WebI'm going over Coleman's derivation of Derrick's theorem for real scalar fields in the chapter Classical lumps and their quantum descendants from Aspects of Symmetry (page 194). Theorem: Let $... WebDerrick's theorem is an argument due to a physicist G.H. Derrick which shows that stationary localized solutions to a nonlinear wave equation or nonlinear Klein–Gordon equation in …

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WebJun 3, 2013 · These objects have to obey Derrick’s theorem , which says that in bulk three-dimensional fields, the configuration can always lower its energy by shrinking. The object generated in Chen et al.’s experiment somehow circumvents this theorem: Once created, the Hopf fibration is stable and doesn’t change size. One possibility is that the ... WebThe well-known Derrick-Hobart theorem [9,10] is a prototypical example of such a constraint: it shows that scalar field theories with two derivatives can have soliton solutions only in one... #include iomanip setw

From the viewpoint of field theory and Derrick

http://export.arxiv.org/pdf/1907.10616 WebWe extend Derrick’s theorem to the case of a generic irrotational curved spacetime adopting a strategy similar to the original proof. We show that a static relativistic star made of real scalar fields is never possible regardless of the geometrical properties of the (static) spacetimes. The generalised theorem offers a tool that can be used to check the … Derrick's theorem is an argument by physicist G. H. Derrick which shows that stationary localized solutions to a nonlinear wave equation or nonlinear Klein–Gordon equation in spatial dimensions three and higher are unstable. See more Derrick's paper, which was considered an obstacle to interpreting soliton-like solutions as particles, contained the following physical argument about non-existence of stable localized stationary solutions to … See more Derrick describes some possible ways out of this difficulty, including the conjecture that Elementary particles might correspond to stable, localized solutions which are periodic in time, rather than time-independent. Indeed, it was later shown that a time … See more We may write the equation $${\displaystyle \partial _{t}^{2}u=\nabla ^{2}u-{\frac {1}{2}}f'(u)}$$ in the Hamiltonian form See more A stronger statement, linear (or exponential) instability of localized stationary solutions to the nonlinear wave equation (in any spatial dimension) is proved by P. … See more • Orbital stability • Pokhozhaev's identity • Vakhitov–Kolokolov stability criterion See more #include conio.h c++