Alexander A. Andrianov

Higher derivative supersymmetry and the Witten index

We propose a higher-order derivative generation of supersymmetric quantum mechanics. It is formally based on the standard superalgebra but supercharges involve differential operators of order n. As a result, their anticommutator entails a polynomial of a Hamiltonian. The Witten index does not characterize spontaneous SUSY breaking in such models. The construction naturally arises after truncation of the order n parasupersymmetric quantum mechanics which in turn is built by glueing of n ordinary supersymmetric systems.

Generalized Schmidt Decomposition and Classification of Three-Quantum-Bit States

We prove for any pure three-quantum-bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.

The factorization method and quantum systems with equivalent energy spectra

Abstract An algorithm for constructing a chain of quantum hamiltonians with interconnected energy spectra is proposed for an arbitrary number of space dimensions. Some physical models of that kind are discussed. The supersymmetric nature of the relation between connected quantum systems is pointed out.

SECOND ORDER DERIVATIVE SUPERSYMMETRY, q DEFORMATIONS AND THE SCATTERING PROBLEM

In a search for pairs of quantum systems linked by dynamical symmetries, we give a systematic analysis of novel extensions of standard one-dimensional supersymmetric quantum mechanics. The most general supercharges involving higher order derivatives are introduced, leading to an algebra which incorporates a higher order polynomial of the Hamiltonian. We investigate the condition for irreducibility of such a higher order generator to a product of standard first derivative Darboux transformations. As a new example of application of this approach we study the quantum-mechanical radial problem including the scattering amplitudes. We also investigate the links between this higher derivative SUSY and a q-deformed supersymmetric quantum mechanics and introduce the notion of self-similarity in momentum space. An explicit model for the scattering amplitude is constructed in terms of a hypergeometric function which corresponds to a reflectionless potential with infinitely many bound states.Extensions of standard one-dimensional supersymmetric quantum mechanics are discussed. Supercharges involving higher order derivatives are introduced leading to an algebra which incorporates a higher order polynomial in the Hamiltonian. We study scattering amplitudes for that problem. We also study the role of a dilatation of the spatial coordinate leading to a q-deformed supersymmetric algebra. An explicit model for the scattering amplitude is constructed in terms of a hypergeometric function which corresponds to a reflectionless potential with infinitely many bound states.

Finite-mode regularization of the fermion functional integral

Abstract Using the finite-mode regularization introduced in a previous paper, we define the functional integral for a theory of Weyl fermions. We check this definition by making sure the resulting triangle anomaly satisfies the Wess-Zumino consistency conditions. We compare our result with others found in the literature. We apply the finite-mode regularization to compute the axial anomaly in any space-time dimension and to find the explicit expression of anomalous currents in terms of the gauge fields. We illustrate the phenomenon of the infrared compensation of the chiral anomaly.

Polynomial SUSY in quantum mechanics and second derivative Darboux transformations

We give the classification of second-order polynomial SUSY Quantum Mechanics in one and two dimensions. The particular attention is paid to the irreducible supercharges which cannot be built by repetition of ordinary Darboux transformations. In two dimensions it is found that the binomial superalgebra leads to the dynamic symmetry generated by a central charge operator.Abstract We give a classification of second-order polynomial SUSY quantum mechanics in one and two dimensions. Particular attention is paid to the irreducible supercharges which cannot be built by repetition of ordinary Darboux transformations. In two dimensions it is found that the binomial superalgebra leads to the dynamic symmetry generated by a central charge operator.

Bosonization in four dimensions due to anomalies and an effective lagrangian for pseudoscalar mesons

Abstract The low-energy lagrangian for light pseudoscalar mesons is obtained from chiral symmetry breaking components of the effective action of QCD. The lagrangian is essentially determined by non-topological anomalies and represents the results of the bosonization in the colour-singlet pseudoscalar sector of QCD. The calculated coupling constants of the self-interaction of pseudoscalar mesons are in good agreement with experimental fitting.

Systems with higher-order shape invariance: spectral and algebraic properties

Abstract We study systems of two intertwining relations of first or second order for the same (up to a constant shift) partner Schrodinger operators. It is shown that the corresponding Hamiltonians possess a higher order shape invariance which is equivalent to the ladder equation. We analyze with particular attention irreducible second order Darboux transformations which together with the first order act as building blocks. For the third order shape-invariance irreducible Darboux transformations entail only one sequence of equidistant levels while for the reducible case the structure consists of up to three infinite sequences of equidistant levels and, in some cases, singlets or doublets of isolated levels.

Lorentz and CPT violations from Chern-Simons modifications of QED

The possibility of a small modification of spinor Quantum Electro-Dynamics is reconsidered, in which Lorentz and CPT non-covariant kinetic terms for photons and fermions are present. The corresponding free field theory is carefully discussed. The finite one-loop parity-odd induced effective action is unambiguously calculated using the physical cutoff method, which manifestly encodes the maximal residual symmetry group allowed by the presence of the Lorentz and CPT breaking axial-vector. This very same induced effective action, which is different from those ones so far quoted in the Literature, is also re-derived by means of the dimensional regularization, provided the maximal residual symmetry is maintained in the enlarged D-dimensional space-time. As a consequence, it turns out that the requirement of keeping the maximal residual symmetry at the quantum level just corresponds to the physical renormalization prescription which naturally fixes the one-loop parity-odd induced effective action.

Supersymmetric origin of equivalent quantum systems

Abstract The previously established equivalence of certain multidimensional quantum hamiltonians is shown to be a consequence of the supersymmetry in quantum mechanics. Thereby the supersymmetric quantum mechanics can serve as a regular source of equivalent quantum systems in arbitrary space dimensions.