Irreducible Fields Research Articles

Towards the Structure of a Cubic Interaction Vertex for Massless Integer Higher Spin Fields

The structure of a cubic Lagrangian vertex is clarified for irreducible fields of helicities $s_1, s_2, s_3$ in a $d$-dimensional Minkowski space. An explicit form of the operator $\mathcal{Z}_j$ entering the vertex in a non-multiplicative way (examined in arXiv:2105.12030[hep-th] for $j=1$) is obtained. The solution is found within the BRST approach with complete BRST operators, which contain all constraints corresponding to the conditions that extract the irreducible fields, including trace operators.

Cubic interactions of arbitrary spin fields in 3d flat space

Using light-cone gauge formulation, massive arbitrary spin irreducible fields and massless (scalar and spin one-half) fields in three-dimensional flat space are considered. Both the integer spin and half-integer spin fields are studied. For such fields, we provide classification for cubic interactions and obtain explicit expressions for all cubic interaction vertices. We study two forms of the cubic interaction vertices which we refer to as first-derivative form and higher-derivative form. All cubic interaction vertices are built by using the first-derivative form.

Precessional Motion of a Rigid Body Acted upon by Three Irreducible Fields

Precessional Motion of a Rigid Body Acted upon by Three Irreducible Fields

Spatial-Temporal Organization of Episodic Memory Analyzed from Molecular Level Perspective by Engaging the Irreducible Field Principle

Spatial-Temporal Organization of Episodic Memory Analyzed from Molecular Level Perspective by Engaging the Irreducible Field Principle

Six-dimensional methods for four-dimensional conformal field theories. II. Irreducible fields

This note supplements an earlier paper on conformal field theories. There it was shown how to construct tensor, spinor, and spinor-tensor primary fields in four dimensions from their counterparts in six dimensions, where conformal transformations act simply as $SO(4,2)$ Lorentz transformations. Here we show how to constrain fields in six dimensions so that the corresponding primary fields in four dimensions transform according to irreducible representations of the four-dimensional Lorentz group, even when the irreducibility conditions on these representations involve the four-component Levi-Civita tensor ${ϵ}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}\ensuremath{\sigma}}$.

Enigma of "The Great Encephalization": Explanation by Means of Irreducible Field Principle

Enigma of "The Great Encephalization": Explanation by Means of Irreducible Field Principle

Singular vortex in magnetohydrodynamics

We obtain an exact solution of the ideal magnetohydrodynamics equations in (3+1) dimensions. The construction of the solution is based on the invariants of the group O(3) of rotations. It is a deep generalization of the known solution, which describes a radial flow with spherical waves. It is shown that in the irreducible solution, the velocity and magnetic field vectors of the particle are coplanar to the radius vector of the particle. The solution is represented as an involutive invariant subsystem of PDEs with two independent variables and finite relation, which contains a functional arbitrariness.

Symmetries of the complex Dirac-K�hler equation

We consider a complex version of a Dirac-Kahler-type equation, the eight-component complex Dirac-Kahler equation with a nonvanishing mass, which can be decomposed into two Dirac equations by only a nonunitary transformation. We also write an analogue of the complex Dirac-Kahler equation in five dimensions. We show that the complex Dirac-Kahler equation is a special case of a Bhabha-type equation and prove that this equation is invariant under the algebra of purely matrix transformations of the Pauli-Gursey type and under two different representations of the Poincare group, the fermionic (for a two-fermion system) and bosonic $$\mathcal{P}$$ -representations. The complex Dirac-Kahler equation is also written in a manifestly covariant bosonic form as an equation for the system ( $$\mathcal{B}$$ μν, Φ, $$\mathcal{V}$$ μ) of irreducible self-dual tensor, scalar, and vector fields. We illustrate the relation between the complex Dirac-Kahler equation and the known 16-component Dirac-Kahler equation.

