Research
Gauge-theoretic Study of Kundt Tube Experiment and Spontaneous Symmetry Transitions
In the Kundt’s experiment of acoustic resonance in closed tubes, two characteristic lengths were observed: one is the wave-length of the sound waves in resonance and the other the scale of dust striation. The latter has remained unresolved for its formation mechanism. Based on the Fluid Gauge Theory proposed recently by the author, formation mechanism of the dust striation is studied. When the sound is weak enough, the striation is unobserved. Once the wave intensity exceeds a threshold value, dust striations are formed. Formation of the dust striation is understood as a spontaneous transition of symmetry in the acoustics. According to the Theory, there is a transition of stress field within the fluid flow. Whereas the stress field is isotropic before transition, it becomes anisotropic after the transition. This is analogous to the spontaneous symmetry breaking known in the field theory. Lagrangian structures of both systems are verified to be analogous either.
Unlocking Galactic Mysteries: Relativistic Insight into Orbital Hyper-Speeds and Dark Matter in Gas-Rich Galactic-Halos
This study is a novel approach to the cosmological issue of the dark matter effect observed in gas-dominated galaxies in rotation. A possible physical mechanism is investigated to produce the hyper orbital-speeds in outer halo parts of galaxies. In the galactic space, gas clouds are abundant. Motion of the gas-clouds is viewed as a flow of a continuous fluid in curved space with gravity. Dynamical motions of the space-fluid are studied by Fluid Dynamics extended to the one of a relativistic gravitational field. The fluid flow to be studied in relativistic gravity field is reinforced by the fluid gauge theory equipped with a background (dark) gauge field. The stress-energy tensor in the general relativity is revised to take account of intrinsic nature of stress field by generalizing the isotropic pressure to an anisotropic stress field. Present study takes a new double-sided approach both dynamically and physically. Namely a gauge-field is newly incorporated in the system as a dynamical term, and the system is studied under a new mechanism of the anisotropic stress fields.
Relativistic Exploration of Dark Matter Effects in Rotating Galaxy, Studied Fluid-Dynamically
Galactic space is filled with interstellar clouds of neutral gases. Motion of the spaceclouds is viewed as a flow of continuous fluid in curved space with gravity. Dynamical motions of the space-fluid of rotating galaxies are investigated by extending Fluid Dynamics to that in the frame of general relativity. Fluid flow field to be extended to that of a relativistic theory is reinforced by the fluid gauge theory equipped with a background (dark) gauge field conditioning the fluid continuity. The Gravity-space Fluid Dynamics thus developed captures main feature of the dark-matter effect as the action of the gauge field on the motion of space fluids. In the present formulation, the stress-energy tensor in the general relativity is revised in order to take account of general nature of stress field by extending the isotropic pressure to an-isotropic stress field.
Gauge Symmetries in Physical Fields (Review)
Gauge invariance is one of the fundamental symmetries in theoretical physics. In this paper, the gauge symmetry is reviewed to see how it is working in fundamental physical fields: Electromagnetism, Quantum ElectroDynamics and Geometric Theory of Gravity. In the 19th century, the gauge invariance was recognized as a mathematical non-uniqueness of the electromagnetic potentials. Real recognition of the gauge symmetry and its physical significance required two new fields developed in the 20th century: the relativity theory for physics of the world structure of linked 4d-spacetime and the quantum mechanics for the new dimension of a phase factor in complex representation of wave function. Finally the gauge theory was formulated on the basis of the gauge principle which played a role of guiding principle in the study of physical fields such as Quantum Electrodynamics, Particle Physics and Theory of Gravitation. Fluid mechanics of a perfect fluid can join in this circles, which is another motivation of the present review. There is a hint of fluid gauge theory in the general representation of rotational flows of an ideal compressible fluid satisfying the Euler’s equation, found in 2013 by the author. In fact, law of mass conservation can be deduced from the gauge symmetry equipped in the new system of fluid-flow field combined with a gauge field, rather than given a priori.
Fluid Gauge Theory
According to the general gauge principle, Fluid Gauge Theory is presented to cover a wider class of flow fields of a perfect fluid without internal energy dissipation under anisotropic stress field. Thus, the theory of fluid mechanics is extended to cover time dependent rotational flows under anisotropic stress field of a compressible perfect fluid, including turbulent flows. Eulerian fluid mechanics is characterized with isotropic pressure stress fields. The study is motivated from three observations. First one is experimental observations reporting largescale structures coexisting with turbulent flow fields. This encourages a study of how such structures observed experimentally are possible in turbulent shear flows, Second one is a theoretical and mathematical observation: the â€General solution to Euler’s equation of motion†(found by Kambe in 2013) predicts a new set of four background-fields, existing in the linked 4d-spacetime. Third one is a physical query, â€what symmetry implies the current conservation law ?â€. The latter two observations encourage a gauge-theoretic formulation by defining a differential one-form representing the interaction between the fluid-current field and a background field . A known relativistic action of a perfect fluid is introduced together with the interaction action just mentioned, and furthermore, a third gauge invariant action is defined to govern the field linearly in its free-state. The general gauge principle is applied to the combined system of the three actions to describe general time-dependent rotational flow fields of an ideal compressible fluid. The combined system can be shown to be invariant under both global and local gauge transformations of variations of . The global gauge transformation is a diagnostic test whether the system is receptive to a new field . Since the test is cleared, a new internal stress field is introduced into the flow field of a perfect fluid, together with the current conservation = 0, where the stress is an anisotropic stress field which is an extension added to the Eulerian isotropic pressure-stress field jμ aμ aμ aμ aμ(xν ( Mik(xν ( ∂μjμ Mik p δik.
