Dual variables for M-branes
Motivated in parts by arXiv:2101.01803, relativistic extended objects will be described by an (over-complete) set of generalized coordinates and momenta that in some sense are 'dual' to each other.
hep-th↗
arXiv subjects
Jens Hoppe
Publications and source records attributed to Jens Hoppe.
Square-roots and Lax-pairs for supersymmetrizable systems
Several examples are given illustrating the (presumably rather general) fact that bosonic Hamiltonians that are supersymmetrizable automatically possess Lax-pairs, and square-roots.
hep-th↗
Another View on the Shape Equation for Strings
The question how an $M$-dimensional extended object must be shaped so that a rigid motion gives an $M$-brane solution ($M+1$ dimensional timelike zero mean curvature surface) in $M+2$ dimensional Minkowski space is discussed for closed strings
hep-th↗
Minimal Surfaces from Rigid Motions
Equations are derived for the shape of a hypersurface in $\mathbb{R}^N$ for which a rigid motion yields a minimal surface in $\mathbb{R}^{N+1}$. Some elementary, but unconventional, aspects of the classical case $N=2$ (solved by H.F. Scherk in 1835) are discussed in some detail.
math.DG↗
The Minimality of Determinantal Varieties
The determinantal variety $Σ_{pq}$ is defined to be the set of all $p\times q$ real matrices with $p\geq q$ whose ranks are strictly smaller than $q$. It is proved that $Σ_{pq}$ is a minimal cone in $\mathbb R^{pq}$ and all its strata are regular minimal submanifolds.
math.DG↗
Lectures on Minimal Surfaces
Some elementary considerations are presented concerning Catenoids and their stability, separable minimal hypersurfaces, minimal surfaces obtainable by rotating shapes, determinantal varieties, minimal tori in S3, the minimality in Rnk of the ordered set of k orthogonal equal-length n-vectors, and U(1)-invariant minimal 3-manifolds.
math.DG↗
Quantum Minimal Surfaces
We discuss quantum analogues of minimal surfaces in Euclidean spaces and tori.
math-ph↗
New construction techniques for minimal surfaces
It is pointed out that despite of the non-linearity of the underlying equations, there do exist rather general methods that allow to generate new minimal surfaces from known ones.
math.DG↗
New Minimal Hypersurfaces in R(k+1)(2k+1) and S(2k+3)k
We find a class of minimal hypersurfaces H(k) as the zero level set of Pfaffians, resp. determinants of real 2k+2 dimensional antisymmetric matrices. While H(1) and H(2) are congruent to a 6-dimensional quadratic cone resp. Hsiang's cubic su(4) invariant in R15, H(k>2) (special harmonic so(2k+2)-invariant cones of degree>3) seem to be new.
math.DG↗
Some minimal submanifolds generalizing the Clifford torus
The Clifford torus is a product surface in $\mathbb S^3$ and it is helicoidal. It will be shown that more minimal submanifolds of $\mathbb S^n$ have these properties.
math.DG↗
A geodesic feedback law to decouple the full and reduced attitude
This paper presents a novel approach to the problem of almost global attitude stabilization. The reduced attitude is steered along a geodesic path on the n-sphere. Meanwhile, the full attitude is stabilized on SO(n). This action, essentially two maneuvers in sequel, is fused into one smooth motion. Our algorithm is useful in applications where stabilization of the reduced attitude takes precedence over stabilization of the full attitude. A two parameter feedback gain affords further trade-offs between the full and reduced attitude convergence speed. The closed loop kinematics on SO(3) are solved for the states as functions of time and the initial conditions, providing precise knowledge of the transient dynamics. The exact solutions also help us to characterize the asymptotic behavior of the system such as establishing the region of attraction by straightforward evaluation of limits. The geometric flavor of these ideas is illustrated by a numerical example.
math.OC↗
Higher dimensional Schwarz's surfaces and Scherk's surfaces
Higher dimensional generalizations of Schwarz's $P$-surface, Schwarz's $D$-surface and Scherk's second surface are constructed as complete embedded periodic minimal hy- persurfaces in $\mathbb R^n$.
math.DG↗
Linear Superposition of Minimal Surfaces: Generalized Helicoids and Minimal Cones
Observing a linear superposition principle, a family of new minimal hypersurfaces in Euclidean space is found, as well as that linear combinations of generalized helicoids induce new algebraic minimal cones of arbitrarily high degree.
math.DG↗
Quasi-Static BMN Solutions
Classical solutions of membrane equations that were recently identified as limits of matrix-solutions are looked upon from another angle
hep-th↗
The Lorentz Anomaly via Operator Product Expansion
The emergence of a critical dimension is one of the most striking features of string theory. One way to obtain it is by demanding closure of the Lorentz algebra in the light-cone gauge quantisation, as discovered for bosonic strings more than fourty years ago. We give a detailed derivation of this classical result based on the operator product expansion on the Lorentzian world-sheet.
hep-th↗
Variational orthogonalization
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.
math-ph↗
Classical mechanics of minimal tori in S^3
We formulate a class of minimal tori in S^3 in terms of classical mechanics, reveal a curious property of the Clifford torus, and note that the question of periodicity can be made more explicit in a simple way.
math.DG↗
Noncommutative Minimal Surfaces
We define noncommutative minimal surfaces in the Weyl algebra, and give a method to construct them by generalizing the well-known Weierstrass-representation.
math.QA↗