scholarly journals POINT PARTICLE IN GENERAL BACKGROUND FIELDS AND FREE GAUGE THEORIES OF TRACELESS SYMMETRIC TENSORS

2003 ◽  
Vol 18 (27) ◽  
pp. 4999-5019 ◽  
Author(s):  
ARKADY Y. SEGAL
Keyword(s):  
Gauge Theories ◽  
Point Particle ◽  
Gauge Fields ◽  
Pure Spin ◽  
Symmetric Tensors ◽  
Gauge Transformations ◽  
Infinite Dimensional ◽  
Higher Spin ◽  
Background Fields ◽  
Nonlocal Deformation

Point particle may interact with traceless symmetric tensors of arbitrary rank. Free gauge theories of traceless symmetric tensors are constructed, which provides a possibility for a new type of interactions, when particles exchange by those gauge fields. The gauge theories are parametrized by the particle's mass m and otherwise are unique for each rank s. For m=0, they are local gauge models with actions of 2s th order in derivatives, known in d=4 as "pure spin," or "conformal higher spin" actions by Fradkin and Tseytlin. For m≠0, each rank-s model undergoes a unique nonlocal deformation which entangles fields of all ranks, starting from s. There exists a nonlocal transform which maps m≠0 theories onto m=0 ones, however, this map degenerates at some m≠0 fields whose polarizations are determined by zeros of Bessel functions. Conformal covariance properties of the m=0 models are analyzed, the space of gauge fields is shown to admit an action of an infinite-dimensional "conformal higher spin" Lie algebra which leaves gauge transformations intact.

POINT PARTICLE–SYMMETRIC TENSORS INTERACTION AND GENERALIZED GAUGE PRINCIPLE

2003 ◽  
Vol 18 (27) ◽  
pp. 5021-5038 ◽  
Author(s):  
ARKADY Y. SEGAL
Keyword(s):  
Symmetric Tensor ◽  
Point Particle ◽  
Gauge Fields ◽  
Symmetric Tensors ◽  
Tensor Fields ◽  
First Order ◽  
Higher Spin ◽  
Infinite Collection ◽  
Higher Rank ◽  
Particle Action

The model of a point particle in the background of external symmetric tensor fields is analyzed from the higher spin theory perspective. It is proposed that the gauge transformations of the infinite collection of symmetric tensor fields may be read off from the covariance properties of the point particle action w.r.t. general canonical transformations. The gauge group turns out to be a semidirect product of all phase space canonical transformations to an Abelian ideal of "hyperWeyl" transformations and includes U(1) and general coordinate symmetries as a subgroup. A general configuration of external fields includes rank-0,1,2 symmetric tensors, so the whole system may be truncated to ordinary particle in Einstein–Maxwell backgrounds by switching off the higher-rank symmetric tensors. When otherwise all the higher rank tensors are switched on, the full gauge group provides a huge gauge symmetry acting on the whole infinite collection of symmetric tensors. We analyze this gauge symmetry and show that the symmetric tensors which couple to the point particle should not be interpreted as Fronsdal gauge fields, but rather as gauge fields of some conformal higher spin theories. It is shown that the Fronsdal fields system possesses twice as many symmetric tensor fields as is contained in the general background of the point particle. Besides, the particle action in general backgrounds is shown to reproduce De Wit–Freedman point particle–symmetric tensors first order interaction suggested many years ago, and extends their result to all orders in interaction, while the generalized equivalence principle completes the first order covariance transformations found in their paper, in all orders.

scholarly journals NON-ABELIAN TENSOR GAUGE FIELDS I

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4931-4957 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Large Integer ◽  
Gauge Fields ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Higher Derivatives ◽  
Vector Gauge ◽  
Dimensionless Coupling ◽  
Dimensionless Coupling Constant ◽  
Derivatives Of

We suggest an infinite-dimensional extension of gauge transformations which includes non-Abelian tensor gauge fields. In this extension of the Yang–Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrarily large integer spins. The invariant Lagrangian does not contain higher derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with dimensionless coupling constant.

