相关论文: Geometric methods for the most general Ginzburg-La…

It is well established that the Hilbert space for charged particles in a plane subject to a uniform magnetic field can be described by two mutually commuting ladder algebras. We propose a similar formalism for Landau level quantization…

We report a microscopic derivation of two-component Ginzburg-Landau (GL) field theory and the conditions of its validity in two-band superconductors. We also investigate the conditions when microscopically derived or phenomenological GL…

We generalize the known method for explicit construction of mirror pairs of $(2,2)$-superconformal field theories, using the formalism of Landau-Ginzburg orbifolds. Geometrically, these theories are realized as Calabi-Yau hypersurfaces in…

Novel procedures to determine the upper critical field $B_{c2}$ have been proposed within a continuous Ginzburg-Landau model. Unlike conventional methods, where $B_{c2}$ is obtained through the determination of the smallest eigenvalue of an…

The $\mathcal{N}=2$ Landau--Ginzburg description provides a strongly interacting Lagrangian realization of an $\mathcal{N}=2$ superconformal field theory. It is conjectured that one such example is given by the two-dimensional…

The authors establish the necessary and sufficient conditions under which certain combinations of Gaussian hypergeometric function and elementary function are monotone in the parameter, which generalize the recent results of generalized…

One parameter family of exact solutions in General Relativity with a scalar field has been found using the Liouville metric. The scalar field potential has exponential form. This model is interesting, because, in particular, the solution…

By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are…

We consider the deformations of ``monomial solutions'' to Generalized Kontsevich Model \cite{KMMMZ91a,KMMMZ91b} and establish the relation between the flows generated by these deformations with those of $N=2$ Landau-Ginzburg topological…

In non-minimal Higgs mechanisms, one often needs to minimize highly symmetric Higgs potentials. Here we propose a geometric way of doing it, which, surprisingly, is often much more efficient than the usual method. By construction, it gives…

We consider the realization of N=2 superconformal models in terms of free first-order $(b,c,\beta,\gamma)$-systems, and show that an arbitrary Landau-Ginzburg interaction with quasi-homogeneous potential can be introduced without spoiling…

A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of…

In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variables. On the example of the traveling wave reduction of the…

Fix a smooth, complete algebraic curve $X$ over an algebraically closed field $k$ of characteristic zero. To a reductive group $G$ over $k$, we associate an algebraic stack $\operatorname{Par}_G$ of quantum parameters for the geometric…

Using results from sheaf theory combined with the phenomenological theory of the two-dimensional superfluid, the precipitation of quantum vortices is shown to be the genesis of a macroscopic order parameter for a phase transition in two…

A pair of the 2D non-unitary minimal models $M(2,5)$ is known to be equivalent to a variant of the $M(3,10)$ minimal model. We discuss the RG flow from this model to another non-unitary minimal model, $M(3,8)$. This provides new evidence…

[GGSM2] showed that height functions give adjoint orbits of semisimple Lie algebras the structure of symplectic Lefschetz fibrations (superpotential of the LG model in the language of mirror symmetry). We describe how to extend the…

A nonlocal mass operator can be consistently set in local form through the introduction of a set of additional fields with geometrical appropriated properties. A local and polynomial gauge invariant action is thus identified. Equations…

In this work, the Ginzburg-Landau theory is represented on a symplectic manifold with a phase space content. The order parameter is defined by a quasi-probability amplitude, which gives rise to a quasi-probability distribution function,…

We introduce a numerical method, based on finite elements and lattice gauge theory, to compute approximate solutions to Schr\"odinger and Pauli equations. The crucial geometric property of the method is discrete gauge invariance. The main…