Related papers: Appearance of Gauge Fields and Forces beyond the a…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.
A brief review of main features of the new approach named ``quantum geometrodynamics in extended phase space'' is given and its possible prospects are discussed. Gauge degrees of freedom are treated as a subsystem of the Universe which…
Berry phases and gauge structures in parameter spaces of quantum systems are the foundation of a broad range of quantum effects such as quantum Hall effects and topological insulators. The gauge structures of interacting many-body systems,…
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is…
We investigate the geometric phases and the Bargmann invariants associated with a multi-level quantum systems. In particular, we show that a full set of `gauge-invariant' objects for an $n$-level system consists of $n$ geometric phases and…
It is sometimes stated in the literature that the quantum anomaly is regarded as an example of the geometric phase. Though there is some superficial similarity between these two notions, we here show that the differences bewteen these two…
We show that a noncyclic phase of geometric origin has to be included in the approximate adiabatic wave function. The adiabatic noncyclic geometric phase for systems exhibiting a conical intersection as well as for an Aharonov-Bohm…
The possibility of non-trivial representations of the gauge group on wavefunctionals of a gauge invariant quantum field theory leads to a generation of mass for intermediate vector and tensor bosons. The mass parameters m show up as central…
Appearance of adiabatic geometric phase shift in the context of noncommutative quantum mechanics is studied using an exactly solvable model of 2D simple harmonic oscilator in Moyal plane, where momentum non-commutativity are also considered…
These notes have been triggered by physicist's considerations on (1)'Pre-quantized wave equations' for matter fields, (2) Conservation laws, (3) Gauge Field extensions. All starting from variational principles. These notes do not contain…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
Systems of interacting charges and fields are ubiquitous in physics. Recently, it has been shown that Hamiltonians derived using different gauges can yield different physical results when matter degrees of freedom are truncated to a few…
Emergence of fundamental forces from gauge symmetry is among our most profound insights about the physical universe. In nature, such symmetries remain hidden in the space of internal degrees of freedom of subatomic particles. Here we…
We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian,…
Cosmological magnetic fields in open Friedmann universes can experience superadiabatic amplification within the realm of conventional electromagnetism. This is possible mathematically, despite the conformal invariance of Maxwell's…
In this paper, we discuss a novel top-down perspective on gauging parameters in quantum field theories (QFTs) by promoting them to partially dynamical fields. Through a generalized notion of symmetry theories, we explore the consequences of…
We report here the status of different gauge conditions in the canonical formulation of quantum electrodynamics on light-front surfaces. We start with the massive vector fields as pedagogical models where all basic concepts and possible…
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be…