HIGHER SPIN ALGEBRAS AND QUANTIZATION ON THE SPHERE AND HYPERBOLOID

1991 ◽  
Vol 06 (07) ◽  
pp. 1115-1135 ◽  
Author(s):  
M.A. VASILIEV
Keyword(s):  
Gauge Theories ◽  
Dimensional Sphere ◽  
Infinite Dimensional ◽  
Matrix Algebras ◽  
Finite Dimensional ◽  
Continuous Parameter ◽  
Oscillator Type ◽  
Heisenberg Type ◽  
Higher Spin ◽  
Quantum Operators

The oscillator-type realization is proposed for the continuous set of infinite-dimensional algebras of quantum operators on the two-dimensional sphere and hyperboloid. This realization is typical for infinite-dimensional higher spin algebras related to higher spin gauge theories. It involves the Klein-type operator that emerges nontrivially in the Heisenberg-type commutation relations for the oscillators. The invariant trace and bilinear form are constructed. The latter is shown to degenerate for all odd-integer values of the continuous parameter ν, which parametrizes the class of algebras under investigation. The degeneration points are shown to correspond to ordinary finite-dimensional matrix algebras and superalgebras. Possible applications of these results to higher spin gauge theories are discussed. In particular, it is noted that the deformation parameter ν can be interpreted as a vacuum value of some auxiliary scalar field in an appropriate higher spin gauge theory.

scholarly journals COMMENTS ON HIGHER-SPIN SYMMETRIES

2009 ◽  
Vol 06 (02) ◽  
pp. 285-342 ◽  
Author(s):  
XAVIER BEKAERT
Keyword(s):  
Lie Algebra ◽  
Differential Operators ◽  
Symmetric Tensor ◽  
Weak Field ◽  
Gauge Fields ◽  
Gauge Parameter ◽  
Gauge Transformations ◽  
First Order ◽  
Gauge Symmetries ◽  
Higher Spin

The unconstrained frame-like formulation of an infinite tower of completely symmetric tensor gauge fields is reviewed and examined in the limit where the cosmological constant goes to zero. By partially fixing the gauge and solving the torsion constraints, the form of the gauge transformations in the unconstrained metric-like formulation are obtained till first order in a weak field expansion. The algebra of the corresponding gauge symmetries is shown to be equivalent, at this order and modulo (unphysical) gauge parameter redefinitions, to the Lie algebra of Hermitian differential operators on ℝn, the restriction of which to the spin-two sector is the Lie algebra of infinitesimal diffeomorphisms.

scholarly journals General Yang–Mills type gauge theories for p-form gauge fields: From physics-based ideas to a mathematical frameworkorFrom Bianchi identities to twisted Courant algebroids

2014 ◽  
Vol 12 (01) ◽  
pp. 1550009 ◽  
Author(s):  
Melchior Grützmann ◽  
Thomas Strobl
Keyword(s):  
Gauge Theories ◽  
Differential Forms ◽  
Coupled System ◽  
Scalar Fields ◽  
Gauge Fields ◽  
Courant Algebroids ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Derived Bracket ◽  
Form Degree

Starting with minimal requirements from the physical experience with higher gauge theories, i.e. gauge theories for a tower of differential forms of different form degrees, we discover that all the structural identities governing such theories can be concisely recombined into what is called a Q-structure or, equivalently, an L∞-algebroid. This has many technical and conceptual advantages: complicated higher bundles become just bundles in the category of Q-manifolds in this approach (the many structural identities being encoded in the one operator Q squaring to zero), gauge transformations are generated by internal vertical automorphisms in these bundles and even for a relatively intricate field content the gauge algebra can be determined in some lines and is given by what is called the derived bracket construction. This paper aims equally at mathematicians and theoretical physicists; each more physical section is followed by a purely mathematical one. While the considerations are valid for arbitrary highest form degree p, we pay particular attention to p = 2, i.e. 1- and 2-form gauge fields coupled nonlinearly to scalar fields (0-form fields). The structural identities of the coupled system correspond to a Lie 2-algebroid in this case and we provide different axiomatic descriptions of those, inspired by the application, including e.g. one as a particular kind of a vector-bundle twisted Courant algebroid.

scholarly journals PROMOTING FINITE TO INFINITE SYMMETRIES: THE (3 + 1)-DIMENSIONAL ANALOGUE OF THE VIRASORO ALGEBRA AND HIGHER-SPIN FIELDS

