arXiv subjects

S. R. Vatsya

Publications and source records attributed to S. R. Vatsya.

6 recordsLinked to original sources

arXiv2018

Geometrical formulation of quantum fields

Path integral formulation of quantum mechanics defines the wavefunction associated with a particle as a sum of phase-factors, which are periodic functions of classical action. In the present article, this periodicity is shown to impart the corresponding periodicity to a one parameter family of wavefunctions generated by the translations of arclength used to parameterize the trajectories. Translation parameter is adjoined to the base to obtain an extended manifold. Periodicity of the family of wavefunctions with respect to the translation parameter together with solutions of the generalized Klein-Gordon equation, which is deducible from the path integral formulation, is used to define a quantized field with zero vacuum energy in the extended manifold with the particle being its quantum. Classical description of essentially the same particle is obtained in the extended higher dimensional space using its properties. This manifold can replace the base in this treatment to continue the program for higher dimensional manifolds generated in the process. Results are illustrated by taking the three-dimensional Euclidean space the base, which yields the classical and quantum particle descriptions of photon in the base and the field description in the resulting extended manifold, which is identified with the Minkowski spacetime. The field formulation yields the quantized Maxwell's equations. A novel interpretation of time as the corresponding translation parameter results in the process. Classical description in the extended manifold, i.e., the Minkowski spacetime, results in the relativistic description of a massive particle related to the photon. The results are further illustrated for this massive particle in the Minkowski spacetime obtaining parallel results.

physics.gen-ph↗

arXiv2018

Geometrical Formulation of Quantum Mechanics

Hamilton's action principle is formulated and extended in conformity with the gauge transformations underlying Weyl's geometry. The extended principle characterizes infinitely many equally likely trajectories with a particle traveling along a randomly selected one. Available similar formulations do not conform as directly to the gauge transformations as the present one. Also, they have not paid much attention to the path-independent, assigned gauges. The freedom available in assigning these gauges is exploited here by defining them in terms of the configuration, and interactions of the observing system with the observed one. Impact of the method of observation on its outcome is described in terms of the assigned gauges so defined and illustrated with examples. A wavefunction is defined in a simply connected region essentially as an aggregate of the gauge transformations over all trajectories; equivalently, an aggregate of the Weyl-lengths acquired by a unit vector transported along all trajectories from everywhere. This representation is similar to Feynman's path integral representation differing only in that it incorporates the assigned gauges yielding an adjusted wavefunction that includes the impact of an observing system on the observed one. Probability density is shown to be a uniquely defined gauge invariant quantity but at the expense of the information about the observable effects contained in the gauge factors, assigned and otherwise. The particle trajectories defined here are thus shown to provide additional significant information about a system than provided by the wavefunction together with the probability density. Present description of the impact of method of observation on its outcome is compared with the descriptions according to the existing major representations of quantum mechanics.

quant-ph↗

arXiv2005

Path integral formulation of quantized fields

Physical path integral formulation of motion of particles in Riemannian spaces is outlined and extended to deduce the corresponding field theoretical formulation. For the special case of a zero rest mass particle in Minkowski manifold, it is shown that the underlying space can be reduced to three-dimensional while similar formulation for a massive particle requires a four-dimensional structure. The solutions obtained by the present procedure are compared with the results obtained from its counterpart for a massive particle by setting the mass equal to zero. Although similar, the present formulation has some additional implications pertaining to the energy spectrum and the associated free field quantization, particularly it yields zero vacuum energy. The results are naturally extended to higher dimensions.

quant-ph↗

arXiv1998

Primal structure of Quantum Mechanics - A critique and an alternative

The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a wave are assumed to be correct. Gauge Mechanics treats the discrete entities as particles, and their motion is described by an extension of the corresponding classical laws. Quantum mechanical interpretations of various observations and their implications, including some issues that are usually ignored, are presented and compared here with the gauge mechanical descriptions. The considerations are confined mainly to the conceptual foundations and the internal consistency of these theories. Although no major differences between their predictions have yet been noticed, some deviations are expected, which are indicated. These cases may provide the testing grounds for further investigations.

quant-ph↗

arXiv1996

Particle Path Formulation of Quantum Mechanics

An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle paths are shown to impart wave like behaviour to a particle in motion and to imply various other assumptions and conjectures attributed to the formalism of Quantum Mechanics. The Klein-Gordon and other similar equations are derived by incorporating these properties in the path-integral formalism.

quant-ph↗

arXiv1994

Mechanics of a Particle in a Gauge Field

The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle is shown here to be an equivalence relation between the infinitesimal elements so defined for a collection of closed curves and the identity element. The action principle is then extended by requiring the equivalence of global elements with the identity and by considering all curves. The resulting equation is generalized further to include the non-Abelian gauge fields. The extended equation has an infinite number, but not all, trajectories as solutions. The properties of these paths are shown to impart wave-like properties to the particles in motion. These results provide an insight into the wave-particle duality and lead to a modified path-integral formalism. The motion of a particle is formulated within the resulting framework which yields a generalized Schrodinger equation. This equation is shown to reduce to a set of equations, one of them being the Klein-Gordon equation.

gr-qc↗