Free Massless Field Research Articles

Higher spin fields in Siegel space, currents and theta functions

Dynamics of four-dimensional massless fields of all spins is formulated in the Siegel space of complex $4\times 4$ symmetric matrices. It is shown that the unfolded equations of free massless fields, that have a form of multidimensional Schrodinger equations, naturally distinguish between positive- and negative-frequency solutions of relativistic field equations, i.e. particles and antiparticles. Multidimensional Riemann theta functions are shown to solve massless field equations in the Siegel space. We establish the correspondence between conserved higher-spin currents in four-dimensional Minkowski space and those in the ten-dimensional matrix space. It is shown that global symmetry parameters of the current in the matrix space should be singular to reproduce a nonzero current in Minkowski space. The $\D$-function integral evolution formulae for 4d massless fields in the Fock-Siegel space are obtained. The generalization of the proposed scheme to higher dimensions and systems of higher ranks is considered.

Thermal Casimir effect with soft boundary conditions

We consider the thermal Casimir effect in systems of parallel plates coupled to a massless free field theory via quadratic interaction terms which suppress (i) the field on the plates and (ii) the gradient of the field in the plane of the plates. These boundary interactions correspond to (i) the presence of an electrolyte in the plates and (ii) a uniform field of dipoles, in the plates, which are polarizable in the plane of the plates. These boundary interactions lead to Robin-type boundary conditions in the case where there is no field outside the two plates. In the appropriate limit, in both cases Dirichlet boundary conditions are obtained but we show that in case (i) the Dirichlet limit breaks down at short interplate distances and in (ii) it breaks down at large distances. The behavior of the two plate system is also seen to be highly dependent on whether the system is open or closed. In addition we analyze the Casimir force on a third plate placed between two outer plates. The force acting on the central plate is shown to be highly sensitive to whether or not the fluctuating scalar field is present in the region exterior to the two confining plates.

Vacuum boundary effects

The effect of boundary conditions on the vacuum structure of quantum field theories is analysed from a quantum information viewpoint. In particular, we analyse the role of boundary conditions on boundary entropy and entanglement entropy. The analysis of boundary effects on massless free field theories points out the relevance of boundary conditions as a new rich source of information about the vacuum structure. In all cases the entropy does not increase along the flow from the ultraviolet to the infrared.

Kaluza-Klein towers for spinors in flat space

Considering a massive or massless free spinor field propagating in a flat five-dimensional space with its fifth dimension compactified either on a strip or on a circle, we analyze the procedure of generation of the four-dimensional Kaluza-Klein spinor mass towers. Requiring the five-dimensional Dirac operator to be symmetric, the set of all the allowed boundary conditions is obtained. In the determination of the boundary conditions and in the Kaluza-Klein reduction equations, the SO(3,1) and parity invariances in the space-time subspace are carefully taken into account. The equations determining the mass towers are written in full generality. A few numerical examples are given.

Electromagnetic dipole moments and radiative decays of particles from exchange of fermionic unparticles

We construct the propagator for a free fermionic unparticle field from basic considerations of scale and Lorentz invariance. The propagator is fixed up to a normalization factor which is required to recover the result of a free massless fermion field in the canonical limit of the scaling dimension. Two new features appear compared to the bosonic case. The propagator contains both γ and non-γ terms, and there is a relative phase of π/2 between the two in the time-like regime for arbitrary scaling dimension. This should result in additional interference effects on top of the one known in the bosonic case. The non-γ term can mediate chirality flipped transitions that are not suppressed by a light fermion mass but are enhanced by a large bosonic mass in loops, compared to the pure particle case. We employ this last feature to set stringent bounds on the Yukawa couplings between a fermionic unparticle and an ordinary fermion through electromagnetic dipole moments and radiative decays of light fermions.

