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Books on the topic 'Lie Symmetry group of SDE'

Author: Grafiati

Published: 1 February 2025

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1

Robinson, Matthew B. Symmetry and the standard model: Mathematics and particle physics. New York: Springer, 2011.

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2

Ortaçgil, Ercüment H. The Symmetry Group. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198821656.003.0016.

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This chapter, which ends Part II on some consequences of the new approach, introduces an alternative prolongation theory of Klein geometries that is more geometric and intuitive than the well-known prolongation theory of a linear Lie algebra developed by Guillemin, Singer, and Sternberg.

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3

Vergados, J. D. Group and Representation Theory. World Scientific Publishing Co Pte Ltd, 2016.

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4

O'Raifeartaigh, L. Group Structure of Gauge Theories. Cambridge University Press, 2012.

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5

O'Raifeartaigh, L. Group Structure of Gauge Theories. Cambridge University Press, 2011.

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6

Wallach, Nolan R., and Roe Goodman. Symmetry, Representations, and Invariants. Springer, 2010.

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7

Sato, Ryuzo, and Rama V. Ramachandran. Symmetry and Economic Invariance. Springer London, Limited, 2013.

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8

Sato, Ryuzo, and Rama V. Ramachandran. Symmetry and Economic Invariance. Springer Japan, 2016.

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9

Sato, Ryuzo, and Rama V. Ramachandran. Symmetry and Economic Invariance. Springer, 2013.

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10

Sato, Ryuzo, and Rama V. Ramachandran. Symmetry and Economic Invariance. T Kobayashi, 2013.

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11

Ceulemans, Arnout, and Pieter Thyssen. Shattered Symmetry: Group Theory from the Eightfold Way to the Periodic Table. Oxford University Press, Incorporated, 2017.

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12

Sato, Ryuzo. Symmetry and Economic Invariance: An Introduction. Springer, 2012.

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13

Sato, Ryuzo, and Rama V. Ramachandran. Symmetry and Economic Invariance: An Introduction. Springer London, Limited, 2012.

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14

Approximate and Renormgroup Symmetries. Springer, 2009.

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15

Ibragimov, N. Kh, and Vladimir F. Kovalev. Approximate and Renormgroup Symmetries. Springer, 2010.

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16

Approximate And Renormgroup Symmetries. Springer, 2009.

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17

Sato, Ryuzo, and Rama V. Ramachandran. Symmetry and Economic Invariance: An Introduction (Research Monographs in Japan-U.S. Business and Economics). Springer, 1997.

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18

Canarutto, Daniel. Gauge Field Theory in Natural Geometric Language. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198861492.001.0001.

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This monograph addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a not-too-short, integrated approach that exploits standard and non-standard notions in natural geometric language. The role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. Two-spinors yield a partly original ‘minimal geometric data’ approach to Einstein-Cartan-Maxwell-Dirac fields. The gravitational field is jointly represented by a spinor connection and by a soldering form (a ‘tetrad’) valued in a vector bundle naturally constructed from the assumed 2-spinor bundle. We give a presentation of electroweak theory that dispenses with group-related notions, and we introduce a non-standard, natural extension of it. Also within the 2-spinor approach we present: a non-standard view of gauge freedom; a first-order Lagrangian theory of fields with arbitrary spin; an original treatment of Lie derivatives of spinors and spinor connections. Furthermore we introduce an original formulation of Lagrangian field theories based on covariant differentials, which works in the classical and quantum field theories alike and simplifies calculations. We offer a precise mathematical approach to quantum bundles and quantum fields, including ghosts, BRST symmetry and anti-fields, treating the geometry of quantum bundles and their jet prolongations in terms Frölicher's notion of smoothness. We propose an approach to quantum particle physics based on the notion of detector, and illustrate the basic scattering computations in that context.

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