Particle creation in asymptotically Minkowskian spacetimes

Exact solutions of Klein–Gordon and Dirac equations are obtained for two classes of Robertson–Walker (RW) spacetimes with asymptotically Minkowskian regions. One class is Minkowskian in the remote past and future. In this class in$in$ and out$out$ vacua are well defined, because the scale factor reduces to a constant at the asymptotic regions. Another class is asymptotically flat only in the far past. Using the obtained exact solutions we calculate the density of scalar and Dirac particles created through the Bogolubov transformations technique. For Dirac field it is shown that the rates of creation of particles and antiparticles are equal.     

Scattering on the hyperbolic plane in the Aharonov-Bohm gauge field

The scattering of a quantum charged particle on the hyperbolic plane in the Abelian Aharonov-Bohm field is considered. S-matrix, scattering amplitude and its flat space limit are constructed in a closed form by the Sommerfeld integral approach.     

Unconstrained supersymmetry

This is a first step towards better superfield formulations of supersymmetric field theories. The simple Wess-Zumino model (including renormalizable interactions) is formulated in terms of an unconstrained, scalar superfield, obeying a wave equation that includes the square of the super Klein-Gordon operator. This wave equation is derived from an action principle, by unconstrained variation of the superfield. The physical content of the theory is the same as for the original formulation by Wess and Zumino, and the Feynman rules are identical to those of Grisaru, Roek and Siegel. Next, super electrodynamics, including minimal interactions with a scalar matter multiplet, is given a similar treatment. There is no need, in this case, to include higher derivatives in the Lagrangian. The matter field is an unconstrained, scalar superfield, and the gauge fields are also contained in an unconstrained, scalar superfield. The scattering matrix coincides with that of the conventional form of super electrodynamics with Wess-Zumino matter fields. Supersymmetric spinorial currents are found by simple and direct application of the Noetherian method, in superfield language. Conservation laws of the formD _a J ^a =0 (resp.D _a J ^ab =0) are derived from gauge invariance (resp. supersymmetry). Extension to super Yang-Mills theories is straightforward.On leave of absence from Universidad Complutense, Madrid. Permanent address: Department of Theoretical Physics, Universidad Complutense, 28040 Madrid, Spain.     

A classical solution of scalar-spinor interaction models with higher derivatives on even-dimensional spaces

We propose a new higher-dimensional model with scalar-spinor interaction on even-dimensional spaces, which is a generalization of the model discussed by Akdeniz and Dane on two-dimensional spaces, and construct an instaton-like solution.     

Free particle in q-deformed configuration space

The SO _q (N)-invariant Schrödinger equation for the free particle is formulated in polar coordinates as a partial differential equation in noncommutative geometry. For each value of the total angular momentum, a Hilbert space of radial functions is constructed as the space of normalizable functions respective to the q-integral. The spectrum of the Hamiltonian is found to be discrete.     

The gravitational anomalies in de Sitter space

All solutions to the consistency equations are determined which have to be satisfied by anomalies in gravitational theories with a de Sitter-invariant groundstate. They turn out to be identical with the solutions for a Poincaré-invariant groundstate.     

On the equivalence of the Lagrangians of massless dirac and supersymmetrical particles

The classical equivalence between the Lagrangians of massless spinning and supersymmetrical particles presented in terms of u _A and Grassmannian _A Weyl spinor variables is established. It is shown that the condition of the inverse Higgs effect for a spinor invariant superform leads to the extension of the Penrose representation and the realization of fermionic string variables in terms of superstring variables. New superfield formulations of the actions for particles and strings invariant under local (world-sheet) and global (spacetime) supersymmetrics are suggested.     

Modular inclusion,the Hawking temperature,and quantum field theory in curved spacetime

A recent result by Borchers connecting geometric modular action, modular inclusion and spectrum condition, is applied in quantum field theory on spacetimes with a bifurcate Killing horizon (these are generalizations of black-hole spacetimes, comprising the familiar black-hole spacetime models). Within this framework, we give sufficient, model-independent conditions ensuring that the temperature of thermal equilibrium quantum states is the Hawking temperature.     

Schrödinger equations for su q (2)-invariant quantum systems

By deforming the Hamiltonian of a spinless particle in a central potential we set up su _q (2)-invariant Schrödinger equations within the usual framework of quantum mechanics. Different deformations correspond to a given Hamiltonian. We explicitly solve different stationary Schrödinger equations for the free particle and for the hydrogen atom, and compare the associated energy spectra.     

