We study topology change in (2+1)D gravity coupling with non-Abelian SO(2, 1) Higgs field from the point of view of Morse theory. It is shown that the Higgs potential can be identified as a Morse function. The critical points of the latter (i.e. loci of change of the spacetime topology) coincide with zeros of the Higgs field. In these critical points twodimensional metric becomes degenerate, bu...

• To propose a direct and “elementary” proof of the main result of [3], namely that the semi-classical spectrum near a global minimum of the classical Hamiltonian determines the whole semi-classical Birkhoff normal form (denoted the BNF) in the non-resonant case. I believe however that the method used in [3] (trace formulas) are more general and can be applied to any non degenerate non resonant...

An analytic ground state is proposed for the unbiased spin-boson Hamiltonian, which is non-Gaussian and beyond the Silbey-Harris ground state with lower ground state energy. The infrared catastrophe in Ohmic and sub-Ohmic bosonic bath plays an important role in determining the degeneracy of the ground state. We show that the infrared divergence associated with the displacement of the nonadiabat...

Take a C function f :M → R on a complete Hilbert manifold which satisfies the Palais–Smale condition. Assume that it is a Morse function, meaning that the second order differential df(x) is non-degenerate at every critical point x. Recall that the Morse index m(x, f) of a critical point x is the dimension of the maximal subspace on which df(x) is negative definite. Then the basic result of Mors...

We study the Multi-critical Point Principle (MPP) in a complex singlet scalar extension of Standard Model (CxSM). The MPP discussed this selects model parameters so that two low-energy vacua realized by fields are degenerate. further note may inhibit electroweak phase transition (EWPT) certain class models where tree-level potential plays an essential role its realization. Despite that, we show...

When the geometry of 3D space is reconstructed from a pair of views, using the \Fundamental matrix" as the object of analysis, then it is known (as early as the 1940s) that there exists a \critical surface" for which the solution of 3-space is ambiguous. We show that when 3-space is reconstructed from a triplet of views, using the \Trilinear Tensor" as the object of analysis, there are no criti...

We study the transient behavior in coupled dissipative dynamical systems based on the linear analysis around the steady state. We find that the transient time is minimized at a specific set of system parameters and show that at this parameter set, two eigenvalues and two eigenvectors of the Jacobian matrix coalesce at the same time; this degenerate point is called the exceptional point. For the...