Physics from Symmetry

Schwichtenberg, Jakob

doi:10.1007/978-3-319-19201-7

Cited by 34 publications

(32 citation statements)

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“…Otherwise, (45)'s higher-dimensional structure would not be a viable CAM unification candidate. zz For example, the geometric objects that the Lie groups U (1) and SU (2) are associated with must be differentiable (smooth) manifolds with a group → manifold operation which induces a differentiable map of the manifold into itself; 16,17,38,86 this group → manifold operation for the unit 1 and 3-spheres is of course division algebraic multiplicative binary composition. Thus the purely topological manifolds S 1 τ and S 3 τ lacking smooth structure are insufficient as the manifolds to associate with U (1) and SU (2), and the additional smooth structure will have to be appended.…”

Section: Source Space Compactificationmentioning

confidence: 99%

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The underlying geometry of the CAM gauge model of the Standard Model of particle physics

Wolk¹

2020

Int. J. Mod. Phys. A

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The Composition Algebra-based Methodology (CAM) [B. Wolk, Pap. Phys. 9, 090002 (2017); Phys. Scr. 94, 025301 (2019); Adv. Appl. Clifford Algebras 27, 3225 (2017); J. Appl. Math. Phys. 6, 1537 (2018); Phys. Scr. 94, 105301 (2019), Adv. Appl. Clifford Algebras 30, 4 (2020)], which provides a new model for generating the interactions of the Standard Model, is geometrically modeled for the electromagnetic and weak interactions on the parallelizable sphere operator fiber bundle [Formula: see text] consisting of base space, the tangent bundle [Formula: see text] of space–time [Formula: see text], projection operator [Formula: see text], the parallelizable spheres [Formula: see text] conceived as operator fibers [Formula: see text] attaching to and operating on [Formula: see text] [Formula: see text] as [Formula: see text] varies over [Formula: see text], and as structure group, the norm-preserving symmetry group [Formula: see text] for each of the division algebras which is simultaneously the isometry group of the associated unit sphere. The massless electroweak [Formula: see text] Lagrangian is shown to arise from [Formula: see text]’s generation of a local coupling operation on sections of Dirac spinor and Clifford algebra bundles over [Formula: see text]. Importantly, CAM is shown to be a new genre of gauge theory which subsumes Yang–Mills Standard Model gauge theory. Local gauge symmetry is shown to be at its core a geometric phenomenon inherent to CAM gauge theory. Lastly, the higher-dimensional, topological architecture which generates CAM from within a unified eleven [Formula: see text]-dimensional geometro-topological structure is introduced.

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Section: Source Space Compactificationmentioning

confidence: 99%

“…This notion of a parallelizable manifold (S n ) smoothly acting point-wise on another manifold (M) is analogous to the mathematical notion of Lie group elements, which are points on differentiable, parallelizable manifolds, smoothly acting on various kinds of objects -such as vectors or other manifolds32,39,71,86 (see, e.g. Ref.…”

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confidence: 99%

The underlying geometry of the CAM gauge model of the Standard Model of particle physics

Wolk¹

2020

Int. J. Mod. Phys. A

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“…Symmetry is primarily a construction that originated from other sciences such as physics, mathematics, and economics [47][48][49][50]. Basically, a system shows symmetry when there exists one transformation that leaves the system unchanged and balanced.…”

Section: Symmetry Between the Brand Strategy And Brand Structural Posmentioning

confidence: 99%

“…Basically, a system shows symmetry when there exists one transformation that leaves the system unchanged and balanced. Theoretically, it was widely acknowledged that the principle of symmetry has formed the basis of the standard model of particle physics and has been a fundamental property of nature [48,49]. Meanwhile, behavioral scientists have extended the importance of symmetry in human perception and cognition in recent years [51,52].…”

Section: Symmetry Between the Brand Strategy And Brand Structural Posmentioning

confidence: 99%

What Drives Sustainable Brand Awareness: Exploring the Cognitive Symmetry between Brand Strategy and Consumer Brand Knowledge

Gong¹,

Wang²,

Yue³

et al. 2020

Symmetry

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The explosive development of social media has given great opportunities to academic and industry research on consumer brand knowledge. Particularly, the brand associative network has been most frequently used to describe consumer brand knowledge structure. However, few researchers have examined the embedded connotation of the brand knowledge structural measurement in regard to sustainable brand performance and adjusted their brand strategies accordingly. Combining psychological cognitive theory and the network analytic method, this paper aims to extend this area by investigating the relationship between brand structural position in consumers’ associative knowledge network and sustainable brand awareness. Using a monthly dataset of around 130 million user posts, we find that compared to a prior determined brand strategy, brand network centrality in consumer’s brand associative knowledge network shows a much more significant positive effect on sustainable brand awareness. Importantly, we further examined the symmetric matching of brand positioning strategy and consumer’s brand knowledge structure for sustainable brand awareness. We find that sustainable brand awareness will be promoted by a symmetric matching brand positioning strategy with its position in the associative knowledge work. Our study facilitates an understanding of brands based on consumer perceptions for managers and enables businesses to adjust their relevant strategies for the achievement of sustainable brand performance.

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“…Direct computation shows that these operators satisfy the commutation relations of the Poincaré Lie algebra (see [34], Page 84; [47], Page 61): As generators of strongly continuous one-parameter unitary groups on ℋ,…”

Section: The Poincaré Lie Algebramentioning

confidence: 99%

An application of the theory of moments to Euclidean relativistic quantum mechanical scattering

Aiello¹

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To my brother, Alan. I admire you for becoming the man you are today and I truly look up to you for having made the climb. Your thoughtfulness, generosity, and devotion impact my life on a daily basis for which I am immeasurably grateful. I am proud to be your brother. To my father, James. Through your example I have learned the importance of values, integrity, dedication, and measuring twice to cut once. That's what makes you that guy. I am proud to be your son. Go Lions! To my love and inspiration, Brittany. Thank you for continually believing in me and being there every step of the way. This road would have been entirely impassable if not for the light you've given to my life. Finally, to my mother, Mary. There are no words. Thank you for always believing in me. Thank you for teaching me to value the beauty of dreams. Thank you for showing me how to sustain grace, conviction, and courage under fire. Thank you for teaching me the difference one person can make. Thank you for showing me what real heroes look like. I am proud to be your son. This one's definitely for you, Ma!

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Physics from Symmetry

Cited by 34 publications

References 0 publications

The underlying geometry of the CAM gauge model of the Standard Model of particle physics

The underlying geometry of the CAM gauge model of the Standard Model of particle physics

What Drives Sustainable Brand Awareness: Exploring the Cognitive Symmetry between Brand Strategy and Consumer Brand Knowledge

An application of the theory of moments to Euclidean relativistic quantum mechanical scattering

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