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Nonstandard analysis in classical physics and quantum formal scattering

1988

After a rigorous introduction to hyperreal numbers, we give in terms of non standard analysis, (1) a Lagrangian statement of classical physics, and (2) a statement of formal quantum scattering. © 1988 Plenum Publishing Corporation.

PhysicsStatement (computer science)Physics and Astronomy (miscellaneous)General MathematicsHyperreal numberClassical physicsSchrödinger equationNon-standard analysisField Theory Elementary Particle Quantum Field Theory Standard Analysis Classical Physicsymbols.namesakeAnalytical mechanicssymbolsScattering theoryQuantumSettore MAT/07 - Fisica MatematicaMathematical physics

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PEPhysical Sciences and Engineering
- PE2Fundamental Constituents of Matter
  - PE2_1Theory of fundamental interactions
  - PE2_2 Phenomenology of fundamental interactions
  - PE2_3Experimental particle physics with accelerators
  - PE2_4Experimental particle physics without accelerators
  - PE2_6Nuclear, hadron and heavy ion physics
  - PE2_8Gas and plasma physics
  - PE2_5Classical and quantum physics of gravitational interactions
  - PE2_7Nuclear and particle astrophysics
  - PE2_9 Electromagnetism
  - PE2_10Atomic, molecular physics
  - PE2_11Ultra-cold atoms and molecules
  - PE2_18Equilibrium and non-equilibrium statistical mechanics: steady states and dynamics
  - PE2_14Lasers, ultra-short lasers and laser physics
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  - PE4_7Chemical instrumentation
  - PE4_8Electrochemistry, electrodialysis, microfluidics, sensors
  - PE4_10Heterogeneous catalysis
  - PE4_9Method development in chemistry
  - PE4_11Physical chemistry of biological systems
  - PE4_15Photochemistry
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  - PE11_2Engineering of metals and alloys
  - PE11_1Engineering of biomaterials, biomimetic, bioinspired and bio-enabled materials
  - PE11_3Engineering of ceramics and glasses
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  - PE11_6Engineering of carbon materials
  - PE11_7Engineering of metal oxides
  - PE11_8Engineering of alternative established or emergent materials
  - PE11_9Nanomaterials engineering, e.g. nanoparticles, nanoporous materials, 1D & 2D nanomaterials
  - PE11_10Soft materials engineering, e.g. gels, foams, colloids
  - PE11_11Porous materials engineering, e.g. covalent-organic, metal-organic, porous aromatic frameworks
  - PE11_12Semi-conducting and magnetic materials engineering
  - PE11_13Metamaterials engineering
  - PE11_14Computational methods for materials engineering
LSLife Sciences
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  - LS1_13Early translational research and drug design
  - LS1_14Innovative methods and modelling in molecular, structural and synthetic biology
  - LS1_10Synthetic biology
  - LS1_8Structural biology
  - LS1_9Molecular mechanisms of signalling processes
  - LS1_7Molecular biophysics, biomechanics, bioenergetics
- LS2Integrative Biology: from Genes and Genomes to Systems
  - LS2_1Genetics
  - LS2_3Epigenetics
  - LS2_2Gene editing
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  - LS2_7Transcriptomics
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  - LS2_16Innovative methods and modelling in integrative biology
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  - LS4_1Organ and tissue physiology and pathophysiology
  - LS4_4Endocrinology
  - LS4_3Physiology of ageing
  - LS4_2Comparative physiology
  - LS4_5Non-hormonal mechanisms of inter-organ and tissue communication
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  - LS4_10The cardiovascular system and cardiovascular diseases
  - LS4_11Haematopoiesis and blood diseases
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  - LS4_13Other non-communicable diseases (except disorders of the nervous system and immunity-related diseases)
- LS3Cell Biology, Development, Stem Cells and Regeneration
  - LS3_4Cell junctions, cell adhesion, the extracellular matrix, cell communication
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  - LS3_17Theoretical modelling in cellular, developmental and regenerative biology
  - LS3_16Functional imaging of cells and tissues
  - LS3_1Cell cycle, cell division and growth
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- LS5Neuroscience and Disorders of the Nervous System
  - LS5_1Neuronal cells
  - LS5_3Neural development and related disorders
  - LS5_5Neural networks and plasticity
  - LS5_10Ageing of the nervous system
  - LS5_11Neurological and neurodegenerative disorders
  - LS5_12Mental disorders
  - LS5_7Sensory systems, sensation and perception, including pain
  - LS5_13Nervous system injuries and trauma, stroke
  - LS5_14Repair and regeneration of the nervous system
  - LS5_15Neuroimmunology, neuroinflammation
  - LS5_16Systems and computational neuroscience (e.g. modelling, simulation, brain oscillations, connectomics)
  - LS5_18Innovative methods and tools for neuroscience
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  - LS5_4Neural stem cells
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  - LS8_15Theoretical developments and modelling in environmental biology, ecology, and evolution
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  - LS9_6Marine biotechnology and bioengineering
  - LS9_7Environmental biotechnology and bioengineering
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  - LS9_10Veterinary and applied animal sciences
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  - LS9_11Biomass production and utilisation, biofuels
  - LS9_12Ecotoxicology, biohazards and biosafety
  - LS9_1Bioengineering for synthetic and chemical biology
SHSocial Sciences and Humanities
- SH2Institutions, Governance and Legal Systems
  - SH2_1Political systems, governance
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  - SH2_3Conflict resolution, war, peace building
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- SH5Texts and Concepts
  - SH5_4Philology; text and image studies
  - SH5_1Classics, ancient literature
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  - SH5_3Book studies
  - SH5_6Philosophy of mind, philosophy of language
  - SH5_7Philosophy of science, epistemology, logic
  - SH5_8Metaphysics, philosophical anthropology; aesthetics
  - SH5_9Ethics and its applications; social philosophy
  - SH5_10History of philosophy
  - SH5_11Digital humanities; digital approaches to literary studies and philosophy
  - SH5_2Theory and history of literature, comparative literature
- SH7Human Mobility, Environment, and Space
  - SH7_2Migration
  - SH7_1Human, economic and social geography
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  - SH7_4Social aspects of health, ageing and society
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  - SH8_5History of art and of architecture
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  - SH8_9Digital approaches to anthropology, cultural studies and art