HS Field Research Articles

Two-dimensional massive integrable models on a torus

The finite-volume thermodynamics of a massive integrable QFT is described in terms of a grand canonical ensemble of loops immersed in a torus and interacting through scattering factors associated with their intersections. The path integral of the loops is evaluated explicitly after decoupling the pairwise interactions by a Hubbard-Stratonovich transformation. The HS fields are holomorphic fields depending on the rapidity and can be expanded in elementary oscillators. The torus partition function is expressed as certain expectation value in the Fock space of these oscillators. In the limit where one of the periods of the torus becomes asymptotically large, the effective field theory becomes mean field type. The mean field describes the infinite-volume thermodynamics which is solved by the Thermodynamical Bethe Ansatz.

Low-Rank and Sparse Representation for Hyperspectral Image Processing: A review

Combining rich spectral and spatial information, a hyperspectral image (HSI) can provide a more comprehensive characterization of the Earth’s surface. To better exploit HSIs, a large number of algorithms have been developed during the past few decades. Due to their very high correlation between spectral channels and spatial pixels, HSIs have intrinsically sparse and low-rank structures. The sparse representation (SR) and low-rank representation (LRR)-based methods have proven to be powerful tools for HSI processing and are widely used in different HS fields. In this article, we present a survey of low-rank and sparse-based HSI processing methods in the fields of denoising, superresolution, dimension reduction, unmixing, classification, and anomaly detection. The purpose is to provide guidelines and inspiration to practitioners for promoting the development of HSI processing. For a listing of the key terms discussed in this article, see “Nomenclature.&#x201D

BRST-BV quantum actions for constrained totally-symmetric integer HS fields

A constrained BRST–BV Lagrangian formulation for totally symmetric massless HS fields in a d-dimensional Minkowski space is extended to a non-minimal constrained BRST–BV Lagrangian formulation by using a non-minimal BRST operator Qc|tot with non-minimal Hamiltonian BFV oscillators C‾,P‾,λ,π, as well as antighost and Nakanishi-Lautrup tensor fields, in order to introduce an admissible self-consistent gauge condition. The gauge-fixing procedure involves an operator gauge-fixing BRST-BFV Fermion ΨH as a kernel of the gauge-fixing BRST–BV Fermion functional Ψ, manifesting the concept of BFV–BV duality. A Fock-space quantum action with non-minimal BRST-extended off-shell constraints is constructed as a shift of the total generalized field-antifield vector by a variational derivative of the gauge-fixing Fermion Ψ in a total BRST–BV action S0|sΨ=∫dη0〈χtot|cΨ0|Qc|tot|χtot|cΨ0〉. We use a gauge condition which depends on two gauge parameters, thereby extending the case of Rξ-gauges. For triplet and doublet formulations we explored the representations with only traceless field-antifield and source variables. For the generating functionals of Green's functions, BRST symmetry transformations are suggested and Ward identities are obtained.

Spin-locality of higher-spin theories and star-product functional classes

The analysis of spin-locality of higher-spin gauge theory is formulated in terms of star-product functional classes appropriate for the β → −∞ limiting shifted homotopy proposed recently in [1] where all ω2C2 higher-spin vertices were shown to be spin-local. For the β → −∞ limiting shifted contracting homotopy we identify the class of functions {mathcal{H}}^{+0} , that do not contribute to the r.h.s. of HS field equations at a given order. A number of theorems and relations that organize analysis of the higher-spin equations are derived including extension of the Pfaffian Locality Theorem of [2] to the β-shifted contracting homotopy and the relation underlying locality of the ω2C2 sector of higher-spin equations.Space-time interpretation of spin-locality of theories involving infinite towers of fields is proposed as the property that the theory is space-time local in terms of original con- stituent fields ϕ and their local currents J(ϕ) of all ranks. Spin-locality is argued to be a proper substitute of locality for theories with finite sets of fields for which the two concepts are equivalent.

