## Trends in Mathematical Physics ResearchPhysics and mathematics have always been closely intertwined, with developments in one field frequently inspiring the other. Currently, there are many unsolved problems in physics which will likely require new innovations in mathematical physics. Mathematical physics is concerned with problems in statistical mechanics, atomic and molecular physics, quantum field theory, and, in general, with the mathematical foundations of theoretical physics. This includes such subjects as scattering theory for n bodies, quantum mechanics (both non-relativistic and relativistic), atomic and molecular physics, the existence and properties of the phases of model ferromagnets, the stability of matter, the theory of symmetry and symmetry breaking in quantum field theory (both in general and in concrete models), and mathematical developments in functional analysis and algebra to which such subjects lead. This book presents leading-edge research in this fast-moving field. |

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### Contents

1 | |

Topological Terms and the Global Symplectic Geometry of the Phase Space in String Theory | 95 |

Deformational Structures on Smooth Manifolds | 113 |

Classes of Smooth Solutions to Multidimensional Balance Laws of Gas Dynamic Type on Riemannian Manifolds | 155 |

### Common terms and phrases

2+1 gravity Alexander polynomial algebraic analog Appendix Berlin boundary brane calculations Chowla-Selberg formula classical coefficients components condition conformal field theories connection const constant coordinate corresponding covariant cyclotomic d-body d-metrics d-structures defined deformational structures deformationally denote density derivative differential dimension dimensional discussed divergency dynamics elliptic curve embedding Euclidean Euler example exists Fermat curve finite function fields given global Hence Hodge homogeneous hyperplane hypersurface integral isomorphism knot Lagrangian lattice Lemma linear profile manifold mapping Math mathematical matrix Mdkxdk metric Milnor mixed Hodge structures modular number theory obtain p-adic paper periods phase space Phys physical prime Proof properties Proposition pseudogroup quadratic fields quantization relation Remark respect Riemann surface satisfying Section singularity smooth solutions Springer-Verlag string theory symmetry symplectic geometry symplectic potential symplectic structure tensor theorem topological terms transformation Varchenko variables variation vector field wave equation zero zeta function