Multi-operator brackets acting thrice
We generalize an identity, first found by Bremner, for the action of three nested Nambu brackets.
math-ph↗
arXiv subjects
Luca Mezincescu
Publications and source records attributed to Luca Mezincescu.
Classical and Quantal Ternary Algebras
We consider several ternary algebras relevant to physics. We compare and contrast the quantal versions of the algebras, as realized through associative products of operators, with their classical counterparts, as realized through classical Nambu brackets. In some cases involving infinite algebras, we show the classical limit may be obtained by a contraction of the quantal algebra, and then explicitly realized through classical brackets. We illustrate this classical-contraction method by the Virasoro-Witt example.
hep-th↗
Unitary Spherical Super-Landau Models
A Hilbert space metric is found for the SU(2|1)-invariant `superflag' Landau models, parametrized by integer 2N' and real number M, such that the Hilbert space norm is positive definite. The spectrum of these unitary super-Landau models is determined. The M=0 case yields a unitary Landau model on the supersphere SU(2|1)/U(1|1) with U(1) charge 2N=2N'+1. For the generic unitary superflag model, the manifest SU(2|1) symmetry is dynamically enhanced to SU(2|2); this is the `spherical' analog of the hidden worldline supersymmetry found previously in the planar limit.
hep-th↗
Supersymmetric Biorthogonal Quantum Systems
We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V_{+/-}(z) = -U(z)^2 +/- z(d/(dz))U(z) where U(z) = \sum_{k>0}u_{k}z^{k}. In particular, we consider the cases generated by U(z) = z and z/(1-z). We also briefly consider the effects of magnetic vector potentials on the partition functions of these systems.
quant-ph↗
Planar Super-Landau Models Revisited
We use the methods of PT-symmetric quantum theory to find a one-parameter family of ISU(1|1)-invariant planar super-Landau models with positive norm, uncovering an `accidental', and generically spontaneously-broken, worldline supersymmetry, with charges that have a Sugawara-type representation in terms of the ISU(1|1) charges. In contrast to standard models of supersymmetric quantum mechanics, it is the norms of states rather than their energies that are parameter-dependent, and the spectrum changes discontinuously in the limit that worldline supersymmetry is restored.
hep-th↗
Biorthogonal Quantum Systems
Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual space fails. The formalism is illustrated by a few exact results for models of the form H=(p+ν)^2+\sum_{k>0}μ_{k}exp(ikx). In some non-trivial cases, equivalent hermitian theories are obtained and shown to be very simple: They are just free (chiral) particles. Field theory extensions are briefly considered.
quant-ph↗
Planar Super-Landau Models
In previous papers we solved the Landau problems, indexed by 2M, for a particle on the ``superflag'' S U (2|1)/[U (1) x U (1)], the M = 0 case being equivalent to the Landau problem for a particle on the ``supersphere'' S U (2|1)/[U (1|1)]. Here we solve these models in the planar limit. For M = 0 we have a particle on the complex superplane C(1|1) ; its Hilbert space is the tensor product of that of the Landau model with the 4-state space of a ``fermionic'' Landau model. Only the lowest level is ghost-free, but for M > 0 there are no ghosts in the first [2M ]+1 levels. When 2M is an integer, the ([2M ] + 1)th level states form short supermultiplets as a consequence of a fermionic gauge invariance analogous to the ``kappa-symmetry'' of the superparticle.
hep-th↗
Non-relativistic strings and branes as non-linear realizations of Galilei groups
We construct actions for non-relativistic strings and membranes purely as Wess-Zumino terms of the underlying Galilei groups.
hep-th↗
Super Chern-Simons Quantum Mechanics
The Super Chern-Simons mechanics, and quantum mechanics of a particle, on the coset super-manifolds SU(2|1)/ U(2) and SU(2|1)/U(1)X U(1), is considered. Within a convenient quantization procedure the well known Chern-Simons mechanics on SU(2)/U(1) is reviewed, and then it is shown how the fuzzy supergeometries arise. A brief discussion of the super-sphere is also included.