Sp(2) renormalization

The renormalization of general gauge theories on flat and curved space–time backgrounds is considered within the Sp(2)-covariant quantization method. We assume the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Sp(2)-covariant formalism one can show that the theory possesses gauge-invariant and diffeomorphism invariant renormalizability to all orders in the loop expansion and the extended BRST-symmetry after renormalization is preserved. The advantage of the Sp(2) method compared to the standard Batalin–Vilkovisky approach is that, in reducible theories, the structure of ghosts and ghosts for ghosts and auxiliary fields is described in terms of irreducible representations of the Sp(2) group. This makes the presentation of solutions to the master equations in more simple and systematic way because they are Sp(2)-scalars.     

Antilocality and a Reeh-Schlieder theorem on manifolds

It is shown that the operatorA ^1/2, whereA is any positive self-adjoint extension of a positive operator of the form -Laplace-Beltrami operator +potential on ann-dimensional Riemannian manifold, is strongly antilocal. Using this result, a Reeh-Schlieder theorem for the canonical vacuum of the Klein-Gordon field propagating in ultrastatic spacetimes is derived. In a further application, we gain weaker versions of the Reeh-Schlieder theorem for more general situations.Supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

Dijkgraaf–Witten invariants of surfaces and projective representations of groups

We compute the Dijkgraaf–Witten invariants of surfaces in terms of projective representations of groups. As an application we prove that the complex Dijkgraaf–Witten invariants of surfaces of positive genus are positive integers.     

Nuclearity,split property,and duality for the Klein-Gordon field in curved spacetime

Nuclearity, split property and duality are established for the nets of von Neumann algebras associated with the representations of distinguished states of the massive Klein-Gordon field propagating in particular classes of curved spacetimes.Supported by the DFG.     

On the Grassmannian Special Functions I

A generalization of the notion of a special function to the case of anticommuting variables is presented. In particular, Grassmann-Hermite multinomials are obtained and their elementary properties are displayed.Work partially supported by Research Program of the Polish Ministry of Higher Education, RPI 10.     

Stochastic quantisation of a gauge field in the spatial axial gauge

The stochastic quantisation method of Nelson can be applied to quantise an Abelian gauge field in the spatial axial gauge.     

Elliptic Wess-Zumino-Witten model from elliptic Chern-Simons theory

This Letter continues the program aimed at analysing of the scalar product of states in the Chern-Simons theory. It treats the elliptic case with group SU₂. The formal scalar product is expressed as a multiple finite-dimensional integral which, if convergent for every state, provides the space of states with a Hilbert space structure. The convergence is checked for states with a single Wilson line where the integral expressions encode the Bethe Ansatz solutions of the Lamé equation. In relation to the Wess-Zumino-Witten conformal field theory, the scalar product renders unitary the Knizhnik-Zamolodchikov-Bernard connection and gives a pairing between conformal blocks used to obtain the genus-one correlation functions.     

Cosmological principle and primordial spinor fields

An exact solution of Dirac's equation in an open Robertson-Walker universe is constructed such that the corresponding energy-momentum densityT _µv obeys the cosmological principle. However, in anopen universe, this principlemust always be violated by the other physical densities of the cosmological solution (e.g. pseudoscalar, (axial-) current and polarization). If the current densityj _µ = isrequired to obey the cosmological principle, then the universe must beflat.     

Resummation of Mass Terms in Perturbative Massless Quantum Field Theory

The neutral massless scalar quantum field Φ in four-dimensional space-time is considered, which is subject to a simple bilinear self-interaction. Is is well-known from renormalization theory that adding a term of the form to the Lagrangean has the formal effect of shifting the particle mass from the original zero value to m after resummation of all two-leg insertions in the Feynman graphs appearing in the perturbative expansion of the S-matrix. However, this resummation is accompanied by some subtleties if done in a proper mathematical manner. Although the model seems to be almost trivial, is shows many interesting features which are useful for the understanding of the convergence behavior of perturbation theory in general. Some important facts in connection with the basic principles of quantum field theory and distribution theory are highlighted, and a remark is made on possible generalizations of the distribution spaces used in local quantum field theory. A short discussion how one can view the spontaneous breakdown of gauge symmetry in massive gauge theories within a massless framework is presented.