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A strain tensor that couples to the Madelung stress tensor  [PDF]
D. H. Delphenich
Physics , 2013,
Abstract: Ordinarily, the stress tensor that one derives for a Madelung fluid is not regarded as being coupled to a strain tensor, which is consistent with the fluid hypothesis. However, based upon earlier work regarding the geometric nature of the quantum potential, one can, in fact, define a strain tensor, which is not, however, due to a deformation of a spatial region, but to a deformation of a frame field on that region. When one expresses the Madelung stress tensor as a function of the strain tensor and its derivatives, one then defines a constitutive law for the Madelung medium that might lead to a more detailed picture of its elementary structure. It is pointed out that the resulting constitutive law is strongly analogous to laws that were presented by Kelvin and Tait for the bending and torsion of elastic wires and plates, as well as the Einstein equations for gravitation if one takes the viewpoint of metric elasticity.
On the geometric foundation of classical gauge gravitation theory  [PDF]
G. Sardanashvily
Physics , 2002,
Abstract: A number of recent works in E-print arXiv have addressed the foundation of gauge gravitation theory again. As is well known, differential geometry of fibre bundles provides the adequate mathematical formulation of classical field theory, including gauge theory on principal bundles. Gauge gravitation theory is formulated on the natural bundles over a world manifold whose structure group is reducible to the Lorentz group. It is the metric-affine gravitation theory where a metric (tetrad) gravitational field is a Higgs field.
The Geometric Origin of the Madelung Potential  [PDF]
D. H. Delphenich
Physics , 2002,
Abstract: Madelung's hydrodynamical forms of the Schrodinger equation and the Klein-Gordon equation are presented. The physical nature of the quantum potential is explored. It is demonstrated that the geometrical origin of the quantum potential is in the scalar curvature of the of the metric that defines the kinetic energy density for an extended particle and that the quantization of circulation (Bohr-Sommerfeld) is a consequence of associating an SO(2)-reduction of the Lorentz frame bundle with wave motion. The Madelung equations are then cast in a basis-free form in terms of exterior differential forms in such a way that they represent the equations for a timelike solution to the conventional wave equations whose rest mass density satisfies a differential equation of the "Klein-Gordon minus nonlinear term" type. The role of non-zero vorticity is briefly examined.
A Class of Self-Trapped and Self-Focusing Wave Functions in Madelung Fluid Picture of A Single Free Particle Quantum System  [PDF]
Agung Budiyono,Ken Umeno
Physics , 2009,
Abstract: Using the Madelung fluid picture of Schr\"odinger equation for a single free particle moving in one spatial dimension, we shall specify a class of wave functions whose quantum probability density is being trapped by the quantum potential it itself generates. The global convexity of the quantum potential generated by the initial self-trapped wave function will then be shown to further localize the quantum probability density through a self-generated focusing equation for a finite interval of time.
Classical Geometric Interaction- picture-like Description  [PDF]
M. X Shao,Z. Y. Zhu
Physics , 1998,
Abstract: In order to get the classical analogue of quantum interaction picture in classical symplectic geometric description, the space of solutions of free equations of motion is suggested to replace the phase space in $T^{*}Q$ description or the space of motions in usual classical symplectic geometric description. The way to determine measured values of observables in this scheme is worked out.
A Geometric Picture For Fermion Masses  [PDF]
Salvatore Esposito,Pietro Santorelli
Physics , 1996, DOI: 10.1142/S0217732395003215
Abstract: We describe a geometric picture for the pattern of fermion masses of the three generations which is invariant with respect to the renormalization group below the electroweak scale. Moreover, we predict the upper limit for the ratio between the Dirac masses of the $\mu$ and $\tau$ neutrinos, $m_{\nu_{\mu}}/ m_{\nu_{\tau}} < (9.6 \pm 0.6) 10^{-3}$.
Geometric Foundation of Spin and Isospin  [PDF]
Ludger Hannibal
Physics , 1996,
Abstract: Various theories of spinning particles are interpreted as realizing elements of an underlying geometric theory. Classical particles are described by trajectories on the Poincare group. Upon quantization an eleven-dimensional Kaluza-Klein type theory is obtained which incorporates spin and isospin in a local SL(2,C) x U(1) x SU(2) theory with broken U(1)x SU(2) part.
A Geometric Picture of Entanglement and Bell Inequalities  [PDF]
R. A. Bertlmann,H. Narnhofer,W. Thirring
Mathematics , 2001, DOI: 10.1103/PhysRevA.66.032319
Abstract: We work in the real Hilbert space H_s of hermitian Hilbert-Schmid operators and show that the entanglement witness which shows the maximal violation of a generalized Bell inequality (GBI) is a tangent functional to the convex set S subset H_s of separable states. This violation equals the euclidean distance in H_s of the entangled state to S and thus entanglement, GBI and tangent functional are only different aspects of the same geometric picture. This is explicitly illustrated in the example of two spins, where also a comparison with familiar Bell inequalities is presented.
The Madelung transform as a momentum map  [PDF]
Daniel Fusca
Mathematics , 2015,
Abstract: The Madelung transform relates the non-linear Schr\"{o}dinger equation and a compressible Euler equation known as the quantum hydrodynamical system. We prove that the Madelung transform is a momentum map associated with an action of the semidirect product group $\mathrm{Diff}(\mathbb{R}^{n})\ltimes C^\infty(\mathbb{R}^{n})$, which is the configuration space of compressible fluids, on the space $\Psi$ of wave functions. In particular, we show that the Madelung transform is a Poisson map taking the natural Poisson bracket on $\Psi$ to the compressible fluid Poisson bracket, and observe that the Madelung transform provides an example of "Clebsch variables" for the hydrodynamical system.
Superstring field theory in the democratic picture  [PDF]
Michael Kroyter
Mathematics , 2009,
Abstract: We present a new open superstring field theory, whose string fields carry an arbitrary picture number and reside in the large Hilbert space. The redundancy related to picture number is resolved by treating picture changing as a gauge transformation. A mid-point insertion is imperative for this formalism. We find that this mid-point insertion must include all multi-picture changing operators. It is also proven that this insertion as well as all the multi-picture changing operators are zero weight conformal primaries. This new theory solves the problems with the Ramond sector shared by other RNS string field theories, while naturally unifying the NS and Ramond string fields. When partially gauge fixed, it reduces in the NS sector to the modified cubic superstring field theory. Hence, it shares all the good properties of this theory, e.g., it has analytical vacuum and marginal deformation solutions. Treating the redundant gauge symmetry using the BV formalism is straightforward and results in a cubic action with a single string field, whose quantum numbers are unconstrained. The generalization to an arbitrary brane system is simple and includes the standard Chan-Paton factors and the most general string field consistent with the brane system.
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