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Register a new userSupersymmetric quantum mechanics requires $g=2$ for vector bosons
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Authors
Georg Junker
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Relativistic arbitrary spin Hamiltonians are shown to obey the algebraic structure of supersymmetric quantum system if their odd and even parts commute. This condition is identical to that required for the exactness of the Foldy-Wouthuysen transformation. Applied to a massive charged spin-$1$ particle in a constant magnetic field, supersymmetric quantum mechanics necessarily requires a gyromagnetic factor $g=2$.
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We consider the self-adjoint extensions (SAE) of the symmetric supercharges and Hamiltonian for a model of SUSY Quantum Mechanics in $mathbb{R}^+$ with a singular superpotential. We show that only for two particular SAE, whose domains are scale invariant, the algebra of N=2 SUSY is realized, one with manifest SUSY and the other with spontaneously broken SUSY. Otherwise, only the N=1 SUSY algebra is obtained, with spontaneously broken SUSY and non degenerate energy spectrum.
The relativistic quantum dynamics of scalar bosons in the background of a full vector coupling (minimal plus nonminimal vector couplings) is explored in the context of the Duffin-Kemmer-Petiau formalism. The Coulomb phase shift is determined for a general mixing of couplings and it is shown that the space component of the nonminimal coupling is a {it sine qua non} condition for the exact closed-form scattering amplitude. It follows that the Rutherford cross section vanishes in the absence of the time component of the minimal coupling. Bound-state solutions obtained from the poles of the partial scattering amplitude show that the time component of the minimal coupling plays an essential role. The bound-state solutions depend on the nonminimal coupling and the spectrum consists of particles or antiparticles depending on the sign of the time component of the minimal coupling without chance for pair production even in the presence of strong couplings. It is also shown that an accidental degeneracy appears for a particular mixing of couplings.
We provide a systematic study on the possibility of supersymmetry (SUSY) for one dimensional quantum mechanical systems consisting of a pair of lines $R$ or intervals [-l, l] each having a point singularity. We consider the most general singularities and walls (boundaries) at $x = pm l$ admitted quantum mechanically, using a U(2) family of parameters to specify one singularity and similarly a U(1) family of parameters to specify one wall. With these parameter freedoms, we find that for a certain subfamily the line systems acquire an N = 1 SUSY which can be enhanced to N = 4 if the parameters are further tuned, and that these SUSY are generically broken except for a special case. The interval systems, on the other hand, can accommodate N = 2 or N = 4 SUSY, broken or unbroken, and exhibit a rich variety of (degenerate) spectra. Our SUSY systems include the familiar SUSY systems with the Dirac $delta(x)$-potential, and hence are extensions of the known SUSY quantum mechanics to those with general point singularities and walls. The self-adjointness of the supercharge in relation to the self-adjointness of the Hamiltonian is also discussed.
Growth of Young diagrams, equipped with Plancherel measure, follows the automodel equation of Kerov. Using the technology of unitary matrix model we show that such growth process is exactly same as the growth of gap-less phase in Gross-Witten and Wadia (GWW) model. The limit shape of asymptotic Young diagrams corresponds to GWW transition point. Our analysis also offers an alternate proof of limit shape theorem of Vershik-Kerov and Logan-Shepp. Using the connection between unitary matrix model and free Fermi droplet description, we map the Young diagrams in automodel class to different shapes of two dimensional phase space droplets. Quantising these droplets we further set up a correspondence between automodel diagrams and coherent states in the Hilbert space. Thus growth of Young diagrams are mapped to evolution of coherent states in the Hilbert space. Gaussian fluctuations of large $N$ Young diagrams are also mapped to quantum (large $N$) fluctuations of the coherent states.
In this paper we apply the previously derived formalism of permutation orbifold conformal field theories to N=2 supersymmetric minimal models. By interchanging extensions and permutations of the factors we find a very interesting structure relating various conformal field theories that seems not to be known in literature. Moreover, unexpected exceptional simple currents arise in the extended permuted models, coming from off-diagonal fields. In a few situations they admit fixed points that must be resolved. We determine the complete CFT data with all fixed point resolution matrices for all simple currents of all Z_2-permutations orbifolds of all minimal N=2 models with k eq 2 mod 4.
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