined in a box.

Two-loop quantum corrections to the soliton mass in two-dimensional scalar field theories

We study higher-order corrections to the soliton mass in two-dimensional scalar field theories. We show that the second quantum correction (two-loop graphs) to the soliton mass ( M S) is finite provided one orders correctly the non-commuting operators in the effective hamiltonian. That is, the vacuum sector UV counterterm suffices to eliminate the ultraviolet and infinite volume divergences of the one-soliton sector. We evaluate explicitly the finite part of the second quantum correction to M S in the sine-Gordon model. We find that the ratio of the soliton mass to the meson mass is the same in our perturbative calculation, as in the semiclassical one by Dashen, Hasslacher and Neveu, up to two-loop contributions.

Mass formulas for static solitons

General explicit formulas are derived for the first quantum-mechanical correction to the mass of a static soliton in a weakly-coupled two-dimensional scalar field theory.

Asymptotic behavior of the elastic form factor in two-dimensional scalar field theory of the bag model

In the framework of the two-dimensional scalar quantum theory of the bag model of Chodos et al. a definition of the physical field and a general scheme for constructing a physical state are given. We expose some of the difficulties associated with such an approach. Expressions for the physical current and the elastic form factor are given. The calculation of the latter is restricted at first to the approximation in which the mapping from a bag of changing shape to a fixed domain is realized only by a term which is a diagonal, bilinear function of the creation and annihilation operators. This is done for the case of a one-mode and an infinite-mode bag theory. By computing the form factor in an exact one-mode bag model we show that the logarithmic falloff of the asymptotic term is the same as the one in the approximation. On the basis of this a form for the asymptotic behavior of the form factor is suggested which may be correct for the general two-dimensional scalar bag theory.