In this paper it is shown that the characteristic vector field associated to a first order PDE: h(x,∇z(x)) = 0 with x ∈ Rn has the same form of an infinitesimal generator of an odd-symplectic transformation with contact Hamiltonian h(x, p) on the level set h = 0. We also study under which condition such PDE has a characteristic vector field commuting with a generator of an odd-symplectic action.

In gauge theories, not all rigid symmetries of the classical action can be maintained manifestly in the quantization procedure, even in the absence of anomalies. If this occurs for an anomaly-free symmetry, the effective action is invariant under a transformation that differs from its classical counterpart by quantum corrections. As shown by Fradkin and Palchik years ago, such a phenomenon occu...

This paper presents a method to compute the quasi-conformal parameterization (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain S onto a punctured disk DS associated with a given Beltrami differential. The Beltrami differential, which measures the conformality distortion, is a complexvalued function μ : S → C with supremum ...

We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set Σ(f) is totally disconnected, then f is topologically conjugate to a conformal transformation.

We study the coupled dark energy model constructed from general conformal transformation in which coefficient of depends on both scalar field and its kinetic term. Under this transformation, action for subclass Degenerate Higher-Order Scalar-Tensor (DHOST) theories is related to Einstein-Hilbert action. The evolution background universe has scaling fixed point corresponds acceleration at late t...