Quartic interaction vertex in the massive integer higher spin field theory in a constant electromagnetic field

We consider the massive integer higher spin fields coupled to an external constant electromagnetic field in flat space of arbitrary dimension and find a gauge invariant quartic interaction vertex which is quadratic in dynamical higher spin field and quadratic in external field. Construction of the vertex is based on the BRST approach to higher spin filed theory where no off-shell constraints on the fields and on the gauge parameters are imposed from the very beginning (unconstrained formulation).Comment: 14 pages. arXiv admin note: substantial text overlap with arXiv:1501.03278; v2: Typos corrected; v3: Typos corrected, version accepted for publication in the European Physical Journal

BRST approach to Lagrangian construction for bosonic continuous spin field

We formulate the conditions defining the irreducible continuous spin representation of the four-dimensional Poincar\'e group based on spin-tensor fields with dotted and undotted indices. Such a formulation simplifies analysis of the Bargmann-Wigner equations and reduces the number of equations from four to three. Using this formulation we develop the BRST approach and derive the covariant Lagrangian for the continuous spin fields.Comment: 10 pages, v2 references adde

On the consistency of the Horava Theory

With the goal of giving evidence for the theoretical consistency of the Horava Theory, we perform a Hamiltonian analysis on a classical model suitable for analyzing its effective dynamics at large distances. The model is the lowest-order truncation of the Horava Theory with the detailed-balance condition. We consider the pure gravitational theory without matter sources. The model has the same potential term of general relativity, but the kinetic term is modified by the inclusion of an arbitrary coupling constant lambda. Since this constant breaks the general covariance under space-time diffeomorphisms, it is believed that arbitrary values of lambda deviate the model from general relativity. We show that this model is not a deviation at all, instead it is completely equivalent to general relativity in a particular partial gauge fixing for it. In doing this, we clarify the role of a second-class constraint of the model.Comment: The wording has been revised in general, specially in abstract, introduction and conclusions. No changes in results. Version published in IJMP

Cubic interactions of d4 irreducible massless higher spin fields within BRST approach

We develop an approach to constructing the manifestly Lorentz covariant cubic interaction vertices for the four-dimensional massless higher spin bosonic fields with two-component dotted and undotted spinor indices. Such fields automatically satisfy the traceless conditions what simplify form of the equations determining the irreducible massless representation of the Poincar'e group with given helicity. The cubic vertex is formulated in the framework of the BRST approach to higher spin field theory. Use of the above spin-tensor fields allows to simplify a form of the BRST-charge and hence to find the cubic vertices just in terms of irreducible higher spin fields. We derive an equation for the cubic vertex and find solutions for arbitrary spins $s_1,s_2,s_3$ with the number of derivatives $s_1+s_2+s_3$ in the vertex. As an example, we explicitly construct a vertex corresponding to the interaction of a higher spin field with scalars.Comment: 1+13 pages; V2: comments and references added, typos correcte

Lagrangian formulation for free 6D6D infinite spin field

We construct a Lagrangian that describes the dynamics of a six-dimensional free infinite (continuous) spin field in $6D$ Minkowski space. The Lagrangian is formulated in the framework of the BRST approach to higher spin field theory and is based on a system of constraints defining an irreducible representation of the corresponding Poincar\'e group. The field realization of generators in the $6D$ Poincar\'e algebra and the second-, fourth-, and sixth-order Casimir operators are obtained in explicit form using additional spinor coordinates. Specific aspects of such a realization in six dimensions are discussed. We derive the conditions that determine the irreducible representation $6D$ infinite spin field and reformulate them as operators in the Fock space forming a first-class algebra in terms of commutators. These operators are used to construct the BRST charge and the corresponding Lagrangian. We prove that the conditions of the irreducible representation are reproduced as the consequence of the Lagrangian equations of motion, which finally provides the correctness of the results obtained