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.     

Infrared regularization of the massless scalar free field in two-dimensional space-time via Lorentz expansion

It is shown that Lorentz harmonics provide a natural basis for the expansion and infrared regularization of a massless scalar field in two dimensions. The negative metric operators separate out simply. Each Lorentz component of the field is partially local.     

On free massless (pseudo)scalar quantum field theory in 1+1-dimensional space-time

We construct a consistent quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-times free of infrared divergences. We show that in such a quantum field theory (i) a continuous symmetry of (pseudo)scalar field translations is spontaneously broken, (ii) Goldstone bosons appear as quanta of a free massless (pseudo)scalar field and (iii) there is a non-vanishing spontaneous {magnetization}. In spite of the existence of a spontaneous {magnetization} the main inequality between vacuum expectation values of certain operators which have been used for the derivation of the Mermin–Wagner–Hohenberg theorem (C. Itzykson and J.-M. Drouffe, {Statistical field theory}, Vol. I, 1989, pp. 219–224) is fulfilled. Received: 19 December 2001 / Revised version: 31 March 2002 / Published online: 14 June 2002     

On the bound states of the massless free field in two space-time dimensions

We point out the peculiar kinematics of zero-mass fields in two space-time dimensions by showing that the n-fold tensor product of one-particle representations of the Poincaré group for n ? 2 contains a countable infinity of discrete, zero-mass representations. We relate this result to the well-known “bound” states in every charge sector of the fermion Fock space.     

Fourier representation for the two-point function of the two-dimensional massless scalar field

The Fourier transform of the (indefinite metric) Wightman two-point function of a free massless scalar quantum field in two-dimensional spacetime has been inconsistently reported by various authors. We compute the correct one from the definition of the Fourier transform of tempered distributions.     

The exponential of the two-dimensional massless scalar field as an infrared Jaffe field

The definition of the Wick exponential of the massless scalar field in two dimensions as an operator-valued distribution is discussed in the Krein space realization of the field. It is shown that the exponential Wick power series converges strongly on a suitably dense domain, provided that it is smeared with test functions which satisfy some growth conditions in configuration space. Such conditions are similar to the high energy bounds previously introduced by Jaffe for the definition of strictly localizable fields. In this case it is found that the Wick exponential is strictly localizable in momentum space.     

Parameter estimation in n-dimensional massless scalar field

Quantum Fisher information(QFI) associated with local metrology has been used to parameter estimation in open quantum systems. In this work, we calculated the QFI for a moving Unruh–De Witt detector coupled with massless scalar fields in n-dimensional spacetime, and analyzed the behavior of QFI with various parameters, such as the dimension of spacetime, evolution time, and Unruh temperature. We discovered that the QFI of state parameter decreases monotonically from 1 to 0 over time. Additionall...     

Modular structure of the local algebras associated with the free massless scalar field theory

The modular structure of the von Neumann algebra of local observables associated with a double cone in the vacuum representation of the free massless scalar field theory of any number of dimensions is described. The modular automorphism group is induced by the unitary implementation of a family of generalized fractional linear transformations on Minkowski space and is a subgroup of the conformal group. The modular conjugation operator is the anti-unitary implementation of a product of time reversal and relativistic ray inversion. The group generated by the modular conjugation operators for the local algebras associated with the family of double cone regions is the group of proper conformal transformations. A theorem is presented asserting the unitary equivalence of local algebras associated with lightcones, double cones, and wedge regions. For the double cone algebras, this provides an explicit realization of spacelike duality and establishes the known typeIII ₁ factor property. It is shown that the timelike duality property of the lightcone algebras does not hold for the double cone algebras. A different definition of the von Neumann algebras associated with a region is introduced which agrees with the standard one for a lightcone or a double cone region but which allows the timelike duality property for the double cone algebras. In the case of one spatial dimension, the standard local algebras associated with the double cone regions satisfy both spacelike and timelike duality.Supported by the National Science Foundation under Grant No. PHY-79-23251Supported in part by C. N. R.     

Gravitational stability of a massless scalar field

A solution is obtained to the Einstein equations for a static, spherically symmetric, massless scalar field. The stability of a static, massless scalar field for a point source is studied. It is found that the field is unstable for small ratios of the scalar charge of the source to its mass but is stable for large ratios. It is proven that there exists a dimensionless number which limits the region of stability for the field.Translated from Izvestiya Vysshikh Uchebnyk Zavedenii, Fizika, No. 7, pp. 79–83.     

Massive or massless scalar field and confinement

The generalization of QCD motivated classical SU(2) Yang-Mills theory coupled to a scalar field is discussed. The massive scalar field, corresponding to the scalar glueball, provides a confining potential for static, point-like, external sources. In the case of a massless scalar field screening solutions are found. However, there is a confining sector as well. Both, massive and massless confining solutions, are compared with phenomenological potentials. The case of a non-dynam ical permittivity is also discussed. Received: 15 November 2002 / Revised version: 31 January 2003 / Published online: 7 March 2003 RID="a" ID="a" e-mail: mslus@phys.ualberta.ca RID="b" ID="b" e-mail: wereszcz@alphas.if.uj.edu.pl     

Two-dimensional quantum field theories containing a massless scalar field

The following new findings are briefly reported:

1. A consistent quantum theory can be formulated for a free massless scalar field in two-dimensional spacetime.
2. Satisfactory operator solutions in terms of asymptotic fields can be constructed in the Thirring and Schwinger models.
3. Gauge invariance is spontaneously broken in the Thirring model as well as in the Schwinger model.

     

Long-range scalar field in conformally flat space-time

Consequences of a massless scalar field in conformally flat space-time are studied. Then a wide class of solutions of the scalar field is obtained.     

Nonstatic solutions for the repulsive massless scalar field Einstein equation

Presented in this paper are exact nonstatic solutions for the coupled repulsive sourceless massless scalar field and the gravitational field. The solutions have the same form as the spatially conformally flat static metricds ² =e ^2ψ dt ² +e ^?2ψ(dx ² +dy ² +dz ²).     

Classical limit of the Casimir entropy for scalar massless field

We study the Casimir effect at finite temperature for a massless scalar field in the parallel plates geometry in N spatial dimensions, under various combinations of Dirichlet and Neumann boundary conditions on the plates. We show that in all these cases the entropy, in the limit where energy equipartitioning applies, is a geometrical factor whose sign determines the sign of the Casimir force.     

Resonant frequencies of massless scalar field in rotating black-brane spacetime

This paper investigates the resonant frequencies of the massless scalar field in the near extremal Kerr-like black-brane spacetime. It is shown that the different angular quantum number will present different resonant frequencies. It is also shown that the real part of the resonant frequencies increases as the compact dimensions parameter μi increases, but the magnitude of the imaginary part decreases as μi increases.     

Electromagnetic interpretation of the massless spin-1 field equation in curved space-time

The source-free Maxwell equations associated to the massless spin-1 free field equation are considered in curved space-time. The gauge invariance of the theory is discussed by using as starting point the notion of the spinor potential. The structure of the electromagnetic field in the case of the Robertson-Walker space-time is discussed by using the solutions of the massless spin-1 equations previously determined. The flat-universe case of the standard cosmology is studied exactly and considered in some limiting physical situations.     

The problem of scalar field theory in curved space-time

It is demonstrated that (1) there exist infiniteG ₁ that satisfy Lichnerowicz's conditions (L conditions) in a globally hyperbolic manifold; and, (2) there is noG ₁ in an expanding universe that would satisfy those conditions and that would behave as the ordinary ₁ of flat space whenx x. The author thinks that these results present a serious problem for finding a semiclassical theory of scalar field in curved space-time.