No cross-interactions among different tensor fields with the mixed symmetry (3, 1) intermediated by a vector field

Under the hypotheses of analyticity in the coupling constant, locality, Lorentz covariance and Poincaré invariance of the deformations, combined with the preservation of the number of derivatives on each field, the consistent interactions between a collection of free massless tensor gauge fields with the mixed symmetry of a two-column Young diagram of the type (3,1) and one Abelian vector field, respectively a p-form gauge field, are addressed. The main result is that a single mixed-symmetry tensor field from the collection gets coupled to the vector field/p-form. Our final result resembles the well-known fact from general relativity according to which there is one graviton in a given world.

A Sharpened Nuclearity Condition for Massless Fields

A recently proposed phase space condition which comprises information about the vacuum structure and timelike asymptotic behavior of physical states is verified in massless free field theory. There follow interesting conclusions about the momentum transfer of local operators in this model.

Harmonic Bilocal Fields Generated by Globally Conformal Invariant Scalar Fields

The twist two contribution in the operator product expansion of \(\phi_{1} ({\rm x}_{1})\phi_{2}({\rm x}_{2})\) for a pair of globally conformal invariant, scalar fields of equal scaling dimension d in four space–time dimensions is a field V 1 (x1, x2) which is harmonic in both variables. It is demonstrated that the Huygens bilocality of V 1 can be equivalently characterized by a “single–pole property” concerning the pole structure of the (rational) correlation functions involving the product \(\phi_{1}({\rm x}_{1})\phi_{2}({\rm x}_{2})\). This property is established for the dimension d = 2 of \(\phi_{1}, \phi_{2}\). As an application we prove that any system of GCI scalar fields of conformal dimension 2 (in four space–time dimensions) can be presented as a (possibly infinite) superposition of products of free massless fields.

Higher-spin conformal currents in Minkowski space

Using the unfolded formulation of equations for massless free fields of all spins, we obtain an explicit form of the gauge-invariant higher-spin conformal conserved charges bilinear in four-dimensional massless fields of arbitrary spins.

Generalized Symmetries of Massless Free Fields on Minkowski Space

A complete and explicit classification of generalized, or local, symmetries of massless free fields of spin s 1/2 is carried out. Up to equivalence, these are found to consists of the conformal symmetries and their duals, new chiral symmetries of order 2s, and their higher-order extensions obtained by Lie differentiation with respect to confor- mal Killing vectors. In particular, the results yield a complete classification of generalized symmetries of the Dirac-Weyl neutrino equation, Maxwell's equations, and the linearized gravity equations.

Vacuum energy and renormalization on the edge

The vacuum dependence on boundary conditions in quantum field theories is analysed from a very general viewpoint. From this perspective, the renormalization prescriptions not only imply the renormalization of the couplings of the theory in the bulk but also the appearance of a flow in the space of boundary conditions. For regular boundaries, this flow has a large variety of fixed points and no cyclic orbit. The family of fixed points includes Neumann and Dirichlet boundary conditions. In one-dimensional field theories, pseudo-periodic and quasi-periodic boundary conditions are also RG fixed points. Under these conditions massless bosonic free field theories are conformally invariant. Among all fixed points only Neumann boundary conditions are infrared stable fixed points. All other conformal invariant boundary conditions become unstable under some relevant perturbations. In finite volumes, we analyse the dependence of the vacuum energy along the trajectories of the renormalization group flow providing an interesting framework for dark energy evolution. In contrast, the renormalization group flow on the boundary does not affect the leading behaviour of the entanglement entropy of the vacuum in one-dimensional conformally invariant bosonic theories.

Gaussian free fields for mathematicians

The d-dimensional Gaussian free field (GFF), also called the (Euclidean bosonic) massless free field, is a d-dimensional-time analog of Brownian motion. Just as Brownian motion is the limit of the simple random walk (when time and space are appropriately scaled), the GFF is the limit of many incrementally varying random functions on d-dimensional grids. We present an overview of the GFF and some of the properties that are useful in light of recent connections between the GFF and the Schramm–Loewner evolution.

