The Casimir effect for fields with arbitrary spin

The Casimir force arises when a quantum field is confined between objects that apply boundary conditions to it. In a recent paper we used the two-spinor calculus to derive boundary conditions applicable to fields with arbitrary spin in the presence of perfectly reflecting surfaces. Here we use these general boundary conditions to investigate the Casimir force between two parallel perfectly reflecting plates for fields up to spin-2. We use the two-spinor calculus formalism to present a unified calculation of well-known results for spin-1/2 (Dirac) and spin-1 (Maxwell) fields. We then use our unified framework to derive new results for the spin-3/2 and spin-2 fields, which turn out to be the same as those for spin-1/2 and spin-1. This is part of a broader conclusion that there are only two different Casimir forces for perfectly reflecting plates—one associated with fermions and the other with bosons.     

Exact diffraction calculation from fields specified over arbitrary curved surfaces

Calculation of the scalar diffraction field over the entire space from a given field over a surface is an important problem in computer generated holography. A straightforward approach to compute the diffraction field from field samples given on a surface is to superpose the emanated fields from each such sample. In this approach, possible mutual interactions between the fields at these samples are omitted and the calculated field may be significantly in error. In the proposed diffraction calculation algorithm, mutual interactions are taken into consideration, and thus the exact diffraction field can be calculated. The algorithm is based on posing the problem as the inverse of a problem whose formulation is straightforward. The problem is then solved by a signal decomposition approach. The computational cost of the proposed method is high, but it yields the exact scalar diffraction field over the entire space from the data on a surface.     

Cubic interaction vertices for fermionic and bosonic arbitrary spin fields

Using the light-cone gauge approach to relativistic field dynamics, we study arbitrary spin fermionic and bosonic fields propagating in flat space of dimension greater than or equal to four. Generating functions of parity invariant cubic interaction vertices for totally symmetric and mixed-symmetry massive and massless fields are obtained. For the case of totally symmetric fields, we derive restrictions on the allowed values of spins and the number of derivatives. These restrictions provide a complete classification of parity invariant cubic interaction vertices for totally symmetric fermionic and bosonic fields. As an example of application of the light-cone formalism, we obtain simple expressions for the Yang–Mills and gravitational interactions of massive arbitrary spin fermionic fields. For some particular cases, using our light-cone cubic vertices, we discuss the corresponding manifestly Lorentz invariant and on-shell gauge invariant cubic vertices.     

General trilinear interaction for arbitrary even higher spin gauge fields

Using Noether's procedure we present a complete solution for the trilinear interactions of arbitrary spins s₁$s_1$, s₂$s_2$, s₃$s_3$ in a flat background, and discuss the possibility to enlarge this construction to higher order interactions in the gauge field. Some classification theorems of the cubic (self)interaction with different numbers of derivatives and depending on relations between the spins are presented. Finally the expansion of a general spin s gauge transformation into powers of the field and the related closure of the gauge algebra in the general case are discussed.     

Free massless fermionic fields of arbitrary spin in d-dimensional anti-de sitter space

Free massless fermionic fields of arbitrary spins, corresponding to fully symmetric tensor-spinor irreducible representations of the flat little group SO(d−2), are described in d-dimensional anti-de Sitter space in terms of differential forms. Appropriate linearized higher-spin curvature 2-forms are found. Explicitly gauge invariant higher-spin actions are constructed in terms of these linearized curvatures.     

Explicit construction of conserved currents for massless fields of arbitrary spin

We give an explicit construction of conserved currents for massless fields of arbitrary spin. These currents are gauge invariant and conserved on shell. Also they allow for the construction of a large class of trilinear interaction terms for the interaction between a massless spin-s₁ field and two spin-s₂ fields. The class is restricted only to 2s₂⩽s₁. In case s₁ = 4 and s₂ = 2, the current is the linearized Bel-Robinson tensor. To these conserved currents corresponds an infinite dimensional Lie algebra of global infinitesimal invariances of the action of a free massless field of arbitrary spin.     

New twistorial integral formulas for massless free fields of arbitrary spin

A manifestly scaling-invariant version of the Kirchoff-D'Adhemar-Penrose field integrals is presented. The invariant integral expressions for the spinning massless free fields are directly transcribed into the framework of twistor theory. It is then shown that the resulting twistorial field integrals can be thought of as being equivalent to the universal Penrose contour integral formulas for these fields.     