, supergravity in harmonic superspace

We work out the basics of conformal N=(4,4) , 2D supergravity in the N=(4,4) , 2D analytic harmonic superspace with two independent sets of harmonic variables. We define the relevant most general analytic superspace diffeomorphism group and show that in the flat limit it goes over into the “large” N=(4,4) , 2D superconformal group. The basic objects of the supergravity considered are analytic vielbeins covariantizing two analyticity-preserving harmonic derivatives. For self-consistency they should be constrained in a certain way. We solve the constraints and show that the remaining irreducible field content in a WZ gauge amounts to a new short N=(4,4) Weyl supermultiplet. As in the previously known cases, it involves no auxiliary fields and the number of remaining components in it coincides with the number of residual gauge invariances. We discuss various truncations of this “master” conformal supergravity group and its compensations via couplings to N=(4,4) superconformal matter multiplets. Besides recovering the standard minimal off-shell N=(4,4) conformal and Poincaré supergravity multiplets, we find, at the linearized level, several new off-shell gauge representations.

GAUGE MODEL WITH EXTENDED FIELD TRANSFORMATIONS IN EUCLIDEAN SPACE

An SO(4) gauge-invariant model with extended field transformations is examined in four-dimensional Euclidean space. The gauge field is (Aμ)αβ=½tμνλ(Mνλ)αβ where Mνλ are the SO(4) generators in the fundamental representation. The SO(4) gauge indices also participate in the Euclidean space SO(4) transformations giving the extended field transformations. We provide the decomposition of the reducible field tμνλ in terms of fields irreducible under SO(4). The SO(4) gauge transformations for the irreducible fields mix fields of different spin. Reducible matter fields are introduced in the form of a Dirac field in the fundamental representation of the gauge group and its decomposition in terms of irreducible fields is also provided. The approach is shown to be applicable also to SO(5) gauge models in five-dimensional Euclidean space.

Generalized cohomology for irreducible tensor fields of mixed Young symmetry type

We construct N-complexes of noncompletely antisymmetric irreducible tensor fields on ℝD, thereby generalizing the usual complex (N=2) of differential forms. These complexes arise naturally in the description of higher spin gauge fields. Although, for N ⩾ 3, the generalized cohomology of these N-complexes is nontrivial, we give a generalization of the Poincare lemma. Several results which have appeared in various contexts are shown to be particular cases of this generalized Poincare lemma.

D=6 MASSIVE SPINNING PARTICLE

Massive spinning particle in six-dimensional Minkowski space is described as a mechanical system with the configuration space R5,1×CP3. The action functional of the model is unambiguously determined by the requirement of identical (off-shell) conservation for the phase-space counterparts of three Casimir operators of Poincaré group. The model is shown to be exactly solvable. Canonical quantization of the model leads to the equations on wave functions which prove to be equivalent to the relativistic wave equations for the irreducible 6d fields.

TRANSITIVITY OF LOCALITY AND DUALITY IN QUANTUM FIELD THEORY

Duality conditions for Wightman fields are formulated in terms of the Tomita conjugations S associated with algebras of unbounded operators. It is shown that two fields which are relatively local to an irreducible field fulfilling a condition of this type are relatively local to each other. Moreover, a local net of von Neumann algebras associated with such a field satisfies (essential) duality. These results do not rely on Lorentz covariance but follow from the observation that two algebras of (un)bounded operators with the same Tomita conjugation have the same (un)bounded weak commutant if one algebra is contained in the other.

The Parisi-Sourlas mechanism in pseudo-Euclidean space

The Parisi-Sourlas mechanism is demonstrated directly for fields over pseudo-Euclidean space, without the use of Wick rotations, superspace or Berezin integration. An irreducible field supermultiplet for the Lie superalgebra iosp(m,n/2) is constructed using a modified version of the method of produced representations, and a (1,1)-dimensional reduction obtained through examination of the metric.

