Finite Spatial Volume Research Articles

Nonlinearσmodels solvable by the Aratyn-Ferreira-Zimerman ansatz

Nonlinear sigma models compatible with the aratyn-Ferreira-Zimerman ansatz are discussed, the latter ansatz automatically leading to configurations with definite values of the Hopf index. These models are allowed to involve a weight factor which is a function of one of the toroidal coordinates. Depending on the choice of the weight factor, the field equation takes various forms. In one model with a special weight factor, the field equation turns out to be the fifth Painleve equation. This model suggests the existence of a knot soliton strictly confined in a finite spatial volume. Some other interesting cases are also discussed.

The k -folded sine-Gordon model in finite volume

We consider the k-folded sine-Gordon model, obtained from the usual version by identifying the scalar field after k periods of the cosine potential. We examine (1) the ground state energy split, (2) the lowest lying multi-particle state spectrum and (3) vacuum expectation values of local fields in finite spatial volume, combining the Truncated Conformal Space Approach, the method of the Destri-de Vega nonlinear integral equation (NLIE) and semiclassical instanton calculations. We show that the predictions of all these different methods are consistent with each other and in particular provide further support for the NLIE method in the presence of a twist parameter. It turns out that the model provides an optimal laboratory for examining instanton contributions beyond the dilute instanton gas approximation. We also provide evidence for the exact formula for the vacuum expectation values conjectured by Lukyanov and Zamolodchikov.

The fixed point action for the Schwinger model: a perturbative approach

We compute the fixed point action of a properly defined renormalization group transformation for the Schwinger model through an expansion in the gauge field. It is local, with couplings exponentially suppressed with the distance. We check its perfection by computing the 1-loop mass gap at finite spatial volume, finding only exponentially vanishing cut-off effects, in contrast with the standard action, which is affected by large power-like cut-off effects. We point out that the 1-loop mass gap calculation provides a check of the classical perfection of the fixed point action, and not of the 1-loop perfection, as could be naively expected.

The fixed point action of the Schwinger model

We compute the fixed point action for the Schwinger model through an expansion in the gauge field. The calculation allows a check of the locality of the action. We test its perfection by computing the 1-loop mass gap at finite spatial volume.

Quantum fields in hyperbolic spacetimes with finite spatial volume

The 1-loop effective action for a massive self-interacting scalar field is investigated in four-dimensional ultrastatic spacetime , where is a non-compact hyperbolic manifold with finite volume. Making use of the Selberg trace formula, the -function related to the small disturbance operator is constructed. For an arbitrary gravitational coupling, it is found that has a simple pole at s = 0. The 1-loop effective action is analysed by means of proper-time regularizations and the 1-loop divergences are found explicitly. It is pointed out that, in this special case, -function regularization also requires a divergent counterterm, which however is not necessary in the free massless conformal invariant coupling case. Finite-temperature effects are studied and a high-temperature expansion is presented. A possible application to the problem of the divergences of the entanglement entropy for a free massless scalar field in a Rindler-like spacetime is briefly discussed.

Finite particle creation in 1+1 dimensional spacetime compact in space

In this paper we calculate the massive particle creation as seen by a stationary observer in a 1+1 dimensional spacetime compact in space. The Bogoliubov transformation relating the annihilation and creation operators between two spacelike surfaces is calculated. The particle creation, as observed by a stationary observer who moves from the first spacelike surface to the second, is then calculated and shown to be finite, as is expected for a spacetime with finite spatial volume.

Gravitation in 2+1 dimensions.

We investigate gravitational field theories in 2+1-spacetime dimensions. The consequences of the lack of a Newtonian limit to general relativity are reviewed. Further insight into the implications of this fact is gained by considering a new, general class of exact hydrostatic solutions. We show that all self-gravitating polytropic structures have the same gravitational mass and produce matter-filled spaces of finite spatial volume. Other theories of gravitation are also considered and the behavior of one such theory with a Newtonian limit is studied. Cosmological solutions of these gravitational theories are also studied in detail.

Tunneling amplitude and surface tension in Φ4-theory

If four-dimensional Φ 4-theory in the broken symmetry phase is enclosed in a finite spatial volume L 3 the double degeneracy of states is lifted due to tunneling. The energy splitting between the two lowest states vanishes exponentially with the volume, the coefficient of L 3 being the ‘surface tension”. This finite volume effect is important for numerical studies of Φ 4-theory or the Ising model. In this article the energy splitting and the associated surface tension are calculated by semiclassical methods including one-loop corrections.

Volume dependence of the mass gap for the O(3) nonlinear σ-model: A Monte Carlo study

Abstract The mass gap of the O(3) nonlinear σ-model is investigated by enclosing the system into a finite spatial volume. The main emphasis is put on the comparison of the Monte Carlo results with the analytic predictions available for small and large volume. By a complete reconstruction of the volume dependence we find that the infinite-volume mass gap is consistent with previous numerical results based on the standard action. Our analysis allows to follow the β-function deep into the perturbative domain.

Finite spatial volume approach to finite temperature field theory

A relativistic quantum field theory at finite temperature T = β−1 is equivalent to the same field theory at zero temperature but with one spatial dimension of finite length β. This equivalence is discussed for scalars, for fermions, and for gauge theories. The relationship is checked for free field theory. The translation of correlation functions between the two formulations is described with special emphasis on the nonlocal order parameters of gauge theories. Possible applications are mentioned.