hep-th↗
A Super-Flag Landau Model
We consider the quantum mechanics of a particle on the coset superspace $SU(2|1)/[U(1)\times U(1)]$, which is a super-flag manifold with $SU(2)/U(1)\cong S^2$ `body'. By incorporating the Wess-Zumino terms associated with the $U(1)\times U(1)$ stability group, we obtain an exactly solvable super-generalization of the Landau model for a charged particle on the sphere. We solve this model using the factorization method. Remarkably, the physical Hilbert space is finite-dimensional because the number of admissible Landau levels is bounded by a combination of the U(1) charges. The level saturating the bound has a wavefunction in a shortened, degenerate, irrep of $SU(2|1)$.
hep-th↗
Fuzzy CP(n|m) as a quantum superspace
The `Chern-Simons Quantum Mechanics' of a particle on CP(n|m) is shown to yield the fuzzy descriptions of these superspaces, for which we construct the non-(anti)commuting position operators. For a particle on the supersphere CP(1|1) = SU(2|1)/U(1|1), the particle's wave-function at fuzziness level 2s is shown to be a degenerate irrep of SU(2|1) describing a supermultiplet of SU(2) spins (s-1\2, s).
hep-th↗
Odd coset quantum mechanics
The standard quantum states of $n$ complex Grassmann variables with a free-particle Lagrangian transform as a spinor of SO(2n). However, the same `free-fermion' model has a non-linearly realized $SU(n|1)$ symmetry; it can be viewed as the mechanics of a `particle' on the Grassmann-odd coset space $SU(n|1)/U(n)$. We implement a quantization of this model for which the states with non-zero norm transform as a representation of $SU(n|1)$, the representation depending on the U(1) charge of the wave-function. For $n=2$ the wave-function can be interpreted as a BRST superfield.
hep-th↗
Factorization method and the supersymmetric monopole harmonics
We use the general $N = 1$ supersymmetric formulation of one dimensional sigma models on non trivial manifolds and its subsequent quantization to formulate the classical and quantum dynamics of the $ N= 2 $ supersymmetric charged particle moving on a sphere in the field of a monopole. The factorization method accommodated with the general covariance and it is used to integrate the corresponding system.
hep-th↗
Star Operation in Quantum Mechanics
We outline the description of Quantum Mechanics with noncommuting coordinates within the framework of star operation. We discuss simple cases of integrability.
hep-th↗
Factorization of Multiparticle Scattering in the Heisenberg Spin Chain
We give an explicit proof within the framework of the Bethe Ansatz/string hypothesis of the factorization of multiparticle scattering in the antiferromagnetic spin-1/2 Heisenberg spin chain, for the case of 3 particles.
hep-th↗
Fractional-Spin Integrals of Motion for the Boundary Sine-Gordon Model at the Free Fermion Point
We construct integrals of motion (IM) for the sine-Gordon model with boundary at the free Fermion point which correctly determine the boundary S matrix. The algebra of these IM (``boundary quantum group'' at q=1) is a one-parameter family of infinite-dimensional subalgebras of twisted affine sl(2). We also propose the structure of the fractional-spin IM away from the free Fermion point.
hep-th↗
Boundary S Matrix for the XXZ Chain
We compute by means of the Bethe Ansatz the boundary S matrix for the open anisotropic spin-1/2 chain with diagonal boundary magnetic fields in the noncritical regime (Delta > 1). Our result, which is formulated in terms of q-gamma functions, agrees with the vertex-operator result of Jimbo et al.
hep-th↗
Simplified Calculation of Boundary S Matrices
The antiferromagnetic Heisenberg spin chain with N spins has a sector with N=odd, in which the number of excitations is odd. In particular, there is a state with a single one-particle excitation. We exploit this fact to give a simplified derivation of the boundary S matrix for the open antiferromagnetic spin-1/2 Heisenberg spin chain with diagonal boundary magnetic fields.
hep-th↗