Point particle in general background fields vs. free gauge theories of traceless symmetric tensors

Point particle may interact to traceless symmetric tensors of arbitrary rank. Free gauge theories of traceless symmetric tensors are constructed, that provides a possibility for a new type of interactions, when particles exchange by those gauge fields. The gauge theories are parameterized 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 nonzero m, 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.Comment: 21 pages, remarks on nonlinear generalization added, a mistake in the discussion of degenerate solutions correcte

The body in the library: adventures in realism

This essay looks at two aspects of the virtual ‘material world’ of realist fiction: objects encountered by the protagonist and the latter’s body. Taking from Sartre two angles on the realist pact by which readers agree to lend their bodies, feelings, and experiences to the otherwise ‘languishing signs’ of the text, it goes on to examine two sets of first-person fictions published between 1902 and 1956 — first, four modernist texts in which banal objects defy and then gratify the protagonist, who ends up ready and almost able to write; and, second, three novels in which the body of the protagonist is indeterminate in its sex, gender, or sexuality. In each of these cases, how do we as readers make texts work for us as ‘an adventure of the body’

Twisted equivariant K-theory, groupoids and proper actions

In this paper we define twisted equivariant K-theory for actions of Lie groupoids. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite CW-complexes with equivariant stable projective bundles. A classification of these bundles is shown. We also obtain a completion theorem and apply these results to proper actions of groups.Comment: 26 page

A Geometric Model of Arbitrary Spin Massive Particle

A new model of relativistic massive particle with arbitrary spin (($m,s$)-particle) is suggested. Configuration space of the model is a product of Minkowski space and two-dimensional sphere, ${\cal M}^6 = {\Bbb R}^{3,1} \times S^2$. The system describes Zitterbewegung at the classical level. Together with explicitly realized Poincar\'e symmetry, the action functional turns out to be invariant under two types of gauge transformations having their origin in the presence of two Abelian first-class constraints in the Hamilton formalism. These constraints correspond to strong conservation for the phase-space counterparts of the Casimir operators of the Poincar\'e group. Canonical quantization of the model leads to equations on the wave functions which prove to be equivalent to the relativistic wave equations for the massive spin-$s$ field.Comment: 25 pages; v2: eq. (45.b) correcte

Massive spinning particle on anti-de Sitter space

To describe a massive particle with fixed, but arbitrary, spin on $d=4$ anti-de Sitter space $M^4$, we propose the point-particle model with configuration space ${\cal M}^6 = M^{4}\times S^{2}$, where the sphere $S^2$ corresponds to the spin degrees of freedom. The model possesses two gauge symmetries expressing strong conservation of the phase-space counterparts of the second- and fourth-order Casimir operators for $so(3,2)$. We prove that the requirement of energy to have a global positive minimum $E_o$ over the configuration space is equivalent to the relation $E_o > s$, $s$ being the particle's spin, what presents the classical counterpart of the quantum massive condition. States with the minimal energy are studied in detail. The model is shown to be exactly solvable. It can be straightforwardly generalized to describe a spinning particle on $d$-dimensional anti-de Sitter space $M^d$, with ${\cal M}^{2(d-1)} = M^d \times S^{(d-2)}$ the corresponding configuration space.Comment: 23 pages, LaTe

Testing the Hubble Law with the IRAS 1.2 Jy Redshift Survey

We test and reject the claim of Segal et al. (1993) that the correlation of redshifts and flux densities in a complete sample of IRAS galaxies favors a quadratic redshift-distance relation over the linear Hubble law. This is done, in effect, by treating the entire galaxy luminosity function as derived from the 60 micron 1.2 Jy IRAS redshift survey of Fisher et al. (1995) as a distance indicator; equivalently, we compare the flux density distribution of galaxies as a function of redshift with predictions under different redshift-distance cosmologies, under the assumption of a universal luminosity function. This method does not assume a uniform distribution of galaxies in space. We find that this test has rather weak discriminatory power, as argued by Petrosian (1993), and the differences between models are not as stark as one might expect a priori. Even so, we find that the Hubble law is indeed more strongly supported by the analysis than is the quadratic redshift-distance relation. We identify a bias in the the Segal et al. determination of the luminosity function, which could lead one to mistakenly favor the quadratic redshift-distance law. We also present several complementary analyses of the density field of the sample; the galaxy density field is found to be close to homogeneous on large scales if the Hubble law is assumed, while this is not the case with the quadratic redshift-distance relation.Comment: 27 pages Latex (w/figures), ApJ, in press. Uses AAS macros, postscript also available at http://www.astro.princeton.edu/~library/preprints/pop682.ps.g