Tom D. Imbo

Identical particles, exotic statistics and braid groups

Abstract The inequivalent quantizations of a system of n identical particles on a manifold M, dim M⩾2, are in 1-1 correspondence with irreducible unitary representations of the braid group B n (M). The notion of the statistics of the particles is made precise. We give various examples where all the possible statistics for the system are determined, and find instances where the particle obey statistics different from the well-studied Bose, Fermi para- and θ-statistics

Solitons From Supersymmetry

Supersymmetry transformations constitute a new, powerful technique of generating families of isospectral potentials. We show that isospectral families of reflectionless potentials provide surprisingly simple expressions for the pure multi-soliton solutions of the KdV and other nonlinear evolution equations.

Relating quarkonium wave functions at the origin

Abstract Within the context of nonrelativistic potential models, we obtain several formulas (with varying degrees of rigor) relating the wave functions at the origin of the c c , b c and b b S-wave quarkonium systems. One of our main results is a model-independent relation which seems to hold to within 3% for any reasonable choice of interquark potential and any choice of radial quantum number — namely, |Ψ b c (0)| 2 ⋍ |Ψ c c (0)| 1.3 |Ψ b b (0)| 0.7 (the exponents are motivated in the text). One of the physical consequences of this result is the following relationship between heavy meson masses which we expect to hold at about the 10% level: M B c ∗ − M B c ⋍ (0.7) (M J ψ − M η c ) 0.65 (Mγ − M ηb ) 0.35 .

Discontinuous quantum evolutions in the presence of closed timelike curves

We consider Deutschs computational model of a quantum system evolving in a spacetime containing closed timelike curves. Although it is known that this model predicts nonlinear and nonunitary evolutions of the system, we demonstrate that it also gives rise to evolutions which are a discontinuous function of the input state. These discontinuities persist for the most natural modifications of Deutschs approach.

LEPTO-MESONS, LEPTOQUARKONIUM AND THE QCD POTENTIAL

Abstract We consider bound states of heavy leptoquark-antiquark pairs (lepto-mesons) as well as leptoquark-antileptoquark pairs (leptoquarkonium). Unlike the situation for top quarks, leptoquarks (if they exist) may live long enough for these hadrons to form. We study the spectra and decay widths of these states in the context of a nonrelativistic potential model which matches the recently calculated two-loop QCD potential at short distances to a successful phenomenological quarkonium potential at intermediate distances. We also compute the expected number of events for these states at future colliders.

Novel spin and statistical properties of nonabelian vortices

Abstract We study the statistics of vortices which appear in (2 + 1)-dimensional spontaneously broken gauge theories, where a compact group G breaks to a finite nonabelian subgroup H. Two simple models are presented. In the first, a quantum state which is symmetric under the intercharge of a pair of indistinguishable vortices can be transformed into an antisymmetric state after the passage through the system of the third vortex with an appropriate H-flux element. Further, there exist states containing two indistinguishable spinless vortices which obey Fermi statistics . In the second model, fractional analogues of the above behaviors occur. Also, composites of vortices in this theory may posses fractional “Cheshire spin” which can be changed by passing an additional vortex through the system.

Bott periodicity and realizations of chiral symmetry in arbitrary dimensions

Abstract We compute the chiral symmetries of the Lagrangian for confining “vector-like” gauge theories with massless fermions in d -dimensional Minkowski space and, under a few reasonable assumptions, determine the form of the quadratic fermion condensates which arise through spontaneous breaking of these symmetries. We find that for each type (complex, real, or pseudoreal) of representation of the gauge group carried by the fermions, the chiral symmetries of the Lagrangian, as well as the residual symmetries after dynamical breaking, exactly follow the pattern of Bott periodicity as the dimension changes. The consequences of this for the topological features of the low-energy effective theory are considered.

Simple baryon-meson mass relations from a logarithmic interquark potential☆

Abstract I consider the quantity δ(m 1 m 2 m 3 ) ≡ M q1q2q3 − (M q1 q 2 + M q2 q 3 + M q1 q 3 ) 2 , where the M s represent the ground state spin-averaged hadron masses with the indicated quark content and the m s the corresponding constituent quark masses. I assume a logarithmic interquark potential, the validity of a nonrelativistic approach, and various standard potential model inputs. Simple scaling arguments then imply that the quantity R(x) ≡ δ(mmm 3 ) δ(m 0 m 0 m 0 ) depends only on the ratio x = m m 3 , and is independent of m 0 as well as any parameters appearing in the potential. A simple and accurate analytic determination of δ ( mmm 3 ), and hence R ( x ), is given using the 1 D expansion where D is the number of spatial dimensions. When applicable, this estimate of R ( x ) compares very well to experiment — even for hadrons containing light quarks. A prediction of the above result which is likely to be tested in the near future is M Σ b ∗ 2 + (M Λ b + M Σ b ) 4 = 5774±4 MeV/c 2 .

Topology change and θ-vacua in 2D Yang-Mills theory

We discuss the existence of θ-vacua in pure Yang-Mills theory in two space-time dimensions. More precisely, a procedure is given which allows one to classify the distinct quantum theories possessing the same classical limit for an arbitrary connected gauge group G and compact space-time manifold M (possibly with boundary) possessing a special basepoint. For any such G and M it is shown that the above quantizations are in one-to-one correspondence with the irreducible unitary representations (IURs) of π1(G) if M is orientable, and with the IURs of π1(G)/2π1(G) if M is non-orientable.

Non-abelian vortices on surfaces and their statistics

We discuss the physics of topological vortices moving on an arbitrary surface M in a YangMills-Higgs theory in which the gauge group G breaks to a finite subgroup H. We concentrate on the case where M is compact and/or non-orientable. Interesting new features arise which have no analog on the plane. The consequences for the quantum statistics of vortices are discussed, particularly when H is non-abelian.