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Quantum walks constitute important tools in different applications, especially in quantum algorithms. To a great extent their usefulness is due to unusual diffusive features, allowing much faster spreading than their classical counterparts.…

Mermin's "shut up and calculate!" somehow summarizes the most widely accepted view on quantum mechanics. This conception has led to a rather constraining way to think and understand the quantum world. Nonetheless, a closer look at the…

A weakness which has previously seemed unavoidable in particle interpretations of quantum mechanics (such as in the de Broglie-Bohm model) is addressed here and a resolution proposed. The weakness in question is the lack of action and…

We introduce and analyze a system of relativistic fermions in a space-time continuum, which interact via an action principle as previously considered in a discrete space-time. The model is defined by specifying the vacuum as a sum of Dirac…

Thought experiments about the physical nature of set theoretical counterexamples to the axiom of choice motivate the investigation of peculiar constructions, e.g. an infinite dimensional Hilbert space with a modular quantum logic. Applying…

Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a…

Feynman's Lagrangian path integral was an outgrowth of Dirac's vague surmise that Lagrangians have a role in quantum mechanics. Lagrangians implicitly incorporate Hamilton's first equation of motion, so their use contravenes the uncertainty…

An analysis of the path-integral approach to quantum theory motivates the hypothesis that two experiments with the same classical action should have dual ontological descriptions. If correct, this hypothesis would not only constrain…

Recent astronomical observations indicate that the Universe is presently almost flat and undergoing a period of accelerated expansion. Basing on Einstein's general relativity all these observations can be explained by the hypothesis of a…

Action-at-a-distance electrodynamics - alternative approach to field theory - can be extended to cosmological models using conformal symmetry. An advantage of this is that the origin of arrow of time in electromagnetism can be attributed to…

Active inference is a mathematical framework which originated in computational neuroscience as a theory of how the brain implements action, perception and learning. Recently, it has been shown to be a promising approach to the problems of…

Evidence is growing for the theory of embodied cognition, which posits that action and perception co-determine each other, forming an action-perception loop. This suggests that we humans somehow participate in what we perceive. So, how can…

Long-range effective methods are ubiquitous in physics and in quantum theory, in particular. Furthermore, the reliability of such methods is higher when the nature of short-ranged interactions need not be modeled explicitly. This may be…

World models have recently re-emerged as a central paradigm for embodied intelligence, robotics, autonomous driving, and model-based reinforcement learning. However, current world model research is often dominated by three partially…

This thesis is split into two parts, which are united in the sense that they involve applying ideas from quantum information to fundamental physics. The first part is focused on examining discrete-time models in quantum computation…

Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…

Some well-known examples of constrained quantum systems commonly quantized via Feynman path integrals are re-examined using the notion of conditional integrators introduced in [1]. The examples yield some new perspectives on old results. As…

An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…

A new version of hidden variables theory founded on the generalisation of world's geometry is proposed. The quantum-mechanical motion as the motion in some "inner space", which has a structure of the integrable Weyl space is examined.…

We define proper, free and commuting partial actions on upper semicontinuous bundles of $C^*-$algebras. With such, we construct the $C^*-$algebra induced by a partial action and a partial actions on that algebra. Using those action we give…