Constrained BRST-BFV Lagrangian formulations for higher spin fields in Minkowski spaces

BRST-BFV method to construct constrained Lagrangian formulations for (ir)reducible half-integer higher-spin Poincare group representations in Minkowski space is suggested. The procedure is derived by two ways: first, from the unconstrained BRST-BFV method for mixed-symmetry higher-spin fermionic fields subject to an arbitrary Young tableaux with k rows (suggested in Nucl. Phys.B 869 (2013) 523, arXiv:1211.1273) by extracting the second-class constraints subsystem, Ôα = (Ôa, Ôa+), from a total super-algebra of constraints, second, in self-consistent way by means of finding BRST-extended initial off-shell algebraic constraints, Ôa. In both cases, the latter constraints supercommute on the constraint surface with constrained BRST operator QC and spin operators σCi . The closedness of the superalgebra {QC, Ôa, σCi} guarantees that the final gauge-invariant Lagrangian formulation is compatible with the off-shell algebraic constraints Ôa imposed on the field and gauge parameter vectors of the Hilbert space not depending from the ghosts and conversion auxiliary oscillators related to Ôa, in comparison with the vectors for unconstrained BRST-BFV Lagrangian formulation. The suggested constrained BRST-BFV approach is valid for both massive HS fields and integer HS fields in the second-order formulation. It is shown that the respective constrained and unconstrained Lagrangian formulations for (half)-integer HS fields with a given spin are equivalent. The constrained Lagrangians in ghost-independent and component (for initial spin-tensor field) are obtained and shown to coincide with the Fang-Fronsdal formulation for totally-symmetric HS field with respective off-shell gamma-traceless constraints. The triplet and unconstrained quartet Lagrangian formulations for the latter field are derived. The constrained BRST-BFV methods without off-shell constraints describe reducible half-integer HS Poincare group representations with multiple spins as a generalized triplet and provide a starting point for constructing unconstrained Lagrangian formulations by using the generalized quartet mechanism. A gauge-invariant Lagrangian constrained description for a massive spin-tensor field of spin n + 1/2 is obtained using a set of auxiliary Stueckelberg spin-tensors. A concept of BRST-invariant second-class constraints for dynamical systems with mixed-class constraints is suggested, leading to equivalent (w.r.t. the BRST-BFV prescription) results of quantization both at the operator level and in terms of the partition function.

Perturbative analysis in higher-spin theories

A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically simplifies the analysis and results from the application of the standard spectral sequence approach to the higher-spin covariant derivatives, allowing us in particular to reduce multiple homotopy integrals resulting from the successive application of the homotopy trick to a single integral. Efficiency of the proposed method is illustrated by various examples. In particular, it is shown how the Central on-shell theorem of the free theory immediately results from the nonlinear HS field equations with no intermediate computations.

Maxwell group and HS field theory

We consider the master fields for HS multiplets defined on 10-dimensional tensorial extension of D = 4 space-time described as a coset of 16-parameter Maxwell group . The tensorial coordinates provide a geometrization of the coupling to constant uniform EM fields. We describe the spinorial model in extended space-time and by its first quantization we obtain new infinite HS-Maxwell multiplets with their massless components coupled to each other through constant EM background. We conclude our report by observing that three-dimensional spinorial model with a pair of spinors should provide after quantization D = 3 massive HS-Maxwell multiplets.

On representations of Higher Spin symmetry algebras for mixed-symmetry HS fields on AdS-spaces. Lagrangian formulation

We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux Y(s1,…, sk) with κ ≥ 2 rows on d-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for κ = 2 Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic sp(2κ) algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin (s1, s2) is derived.

Current exchanges for reducible higher spin multiplets and gauge fixing

We compute the current exchanges between triplets of higher spin fields which describe reducible representations of the Poincare group. Through this computation we can extract the propagator of the reducible higher spin fields which compose the triplet. We show how to decompose the triplet fields into irreducible HS fields which obey Fronsdal equations, and how to compute the current-current interaction for the cubic couplings which appear in ArXiv:0708.1399 [hep-th] using the decomposition into irreducible modes. We compare this result with the same computation using a gauge fixed (Feynman) version of the triplet Lagrangian which allows us to write very simple HS propagators for the triplet fields.

Effect of Single-Ion Anisotropy on S = 1 Heisenberg Antiferromagnetic Chain in Schwinger Boson Mean-Field Theory

We use the Schwinger boson mean-field theory, in which the constraint is imposed on the average, to the quantum Heisenberg antiferromagnetic chain with single-ion anisotropy (D > 0). Under the mean-field approximation to decouple the biquadratic term by introducing two HS fields and take the short range correlation and the coupling of on-site bosons into account, we find a clear and direct description for this system, and get two excitation spectra at T = 0 K, which distinguish the sz = 0 singlet and sz = ± 1 doublet. We also see that the relative phase of the two HS fields, having the lowest energy, is the one equal to zero.