The Grassmann Euclidean group Sp(2)∧T(2) and its representations

Extended BRST supersymmetry, wherein the ghosts are treated equally, can be viewed as the Grassmann inhomogeneous rotation group in two dimensions, Sp(2) wedge-product T(2). The representations are labelled by pseudomass and pseudospin, and the physical state vectors correspond to wavepackets over the fermionic momentum. Irreducible field representations are constructed.

Weyl field strength symmetries for arbitrary helicity and gauge invariant Fierz-Pauli and Rarita-Schwinger wave equations

The algebra of the restricted Lorentz group and the Weyl formulation of massless Poincare irreducible fields have been developed by primarily Lorentz-covariant Pauli matrix methods which facilitate the generation of both indexed Weyl spinor identities and Dirac identities. The results have been used to display a complex set of symmetries for the (anti)self-dual Weyl field strengths of arbitrary helicity j(>or=1). These symmetries and the requirement of Poincare irreducibility have then been used to give a direct and uniform determination of the forms of the gauge invariant (Lagrangian) free field wave equations for the Fierz-Pauli and Rarita-Schwinger potentials of spin 1, 3/2 and 2. The procedures set out indicate that it should be possible to establish the gauge invariant Lagrangian free field wave equations of arbitrary helicity in a uniform and direct manner from the corresponding much simpler equations governing the field strengths in unmixed spin representations.

Three remarks on Powers’ theorem about irreducible fields fulfilling CAR

First it is shown that within a relativistic Fermi field theory, a bound ∥Ψk( f,t)∥ ≤C∥ f ∥2 already implies canonical anticommutation relations (CAR). Then under Powers’ assumptions a linear, first-order differential equation for the fields ψk(x,t) is derived. This shows that in the set of generalized free fields fulfilling CAR only the free fields are irreducible at time zero. Finally Fermi fields in two space-time dimensions are considered. It is shown that only four-fermion interaction might be compatible with CAR and a bound on the coupling strength is derived.

Supercurrents

Supercurrents that provide irreducible off-shell representation of N-extended supersymmetry with maximum spin⩾ 1 2 N are constructed as bilinears of massless on-shell superfields. The corresponding prepotentials are derived and used to construct maximally gauge-invariant field theories with maximum spin⩾ 1 2 N . The construction of non-conformal theories using these irreducible field multiplets is discussed; in particular the superfield form of massive spin 1 is given for N = 2 and compensating fields are proposed for N = 4 Poincarésupergravity. We also show how the components of supercurrents may be simply obtained with the aid of the “tableaux calculus” and we work out in detail several N = 4 and N = 8 examples.

Extremal decomposition of Wightman functions and of states on nuclear *-algebras by Choquet theory

We give a short proof for the decomposability of states on nuclear *-algebras into extremal states by using the integral decompositions of Choquet and the nuclear spectral theorem, recovering a recent result by Borchers and Yngvason. The decomposition of Wightman fields into irreducible fields is a special case of this. We also indicate a quick solution of the moment problem on nuclear spaces.

New scalar and conserved vector currents in dual-resonance models

S U1.1 invarianee of an ampl i tude guarantees i ts dual character (1), while conformal invariance allows the elimination of all ghosts (~). Faetor izable dual models are buil t from irreducible fields ~d,~ Of the conformal group in two dimensions (3). The ~Yd,t'S are labelled by their dimension d and eonformal spin j. In this let ter , s tar t ing from conformal scalar and spinor fields, we present a new class of dual models of scalar and vector currents. Our work stems from the notion (a) tha t off-shell mesons (currents) are emit ted from the interior of the Kova-Nielsen disc, while on-shell mesons are emit ted from the unit circle. We choose to work in the upper half-plane Z = X ~ iY , which is simply related to the Nambu-Susskind str ip w = ~ ~i0 by the mapping Z = e% Let us consider two d= ] : 0 fields tha t obey the eonformally invar iant Laplace equation (~2/~Z~Z) q~,= 0 (***)