Dynamical supersymmetry of spin particle-magnetic field interaction

We study the super and dynamical symmetries of a fermion in a monopole background. The Hamiltonian also involves an additional spin-orbit coupling term, which is parameterized by the gyromagnetic ratio. We construct the superinvariants associated with the system using a SUSY extension of a previously proposed algorithm, based on Grassmann-valued Killing tensors. Conserved quantities arise for certain definite values of the gyromagnetic factor: $\N=1$ SUSY requires $g=2$; a Kepler-type dynamical symmetry only arises, however, for the anomalous values $g=0$ and $g=4$. The two anomalous systems can be unified into an $\N=2$ SUSY system built by doubling the number of Grassmann variables. The planar system also exhibits an $\N=2$ supersymmetry without Grassmann variable doubling.Comment: 23 page

Radiation reaction and renormalization in classical electrodynamics of point particle in any dimension

The effective equations of motion for a point charged particle taking account of radiation reaction are considered in various space-time dimensions. The divergencies steaming from the pointness of the particle are studied and the effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogs of the Lorentz-Dirac equation are explicitly derived.Comment: minor changes in concluding section, misprints corrected, LaTeX2e, 15 page

Quantum 1/4 BPS Dyons

Classical properties of 1/4 BPS dyons were previously well understood both in field theory context and in string theory context. Its quantum properties, however, have been more difficult to probe, although the elementary information of the supermultiplet structures is known from a perturbative construction. Recently, a low energy effective theory of monopoles was constructed and argued to contain these dyons as quantum bound states. In this paper, we find these dyonic bound states explicitly in the N=4 supersymmetric low energy effective theory. After identifying the correct angular momentum operators, we motivate an anti-self-dual ansatz for all BPS bound states. The wavefunctions are found explicitly, whose spin contents and degeneracies match exactly the expected results.Comment: 20 pages, no figure

Geometrical Aspects Of BRST Cohomology In Augmented Superfield Formalism

In the framework of augmented superfield approach, we provide the geometrical origin and interpretation for the nilpotent (anti-)BRST charges, (anti-)co-BRST charges and a non-nilpotent bosonic charge. Together, these local and conserved charges turn out to be responsible for a clear and cogent definition of the Hodge decomposition theorem in the quantum Hilbert space of states. The above charges owe their origin to the de Rham cohomological operators of differential geometry which are found to be at the heart of some of the key concepts associated with the interacting gauge theories. For our present review, we choose the two $(1 + 1)$-dimensional (2D) quantum electrodynamics (QED) as a prototype field theoretical model to derive all the nilpotent symmetries for all the fields present in this interacting gauge theory in the framework of augmented superfield formulation and show that this theory is a {\it unique} example of an interacting gauge theory which provides a tractable field theoretical model for the Hodge theory.Comment: LaTeX file, 25 pages, Ref. [49] updated, correct page numbers of the Journal are give

Influence of wiring cost on the large-scale architecture of human cortical connectivity

In the past two decades some fundamental properties of cortical connectivity have been discovered: small-world structure, pronounced hierarchical and modular organisation, and strong core and rich-club structures. A common assumption when interpreting results of this kind is that the observed structural properties are present to enable the brain's function. However, the brain is also embedded into the limited space of the skull and its wiring has associated developmental and metabolic costs. These basic physical and economic aspects place separate, often conflicting, constraints on the brain's connectivity, which must be characterized in order to understand the true relationship between brain structure and function. To address this challenge, here we ask which, and to what extent, aspects of the structural organisation of the brain are conserved if we preserve specific spatial and topological properties of the brain but otherwise randomise its connectivity. We perform a comparative analysis of a connectivity map of the cortical connectome both on high- and low-resolutions utilising three different types of surrogate networks: spatially unconstrained (‘random’), connection length preserving (‘spatial’), and connection length optimised (‘reduced’) surrogates. We find that unconstrained randomisation markedly diminishes all investigated architectural properties of cortical connectivity. By contrast, spatial and reduced surrogates largely preserve most properties and, interestingly, often more so in the reduced surrogates. Specifically, our results suggest that the cortical network is less tightly integrated than its spatial constraints would allow, but more strongly segregated than its spatial constraints would necessitate. We additionally find that hierarchical organisation and rich-club structure of the cortical connectivity are largely preserved in spatial and reduced surrogates and hence may be partially attributable to cortical wiring constraints. In contrast, the high modularity and strong s-core of the high-resolution cortical network are significantly stronger than in the surrogates, underlining their potential functional relevance in the brain

New Gauge Supergravity in Seven and Eleven Dimensions

Locally supersymmetric systems in odd dimensions whose Lagrangians are Chern-Simons forms for supersymmetric extensions of anti-de Sitter gravity are discussed. The construction is illustrated for D=7 and 11. In seven dimensions the theory is an N=2 supergravity whose fields are the vielbein ($e_{\mu}^{a}$), the spin connection ($\omega_{\mu}^{ab}$), two gravitini ($\psi_{\mu}^{i}$) and an $sp(2)$ gauge connection ($a_{\mu j}^{i}$). These fields form a connection for $osp(2|8)$. In eleven dimensions the theory is an N=1 supergravity containing, apart from $e_{\mu}^{a}$ and $\omega_{\mu}^{ab}$, one gravitino $\psi_{\mu}$, and a totally antisymmetric fifth rank Lorentz tensor one-form, $b_{\mu}^{abcde}$. These fields form a connection for $osp(32|1)$. The actions are by construction invariant under local supersymmetry and the algebra closes off shell without requiring auxiliary fields. The $N=2^{[D/2]}$-theory can be shown to have nonnegative energy around an AdS background, which is a classical solution that saturates the Bogomolnyi bound obtained from the superalgebra.Comment: 5pages, RevTeX, no figures, two columns, minor typos correcte

Nonlinear Bogolyubov-Valatin transformations and quaternions

In introducing second quantization for fermions, Jordan and Wigner (1927/1928) observed that the algebra of a single pair of fermion creation and annihilation operators in quantum mechanics is closely related to the algebra of quaternions H. For the first time, here we exploit this fact to study nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for a single fermionic mode. By means of these transformations, a class of fermionic Hamiltonians in an external field is related to the standard Fermi oscillator.Comment: 6 pages REVTEX (v3: two paragraphs appended, minor stylistic changes, eq. (39) corrected, references [10]-[14], [36], [37], [41], [67]-[69] added; v4: few extensions, references [62], [63] added, final version to be published in J. Phys. A: Math. Gen.