Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory

We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N   of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate the level N?3$N?3$ part and obtain the consistent actions for massive graviton field, massive 3rd rank symmetric tensor field, or anti-symmetric field. We also investigate the tensionless limit of the actions and explicitly derive the gauge invariant and gauge fixed actions for general rank n symmetric and anti-symmetric tensor fields.     

Gauge invariants and Killing tensors in higher-spin gauge theories

In free completely symmetric tensor gauge field theories on Minkowski space–time, all gauge invariant functions and Killing tensor fields are computed, both on-shell and off-shell. These problems are addressed in the metric-like formalisms.     

On generating functions of higher-spin cubic interactions

We present off-shell generating functions for all cubic interactions of totally symmetric massless Higher-Spin gauge fields and discuss their properties.     

On higher derivatives in 3D gravity and higher-spin gauge theories

The general second-order massive field equations for arbitrary positive integer spin in three spacetime dimensions, and their “self-dual” limit to first-order equations, are shown to be equivalent to gauge-invariant higher-derivative field equations. We recover most known equivalences for spins 1 and 2, and find some new ones. In particular, we find a non-unitary massive 3D gravity theory with a 5th order term obtained by contraction of the Ricci and Cotton tensors; this term is part of an N=2 super-invariant that includes the “extended Chern-Simons” term of 3D electrodynamics. We also find a new unitary 6th order gauge theory for “self-dual” spin 3.     

On the BFT-BFV quantization of gauge invariant systems with linear second class constraints

We study the Hamiltonian path integral formulation for generic systems with first class and linear second class constraints.ift01001@ufrj     

Theory of nonlinear optical response of gauge invariant currents to linear and nonlinear couplings

When a gauge field interacts with a quantum condensed matter system, at first order of the gauge field it couples to the current operator of the electrons. Higher orders of the gauge field couple to electrons through other operators such as the stress tensor, etc. On the other hand, when one performs a measurement on a quantum system, not only the current operator, but also stress tensor operator of the electrons, etc. are hidden in the measurement, as they contribute to the gauge invariant current. We formulate a general problem of nonlinear optical response of the gauge invariant currents in presence of nonlinear couplings. We show that the new couplings along with new responses arising from field current have a very simple structure which can be formulated as time ordered multi-particle correlation functions. We also obtain their Lehman representation and thereby show that one need not use non-equilibrium formulations to deal with them. These new correlation functions suggest that in nonlinear optical response many new processes are possible. The experimental detection of the new terms in the current operator, and application corresponding multi-photon processes needs further theoretical and experimental investigations.     

Local potentials phase equivalent to separable two-nucleon interactions

Local energy-dependent potentials have been constructed phase equivalent to members of a family of phase-equivalent separable two-nucleon potentials in the¹ S ₀-state. It has been shown that these potentials obey the known off-shell constraints in the¹ S ₀-state and can therefore not be regarded as unrealistic in this sense. They have the same shape as the energy-independent local Kermode potentials. However we also find that the off-shell behaviour of a separable¹ S ₀ potential and its local equivalent can differ considerably.     

Conformal equations that are not Virasoro or Weyl invariant

Letters in Mathematical Physics - While the argument by Zamolodchikov and Polchinski suggests global conformal invariance implies Virasoro invariance in two-dimensional unitary conformal field...     

Chemical potentials in gauge theories

One-loop calculations of the thermodynamic potential Ω are presented for temperature gauge and non-gauge theories. Prototypical formulae are derived which give Ω as a function of both (i) boson and/or fermion chemical potential, and in the case of gauge theories (ii) the thermal vacuum parameter A₀=const (A_μ is the euclidean gauge potential). From these basic abelian gauge theory formulae, the one-loop contribution to Ω can readily be constructed for Yang-Mills theories, and also for non-gauge theories.     

On the structure of gauge invariant classical observables in lattice gauge theories

For a lattice gauge theory a necessary and sufficient condition on the gauge group is stated, which assures that the linear span of products of Wilson loop observables is dense in the space of continuous, gauge invariant functions on the configuration space. Some groups which fulfill this condition are exhibited, among themU(N) andSU(N),N=1, 2, 3, ... Finally we prove that generically it is fulfilled for all connected, compact Lie groups.     

Perturbative QED in terms of gauge invariant fields

A formulation of QED using only gauge invariant fields acting on a physical state space is discussed. The fields are the electromagnetic tensor F_μν and a non-local electron field ψ_f depending on a quadruple {f^μ} of auxiliary functions. The f-ambiguity is physically meaningful: the f^μ contain information on the asymptotic configuration of the electromagnetic field accompanying charged particles. Equations of motion are introduced and solved perturbatively, in the sense that expressions for the Wightman functions of the theory are derived. No information on the commutation relations between the basic fields is needed.     

