Berry phase and quantum structure

Lyre, Holger

doi:10.1016/j.shpsb.2014.08.013

Cited by 8 publications

(10 citation statements)

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“…This programme was initiated byMackey (1963); seeRédei (1998) for an introduction. I say 'isolated' because physical features of subtly interacting systems like global phase are neglected the lattice description(Lyre 2014).…”

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Observables, disassembled

Roberts¹

2018

Studies in History and Philosophy of Science Part B: Studies in

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This paper argues that non-self-adjoint operators can be observables.There are only four ways for this to occur: non-self-adjoint observables can either be normal operators, or be symmetric, or have a real spectrum, or have none of these three properties. I explore each of these four classes of observables, arguing that the class of normal operators provides an equivalent formulation of quantum theory, whereas the other classes considerably extend it. arXiv:1610.07637v1 [physics.hist-ph] 21 Oct 2016 Observables, Disassembled 3The plan of the paper is as follows. The second section will introduce the dogma of self-adjoint operators, and then propose a way to classify the possible nonself-adjoint observables. The third section considers non-self-adjoint operators that are normal. Here I formulate a sense in which normal operators provide an equivalent framework for doing quantum mechanics. The fourth section explores the physics of non-normal operators: first operators that are symmetric but not real, which allow for

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Observables, disassembled

Roberts¹

2018

Studies in History and Philosophy of Science Part B: Studies in

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“…Antes dos trabalhos (Aharonov e Bohm, 1959) e (Berry, 1984) a fase de um vetor de estado era considerada irrelevante, pois a mesma desaparecia na regra de Born ou na projeção em um dado estado, mas graças aos trabalhos citados anteriormente e inúmeros outros os físicos foram obrigados a considerar a fase como uma componente da realidade. Então nesse sentido torna-se necessário construir uma teoria que tenha essa ambiguidade na escolha da fase em seu cerne (Lyre, 2014) . De forma rigorosa seja H o espaço de Hilbert e P o espaço projetivo do espaço de Hilbert, diz-se que P é o cojunto quociente de H por uma relação de equivalência, (Grigorenko, 1992) ψ ∼ λψ tal que define-se uma operação de projeção π : H → P…”

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“…De forma análoga, a subtração das equações descritas em 5.24 permite definir um operador , Supondo um hamiltoniano dado pela equação(referenciar equação modelo efetivo) introduzimos um termo massivo ∆Q 14 , De modo que a simetria de subrede associada a C 2 e Q 14 é quebrada. Como dito anteriormente a cada conjunto de tuplas de duas a duas simetrias de rede é possível construir um operador que comuta com H. Portanto a inserção de um termo proporcional a C 3 quebrará a corrente associada aos observáveis associados aos operadores C 1 C 2 , 29) onde como mostrado anteriormente iC 1 C 2 formam um conjunto de autovalores (−1, −1, 1, 1) Podemos construir os operadores de projeção…”

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“…Each of them presents its own advantages and disadvantages. There is, however, a common and seemingly unsolvable problem: As required by the Nielsen-Ninomiya theorem (NNT) [29,30], all these approaches introduce a symmetry breaking or nonlocality.…”

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“…, where the integer j labels the points in the discrete lattice of spacing a. Consequently, it allows for low-energy, highly oscillating states of a topological origin [29,30], thus yielding the doublers shown in Fig. 1(a).…”

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Modelos matemáticos para isolantes topológicos em redes

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Hamiltonians of Dirac type are ubiquitous. Appearing in materials such as graphene, topological insulators or recently in the Weyl semimetals. Due to the technological and academic interest of these materials, characterizing their properties is essential. A mathematical approach to study these systems consists of discretizing the Hamiltonian in the space of positions, but such an approach causes the problem of doubling fermions (FDP). We demonstrate the FDP should not be a cause of concern for the study of confined systems because we can use the broken symmetry to confine in the system to remove the duplicate states. Such removal is achieved by inserting a quadratic term with respect to the moment, known as the Wilson mass. In this sense we can insert a Wilson term with symmetry breaking required for confinement, rendering the fermion duplication problem irrelevant, this relationship had not been noticed until the present work, and recent literature results erroneously attribute Wilson's mass to break of a symmetry of time reversal, which is not necessarily true. In this context, in addition to addressing this relationship, the present dissertation also aims to elucidate some misconceptions regarding the Wilson masses, chirality and other symmetries. In order to validate our central argument we study several systems of interest and compare it with the results in the literature.