Some remarks on zeta function regularization in curved space-times

The question of to what extent zeta function regularization respects the invariances of a quantum field theory in a background gravitational field is investigated. It is shown that zeta function regularization provides a generalization to curved space-time of analytic propagator regularization which is known not to respect gauge invariance. Furthermore, a study of the regularized stress tensor of a conformally invariant scalar field indicates that both conformai and general coordinate invariance are violated.     

Conformal invariant two and three-point functions for fields with arbitrary spin

The conformal invariant two and three-point functions for any “fundamental” fields with an arbitrary spin and scale dimensions are found in the Minkowsky x-space. The two-point functions for Dirac, symmetric and antisymmetric tensor fields are given. The three-point functions for two Dirac fields and one symmetrical tensor field, as well as any other field for which this function is nonvanishing, are given. In the case of conserved currents the Ward identities are considered.     

Generalized spin structures on four dimensional space-times

We discuss various methods for investigating the existence and uniqueness of generalized spin structures. We show that on a four dimensional manifold whole families may be constructed using any internal symmetry group of the formG/₂, whereG is a simply connected Lie group.     

On quantization of free fields in stationary space-times

In Section 1 we analyse the structure of the infinite-dimensional Hamiltonian system described by the Klein-Gordon equation (free real scalar field) in stationary space-times with closed space sections; we give an existence and uniqueness theorem for the Lichnerowicz distribution kernelG ₁ together with its proper Fourier expansion, and we construct the Hilbert spaces of frequency-part solutions defined by means ofG ₁.In Section 2 an analysis, a theorem and a construction similar to the above are formulated for thefree real field spin 1, massm>0, in one kind of static space-times.In this letter, only results are given. For detailed proofs and further results, see reference [9], [10] and [11].     

Temperature in Friedmann thermodynamics and its generalization to arbitrary space-times

In recent articles we have introduced Friedmann thermodynamics, where certain geometric parameters in Friedmann models were treated like their thermodynamic counterparts (temperature, entropy, Gibbs potential, etc.). This model has the advantage of allowing us to determine the geometry of the universe by thermodynamic stability arguments. In this paper, in search for evidence for the definition of gravitational temperature, we will investigate a massless conformal scalar field in an Einstein universe in detail. We will argue that the gravitational temperature of the Einstein universe is given asT _g=1/2) (c/k) (1/R ₀), where R₀ is the radius of the Einstein universe. This is in accord with our definition of gravitational temperature in Friedmann thermodynamics and determines the dimensionless constant as 1/2. We discuss the limitations of the model we are using. We also suggest a method to generalize our gravitational temperature to arbitrary space-times granted that they are sufficiently smooth.Based on three essays awarded honorable mention in the years 1987, 1988 and 1989 by the Gravity Research Foundation—Ed.     

Cauchy's problem and Huygens' principle for relativistic higher spin wave equations in an arbitrary curved space-time

Relativistic spins (s >/ 1/2), nonzero mass equations are given which in an arbitrary curved space-time are internally consistent. By means of Riesz' integration method a representation theorem for the solution of Cauchy's problem, using the constraints of the Cauchy data on the initial hypersurface and suitable Green's formulas, is proved. Finally, a necessary and sufficient condition for the validity of Huygens' principle is stated from which it follows that only in space-times of constant curvature do the field equations satisfy Huygens' principle.     

The hypergeneralized Heun equation in quantum field theory in curved space-times

We show for the first time the role played by the hypergeneralized Heun equation (HHE) in the context of quantum field theory in curved space-times. More precisely, we find suitable transformations relating the separated radial and angular parts of a massive Dirac equation in the Kerr-Newman-deSitter metric to a HHE.     

Characterizing killing vector fields of standard static space-times

We provide a global characterization of the Killing vector fields of a standard static space-time by a system of partial differential equations. By studying this system, we determine all the Killing vector fields in the same framework when the Riemannian part is compact. Furthermore, we deal with the characterization of Killing vector fields with zero curl on a standard static space-time.     

Local quantum statistics in arbitrary curved space-time

A local quantum statistics based on a finite temperature field theory in an arbitrary Riemann space-time is considered. The expressions have been derived for the partition functions, the grand thermodynamic potential and the particle distributions 〈n _k〉 of massive scalar gas and fermion gas in arbitrary space-time. It is shown that the chemical potential depends on the geometry of manifold.