Related papers: Fibre bundle formulation of relativistic quantum m…
We consider the geometric formulation of the Hamiltonian formalism for field theory in terms of {\em Hamiltonian connections} and {\em multisymplectic forms}. In this framework the covariant Hamilton equations for Mechanics and field theory…
We provide geometric quantization of the vertical cotangent bundle V^*Q equipped with the canonical Poisson structure. This is a momentum phase space of non-relativistic mechanics with the configuration bundle Q -> R. The goal is the…
We review two approaches to the definition of the Hilbert space and evolution in mechanical theories with local time-reparametrization invariance, which are often used as toy models of quantum gravity. The first approach is based on the…
We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…
We describe the time evolution of quantum systems in a classical background space-time by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve $\cC$…
Transports along path in fibre bundles are axiomatically introduced. Their general functional form and some their simple properties are investigated. The relationships of the transports along paths and lifting of paths are studied.
Relativistic Quantum Information Theory (RQI) is a flourishing research area of physics, yet, there has been no systematic mathematical treatment of the field. In this paper, we suggest bundle theoretic descriptions of massive…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
Smooth composite bundles provide the adequate geometric description of classical mechanics with time-dependent parameters. We show that the Berry's phase phenomenon is described in terms of connections on composite Hilbert space bundles.
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
We present a bundle geometric formulation of non-relativistic many-particles Quantum Mechanics. A wave function is seen to be a $\mathbb{C}$-valued cocyclic tensorial 0-form on configuration space-time seen as a principal bundle, while the…
The present essay provides a new metaphysical interpretation of Relational Quantum Mechanics (RQM) in terms of mereological bundle theory. The essential idea is to claim that a physical system in RQM can be defined as a mereological fusion…
In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. Starting with the Covariant Force Law, we first develop autonomous…
This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…
In this paper we propose the time & fitness-dependent Hamiltonian form of human biomechanics, in which total mechanical + biochemical energy is not conserved. Starting with the Covariant Force Law, we first develop autonomous Hamiltonian…
Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for…
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained…
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…