Self-duality and octonionic analyticity of S7-valued antisymmetric fields in eight dimensions

We exhibit two octonionic extensions of the Kalb-Ramond type fields with rank two and four in eigth dimensions. By analogy to the d = 4 (anti-) self-duality of the SU(2) ≈ S³ quaternionic gauge field we consider the respective d = 8 (anti-) self-duality equations for these nonlinear, S⁷-valued antisymmetric fields. By way of an octonionic 't Hooft ansatz these equations reduce to the same generalized Fueter-Cauchy-Riemann equations over S⁸. Explicit (9n + 8) parameter S⁷ → S⁷ mapping solutions, n being a winding number, are found in terms of holomorphic functions of the spacetime octonion. An infinite number of local continuity equations results.     

Algebraic solution of the supersymmetric hydrogen atom in d dimensions

In this paper the supersymmetric extension of the Schrödinger Hamiltonian with 1/r-potential in arbitrary space-dimensions is constructed. The supersymmetric hydrogen atom admits a conserved Laplace-Runge-Lenz vector which extends the rotational symmetry SO(d) to a hidden SO(d+1) symmetry. This symmetry of the system is used to determine the discrete eigenvalues with their degeneracies and the corresponding bound state wave functions.     

N = 8 supergravity in various dimensions and the implications for four dimensions

The possibilities for constructing new spontaneously broken N = 8 supergravity theories in four dimensions by applying the generalized dimensional reduction method to symmetrical theories in higher dimensions are explored.     

Exact solution to a class of generalized Kitaev spin-1/2 models in arbitrary dimensions

We construct a class of exactly solvable generalized Kitaev spin-1/2 models in arbitrary dimensions, which is beyond the category of quantum compass models. The Jordan-Wigner transformation is employed to prove the exact solvability. An exactly solvable quantum spin-1/2 model can be mapped to a gas of free Majorana fermions coupled to static Z2 gauge fields. We classify these exactly solvable models according to their parent models. Any model belonging to this class can be generated by one of the parent models. For illustration, a two dimensional(2D) tetragon-octagon model and a three dimensional(3D) xy bond model are studied.     

On the equivalence between the Wess-Zumino action and the free Fermi theory in two dimensions

Using the functional technique we prove the bosonization rules of Witten for the currents in a non-abelian two-dimensional theory with a particular regularization of the Fermi theory.     

Haldane's instanton in 2D Heisenberg model revisited: Along the avenue of topology

Deconfined quantum phase transition from Néel phase to valence bond crystal state in 2D Heisenberg model is under debate nowadays. One crucial issue is the suppression of Haldane's instanton on quantum critical point which drives the spinon deconfined. In this Letter, by making use of the ?-mapping topological current theory, we reexamine the Haldane's instanton in an alternative way along the direction of topology. We find that the monopole events are space-time singularities of Néel field , the corresponding topological charges are the wrapping number of around the singularities which can be expressed in terms of the Hopf indices and Brouwer degrees of ?-mapping. The suppression of the monopole events can only be guaranteed when the ?-field possesses no zero points. Moreover, the quadrapolarity of monopole events in the Heisenberg model due to the Berry phase is also reproduced in this topological argument.     

n维相对论粒子的量子态密度及其应用

利用半经典近似的方法,推导出了n维相对论自由粒子量子态密度以及黑体辐射中两类粒子的辐射公式的统一表达式,并且给出了低维情况下的表达式,所得结果与三维空间的预期结果一致.这对于深化低维体系的教学与研究具有重要的意义.     

Exploiting the equivalence of reggeon field theory in zero transverse dimensions and reaction–diffusion processes

The reggeon field theory in zero transverse dimensions is investigated. Two versions of the theory are considered: one that allows for at most triple pomeron interactions and the other that embodies an additional 2→2 quartic reggeon coupling. The behavior of the scattering amplitude at asymptotic rapidities is obtained in both cases. In an s-channel picture of the high energy scattering both models can be viewed as reaction–diffusion processes. We derive known results in reggeon field theory rather easily using the reaction–diffusion formalism. We find that some results which are surprising from the reggeon field theory point of view turn out to have a simple interpretation from the reaction–diffusion point of view.     

Self-dual tensors and gravitational anomalies in 4n + 2 dimensions

Starting from a manifestly Lorentz- and diffeomorphism-invariant classical action we perform a perturbative derivation of the gravitational anomalies for chiral bosons in 4n + 2 dimensions. The manifest classical invariance is achieved using a newly developed method based on a scalar auxiliary field and two new bosonic local symmetries. The resulting anomalies coincide with the ones predicted by the index theorem. In the two-dimensional case, moreover, we perform an exact covariant computation of the effective action for a chiral boson (a scalar) which is seen to coincide with the effective action for a two-dimensional complex Weyl fermion. All these results support the quantum reliability of the new, at the classical level manifestly invariant, method.     

Supersymmetric gauge anomalies in 2 and 4 dimensions from generalized descent-equations

Via a supersymmetric generalization of the descent-equations we derive in Wess-Zumino gauge explicit expressions for chiral anomalies inN=1 supersymmetric Yang-Mills theory for space-time dimensions 2 and 4.     

Instantons and fermions in the field of instanton

The number of instantons and the number of zero fermion modes in the field of instanton are calculated. The quantum fluctuations of instantons are studied.     

Exact solution of the linearized Boltzmann equation in p dimensions

The solution of the transport in p-dimensional space is given for a system of convex boundary surfaces with arbitrary shape and finite diameter. It satisfies homogeneous or non-homogeneous Dirichlet boundary conditions. The equation for the determination of the point spectrum of the Boltzmann operator is also given.