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Torsion Geometry 5-Fold Symmetry, Anholonomic Phases, Klein Bottle Logophysics, Chaos, Resonance: Applications Towards a Novel Paradigm for the Neurosciences and Consciousness

Rapoport

2023

J. Phys.: Conf. Ser.

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We discuss the torsion geometries as the universal dynamical setting for the five-fold symmetry and its relation to nonorientable surfaces of selfreference embodying a supradual logophysics, rooted in the Möbius strip and Klein Bottle. We frame the discussion in terms of image-schemas in cognitive semantics and their disruption stemming from supraduality and nonorientability. We present the relation with anholonomic phases, chaos and the brain-mind as an integrated dynamical system. We discuss nonorientability as the characteristic transcendental metapattern of resonant connection, pattern formation and recognition. We present the torsion geometry and nonorientability in psychophysics and the neurosciences. We discuss the homology of the torsion geometry of physical space or spacetime with that of the unconscious modelization by the brain-mind of the kinematics of objects in physical space and in the perception of music, elaborating on the Principle of Complementarity of cognitive psychology due to Shepard. We elaborate on the phenomenological construal of experience, the world as experience. We discuss the supraduality of the liminal states of consciousness and the basis of awareness in memory. We introduce the cognitive psychology foundations of memory on nonorientability and its relations to the short-memory space and its quantumlike nature, and the hyperbolicity of the psychophysics of vision. We discuss the chaotic behaviour of dynamical systems as a manifestation of supraduality as their nonorientability. We propose a basis for the source of consciousness, the Hard Problem, given by the principles of selfreference and hetero-reference which generate the Klein Bottle supradual logophysics. We present the supradual logophysics of neuron cytoskeletal structures, its relation to torsion, resonances, topological and geometrical phases and the microtubule dynamics in terms of nonlinear buckling patterns and nonorientability, and still the torsion geometry of the irreversible thermodynamical processes supporting interactions-at-a-distance. We discuss the primal relation of torsion, nonorientability and memory, particularly arising in the buckling of microtubules. We discuss the primal morphogenesis of the cell as a tensegrity structure, torsion and the indiscernibility of elastodynamics, electromagnetic and gravitational wavefronts as morphogenetic fields. We discuss nonorientability as the metaform pattern of connection and resonance, particularly of interaction-at-a-distance. We apply it to a topological allosteric effect mediated by electromagnetic fields. We discuss the topological chemistry paradigm, particularly of organic chemistry where conformation superposition is crucial, its relation to anaesthetics and its application to the ORC OR theory of Penrose and Hameroff for consciousness as arising from the collapse of the wave function which we relate to the multiconformation in the topological chemistry paradigm. We propose a model of continuous signal processing in digital terms which allows an optimal reconstruction -from digital to continuous-in terms of the Nyquist-Shannon theorem whose constraints on frequencies and bandwidths is naturally interpreted in the terms of the 2:1 harmonics of nonorientability in the Möbius strip or Klein Bottle. We discuss the non-dual logic of the tubulin code and the resonator nature of the neuronal cytoskeleton. We propose that the topological phases appearing in the cytoskeleton may correspond to the topological anholonomity, namely, nonorientability, as was elicited empirically by the Bandyopadhyay group, the existence of anholonomity corresponding to the 360° rotation characteristic of the topological anholonomity, Möbius strip. We propose the Matrix Logic representation of the Klein Bottle logic as the basis for microtubule computations, and discuss the relation to quantum computation, topological entanglement and the topological coherence/decoherence Klein Bottle cycle. We also relate it to holography, the brain’s integration and Velmans’ Reflexive Monism extended by Rapoport. We discuss the multiconformation orientable and nonorientable resonators electronic devices and antennas as classical-quantum realisations of microtubule coherent behaviour. We discuss the relation of life and consciousness and the topological nonorientable embodiment of memory. We introduce the dynamical reduction program for the collapse of the quantum state in terms of the torsion stochastic differential geometry of the quantum geometry of Quantum Mechanics as projective space, and particularly the stochastic extension of the Schroedinger equation to account for the coupling of quantum system and environment, say a measurement apparatus. Thus we identify a realisation of the dynamical reduction program which is based on the torsion geometry, yet supports an agent-free collapse of the quantum state, as an objective albeit random process due to quantum fluctuations. We shall discuss the present supradual logophysics in several aspects such as 1) microtubule structure and dynamics, 2) the orientable and nonorientable conformations of organic molecules, 3) the relation with anaesthetics and the altered states of consciousness and 4) confront them with the tenets of Penrose & Hameroff ORC OR theory for the origin of consciousness, not only the topological chemistry but their choice of a superposition of null torsion as in General Relativity, which renders a trivial selfreferentiality, with the topological chemistry multiconformations which requires non-null torsion. The nontrivial selfreferentiality is both proper to the mind and the torsion geometry, be that on the physical, chemical, perceptual or cognitive domains. All in all, we propose that consciousness is neither based on panpsychism nor the collapse of quantum states, nor exclusively on the control of superposition of conformations of organic chemistry, but rather on the torsion-nonorientable geometry-topology based on the principles of selfreference and hetero-reference, operating in all domains: that of meaning, the mental-anatomical-physiological domain, structural processes of matter energy and in-formation, be that physical, chemical, biological, cognitive and perception. We present a remarkable connection between them. Our approach rather than multidisciplinary will be transdisciplinary, a possibility supported on supraduality - transcending the dual-logic based logophysics-from which the theory will follow in a rather smooth way.

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Berry phase and quantum structure

Cited by 8 publications

References 23 publications

Observables, disassembled

Observables, disassembled

Modelos matemáticos para isolantes topológicos em redes

Torsion Geometry 5-Fold Symmetry, Anholonomic Phases, Klein Bottle Logophysics, Chaos, Resonance: Applications Towards a Novel Paradigm for the Neurosciences and Consciousness

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