Pattern Densities in Non-Frozen Planar Dimer Models

In this paper, we introduce a family of observables for the dimer model on a bi-periodic bipartite planar graph, called pattern density fields. We study the scaling limit of these objects for liquid and gaseous Gibbs measures of the dimer model, and prove that they converge to a linear combination of a derivative of the Gaussian massless free field and an independent white noise.

BTZ black hole as a solution of a higher-spin gauge theory in three-dimensional space-time

We show that the BTZ black hole is an exact solution of a higher-spin gauge theory in three-dimensional space-time. We find solutions for free massless fields in the black-hole metric using the star algebra formalism underlying the higher-spin theory. We find that some of the higher-spin symmetries remain unbroken for special values of the BTZ parameters.

Mixed-symmetry massless gauge fields in AdS5

Using the su(2, 2) spinor language, we describe free mixed-symmetry massless bosonic and fermionic gauge fields of arbitrary spins in the AdS5 space. We construct manifestly covariant action functionals and derive field equations.

Couplings between a single massless tensor field with the mixed symmetry (3,1) and one vector field

Under the hypotheses of smoothness in the coupling constant, locality, Lorentz covariance, and Poincar\'e invariance of the deformations, combined with the preservation of the number of derivatives on each field, the consistent interactions between a single free massless tensor gauge field with the mixed symmetry of a two-column Young diagram of the type (3,1) and one Abelian vector field have been investigated. The computations are done with the help of the deformation theory based on a cohomological approach, in the context of the antifield-BRST formalism. The main result is that there exist nontrivial cross-couplings between these types of fields in five spatiotemporal dimensions, which break the PT invariance and allow for the deformation of the gauge transformations of the vector field, but not of the gauge algebra.

Lagrangian formulation for free mixed-symmetry bosonic gauge fields in (A)dSd

Covariant Lagrangian formulation for free bosonic massless fields of arbitrary mixed-symmetry type in (A)dS(d) space-time is presented. The analysis is based on the frame-like formulation of higher-spin field dynamics [1] with higher-spin fields described as p-forms taking values in appropriate modules of the (A)dS(d). The problem of finding free field action is reduced to the analysis of an appropriate differential complex, with the derivation Q associated with the variation of the action. The constructed action exhibits additional gauge symmetries in the flat limit in agreement with the general structure of gauge symmetries for mixed-symmetry fields in Minkowski and (A)dS(d) spaces.

Thermofield dynamics and Casimir effect for fermions

A generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermionic counterpart of the formalism introduced earlier for bosons [Phys. Rev. A 66 (2002) 052101], and is based on the thermofield dynamics approach. We analyze the energy–momentum tensor for the Casimir effect of a free massless fermion field in a d-dimensional box at finite temperature. As a particular case the Casimir energy and pressure for the field confined in a three-dimensional parallelepiped box are calculated. It is found that the attractive or repulsive nature of the Casimir pressure on opposite faces changes depending on the relative magnitude of the edges. We also determine the temperature at which the Casimir pressure in a cubic box changes sign and estimate its value when the edge of the cube is of the order of the confining lengths for baryons.

Dimensional reduction from entanglement in Minkowski space

Using a quantum field theoretic setting, we present evidence for dimensional reduction of any sub-volume of Minkowksi space. First, we show that correlation functions of a class of operators restricted to a sub-volume of D-dimensional Minkowski space scale as its surface area. A simple example of such area scaling is provided by the energy fluctuations of a free massless quantum field in its vacuum state. This is reminiscent of area scaling of entanglement entropy but applies to quantum expectation values in a pure state, rather than to statistical averages over a mixed state. We then show, in a specific case, that fluctuations in the bulk have a lower-dimensional representation in terms of a boundary theory at high temperature.

Duality invariance of all free bosonic and fermionic gauge fields

We give a simple general extension to all free bosonic and fermionic massless gauge fields of a recent proof that spin 2 is duality invariant in flat space. We also discuss its validity in (A)dS backgrounds and the relevance of supersymmetry.