On the theoretical problems in constructing interactions involving higher-spin massless particles

It is shown that a gauge theory of self-interacting massless spin-3 particles which is analogous to Yang-Mills or the theory of gravity does not exist. A way out may be the existence of an interacting infinite family of massless particles of various spins. The first-order interactions which are possible between such particles show a remarkable structure. This is established by explicit construction. Detailed results are obtained for the possible algebraic structures which one may obtain for gauge theories which are induced from the gauge invariance of free lagrangians.     

Local and global gauge symmetries in temporal gauge

In the temporal gauge formalism, in order to make a distinction between the global limit of local gauge transformations and global ones a non-local operator, θ, is introduced. It is claimed that what kind of θ is used is equivalent to what kind of gauge-fixing schemes is chosen. Along this idea, in non-abelian theories the coulomb, axial and unitary gauges have been investigated. In the unitary gauge spontaneous breakdown of global gauge symmetry has been found to be reduced to a problem of the boundary condition for the Higgs field and the occurrence of symmetry breaking has been concluded.     

Shape invariant potentials in higher dimensions

In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended to arrive at a large class of new shape invariant potentials in arbitrary dimensions. A reformulation of the shape invariance property and possible generalizations are proposed. These may lead to an important extension of the shape invariance property to Hamiltonians that are related to standard potential problems via space time transformations, which are found useful in path integral formulation of quantum mechanics.     

On the approximation of invariant measures

Given a discrete dynamical system defined by the map :X X, the density of the absolutely continuous (a.c.) invariant measure (if it exists) is the fixed point of the Frobenius-Perron operator defined on L¹(X). Ulam proposed a numerical method for approximating such densities based on the computation of a fixed point of a matrix approximation of the operator. T. Y. Li proved the convergence of the scheme for expanding maps of the interval. G. Keller and M. Blank extended this result to piecewise expanding maps of the cube in ⁿ. We show convergence of a variation of Ulam's scheme for maps of the cube for which the Frobenius-Perron operator is quasicompact. We also give sufficient conditions on for the existence of a unique fixed point of the matrix approximation, and if the fixed point of the operator is a function of bounded variation, we estimate the convergence rate.     

Expansion of EYM amplitudes in gauge invariant vector space

Motivated by the problem of expanding the single-trace tree-level amplitude of Einstein-Yang-Mills theory to the BCJ basis of Yang-Mills amplitudes, we present an alternative expansion formula in gauge invariant vector space. Starting from a generic vector space consisting of polynomials of momenta and polarization vectors, we define a new sub-space as a gauge invariant vector space by imposing constraints on the gauge invariant conditions. To characterize this sub-space, we compute its dimension and construct an explicit gauge invariant basis from it. We propose an expansion formula in this gauge invariant basis with expansion coefficients being linear combinations of the Yang-Mills amplitude, manifesting the gauge invariance of both the expansion basis and coefficients. With the help of quivers, we compute the expansion coefficients via differential operators and demonstrate the general expansion algorithm using several examples.     

3-dimensionalSU(2) lattice gauge theory in terms of gauge invariant variables

As a first step towards a duality transformation for theSU(2) lattice gauge theory in 3 dimensions, the integration over all gauge variant variables is performed explicitly after introducing gauge invariant auxiliary variables. The resulting new Hamiltonian is complex and involves a sum over closed loops. Each of these loops is confined to an elementary cube of a dual lattice. Like in a previous investigation for theO(4) symmetric Heisenberg ferromagnet Rühl's boson representation is used to derive the result.     

General theory of renormalization of gauge invariant operators

We study the question of renormalization of gauge invariant operators in the gauge theories. Our discussion applies to gauge invariant operators of arbitrary dimensions and tensor structure. We show that the gauge noninvariant (and ghost) operators that mix with a given set of gauge invariant operators form a complete set of local solutions of a functional differential equation. We show that this set of gauge noninvariant operators together with the gauge invariant operators close under renormalization to all orders. We obtain a complete set of local solutions of the differential equation. The form of these solutions has recently been conjectured by Kluberg Stern and Zuber. With the help of our solutions, we show that there exists a basis of operators in which the gauge noninvariant operators “decouple” from the gauge invariant operators to all orders in the sense that eigenvalues corresponding to the eigenstates containing gauge invariant operators can be computed without having to compute the full renormalization metrix. We further discuss the substructure of the renormalization matrix.