2000 ◽  
Vol 15 (14) ◽  
pp. 939-944 ◽  
Author(s):  
M. CALIXTO
Keyword(s):  
Gauge Theories ◽  
Conformal Symmetry ◽  
Virasoro Algebra ◽  
De Sitter ◽  
Infinite Dimensional ◽  
Higher Spin ◽  
Spin Fields ◽  
Conformal Gauge ◽  
Matter Fields ◽  
Integrable Field

Infinite enlargements of finite pseudo-unitary symmetries are explicitly provided in this letter. The particular case of u (2, 2) ≃ so (4, 2) ⊕ u (1) constitutes a (Virasoro-like) infinite-dimensional generalization of the (3 + 1) -dimensional conformal symmetry, in addition to matter fields with all conformal spins. These algebras provide a new arena for integrable field models in higher dimensions; for example, anti-de Sitter and conformal gauge theories of higher-so(4, 2)-spin fields. A proposal for a noncommutative geometrical interpretation of space is also outlined.

scholarly journals Curvature tensors of higher-spin gauge theories derived from general Lagrangian densities

2021 ◽  
Author(s):  
Mark Robert Baker ◽  
Julia Bruce-Robertson
Keyword(s):  
Unique Solution ◽  
Curvature Tensor ◽  
Gauge Theories ◽  
Classical Electrodynamics ◽  
Gauge Transformations ◽  
Symmetry Properties ◽  
Tensor Potential ◽  
Higher Spin ◽  
Curvature Tensors ◽  
Lagrangian Densities

Curvature tensors of higher-spin gauge theories have been known for some time. In the past, they were postulated using a generalization of the symmetry properties of the Riemann tensor (curl on each index of a totally symmetric rank-n field for each spin-n). For this reason they are sometimes referred to as the generalized 'Riemann' tensors. In this article, a method for deriving these curvature tensors from first principles is presented; the derivation is completed without any a priori knowledge of the existence of the Riemann tensors or the curvature tensors of higher-spin gauge theories. To perform this derivation, a recently developed procedure for deriving exactly gauge invariant Lagrangian densities from quadratic combinations of N order of derivatives and M rank of tensor potential is applied to the N = M = n case under the spin-n gauge transformations. This procedure uniquely yields the Lagrangian for classical electrodynamics in the N = M = 1 case and the Lagrangian for higher derivative gravity (`Riemann' and `Ricci' squared terms) in the N = M = 2 case. It is proven here by direct calculation for the N = M = 3 case that the unique solution to this procedure is the spin-3 curvature tensor and its contractions. The spin-4 curvature tensor is also uniquely derived for the N = M = 4 case. In other words, it is proven here that, for the most general linear combination of scalars built from N derivatives and M rank of tensor potential, up to N=M=4, there exists a unique solution to the resulting system of linear equations as the contracted spin-n curvature tensors. Conjectures regarding the solutions to the higher spin-n N = M = n are discussed.

scholarly journals Planar solutions of higher-spin theory. Part I. Free field level

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
V. E. Didenko ◽  
A. V. Korybut
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Gauge Theories ◽  
Free Field ◽  
Linear Analysis ◽  
Gauge Fields ◽  
Black Brane ◽  
Higher Spin ◽  
Planar Symmetry ◽  
Black Hole Solutions

Abstract Many black hole solutions of General Relativity are known to be linearly exact. This opens a way to study them in gauge theories that apart from gravity contain fields of higher spin s > 2. Starting with a black brane in AdS4 we find its free field higher- spin generalization that respects static and planar symmetry for all bosonic gauge fields s ≥ 0. The solution is found for both the higher-spin curvatures and potentials in the form suitable for further non-linear analysis and satisfies the multi copy relation.

scholarly journals HIGHER-SPIN GAUGE THEORIES IN FOUR, THREE AND TWO DIMENSIONS

1996 ◽  
Vol 05 (06) ◽  
pp. 763-797 ◽  
Author(s):  
M.A. VASILIEV
Keyword(s):  
Gauge Theories ◽  
Space Time ◽  
Two Dimensions ◽  
Gauge Fields ◽  
Higher Spin ◽  
Three Space ◽  
Matter Fields

We review the theory of higher-spin gauge fields in four and three space-time dimensions and present some new results on higher-spin gauge interactions of matter fields in two dimensions.

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