scholarly journals Spin-1/2 one- and two- particle systems in physical space without eigen-algebra or tensor product

2021 ◽  
Author(s):  
Sokol Andoni
Keyword(s):  
Tensor Product ◽  
Physical Space ◽  
Cross Product ◽  
Expectation Values ◽  
Orientation Space ◽  
Geometric Objects ◽  
Spin Pairs ◽  
The One ◽  
And Inversion ◽  
Geometric Picture

Abstract A novel representation of spin 1/2 combines in a single geometric object the roles of the standard Pauli spin vector and spin state. Under the spin-position decoupling approximation it consists of the ordered sum of three orthonormal vectors comprising a gauge phase. In the one-particle case the representation: (1) is Hermitian; (2) is oriented due to ordering; (3) reproduces all standard expectation values, including the total one-particle spin modulus A; (4) constrains basis opposite spins to have same orientation; (5) allows to formalize irreversibility in spin measurement. In the two-particle case: (1) entangled spin pairs have opposite orientation and precisely related gauge phases; (2) the dimensionality of the spin space doubles due to variation of orientation; (3) the four maximally entangled states are naturally defined by the four improper rotations in 3D: reflections onto the three orthogonal frame planes (triplets) and inversion (singlet). The cross-product terms in the expression for the squared total spin of two particles relates to experiment and they yield all standard expectation values after measurement. Here spin is directly defined and transformed in 3D orientation space, without use of eigen algebra and tensor product as in the standard formulation. The formalism allows working with whole geometric objects instead of only components, thereby helping keep a clear geometric picture of ‘on paper’ (controlled gauge phase) and ‘on lab’ (uncontrolled gauge phase) spin transformations.

scholarly journals Spin-1/2 one- and two- particle systems in physical space without eigen-algebra or tensor product

2021 ◽  
Author(s):  
Sokol Andoni
Keyword(s):  
Tensor Product ◽  
Physical Space ◽  
Cross Product ◽  
Expectation Values ◽  
Orientation Space ◽  
Geometric Objects ◽  
Vector Operator ◽  
The One ◽  
And Inversion ◽  
Geometric Picture

Abstract A novel representation of spin 1/2 combines in a single geometric object the roles of the standard Pauli spin vector operator and spin state. Under the spin-position decoupling approximation it consists of three orthonormal vectors comprising a gauge phase. In the one-particle case the representation: (1) is Hermitian; (2) shows handedness; (3) reproduces all standard expectation values, including the total one-particle spin modulus 𝑆tot = (ℏ/2)√3; (4) constrains basis opposite spins to have same handedness; (5) allows to formalize irreversibility in spin measurement. In the two-particle case: (1) entangled pairs have precisely related gauge phases; (2) the dimensionality of the spin space doubles due to variation of handedness; (3) the four maximally entangled states are naturally defined by the four improper rotations in 3D: reflections onto the three orthogonal frame planes (triplets) and inversion (singlet). Cross-product terms in the expression for the squared total spin of two particles relate to experiment and they yield all standard expectation values after measurement. Here spin is directly defined and transformed in 3D orientation space, without use of eigen algebra and tensor product as done in the standard formulation. The formalism allows working with whole geometric objects instead of only components, thereby helping keep a clear geometric picture of ‘on paper’ (controlled gauge phase) and ‘on lab’ (uncontrolled gauge phase) spin transformations.

scholarly journals Spin-1/2 one- and two- particle systems in physical space without eigen-algebra or tensor product

2021 ◽  
Author(s):  
Sokol Andoni
Keyword(s):  
Tensor Product ◽  
Physical Space ◽  
Cross Product ◽  
Expectation Values ◽  
Orientation Space ◽  
Geometric Objects ◽  
Vector Operator ◽  
The One ◽  
Geometric Picture ◽  
Orthogonal Frame

Abstract A novel representation of spin 1/2 combines in a single geometric object the roles of the standardPauli spin vector operator and spin state. Under the spin-position decoupling approximation it consists ofthree orthonormal vectors comprising a gauge phase. In the one-particle case the representation: (1) isHermitian; (2) shows handedness; (3) reproduces all standard expectation values, including the total one particlespin modulus 𝑆tot = √3ℏ/2; (4) constrains basis opposite spins to have same handedness; (5)allows to formalize irreversibility in spin measurement. In the two-particle case: (1) entangled pairs haveprecisely related gauge phases and can be of same or opposite handedness; (2) the dimensionality of the spinspace doubles due to variation of handedness; (3) the four maximally entangled states are naturally definedby the four improper rotations in 3D: reflections onto the three orthogonal frame planes (triplets) andinversion (singlet). The cross-product terms in the expression for the squared total spin of two particlesrelates to experiment and they yield all standard expectation values after measurement. Here spin is directlydefined and transformed in 3D orientation space, without use of eigen algebra and tensor product as in thestandard formulation. The formalism allows working with whole geometric objects instead of onlycomponents, thereby helping keep a clear geometric picture of ‘on paper’ (controlled gauge phase) and ‘onlab’ (uncontrolled gauge phase) spin transformations.

scholarly journals Spin-1/2 one- and two- particle systems in physical space without eigen-algebra or tensor product

2021 ◽  
Author(s):  
Sokol Andoni
Keyword(s):  
Tensor Product ◽  
Physical Space ◽  
Cross Product ◽  
Expectation Values ◽  
Spacetime Algebra ◽  
Orientation Space ◽  
Spin Pairs ◽  
The One ◽  
Spinor Basis ◽  
Geometric Picture

Abstract A new representation for spin 1/2 in the even 3D subalgebra of the spacetime algebra (STA) combines in a single geometric object the roles of the standard Pauli spin vector and spin state. It is a vector quantity comprising a gauge phase. In the one-particle case the representation (1) is Hermitian; (2) chiral; (3) reproduces all standard expectation values, including the total one-particle spin modulus ; (4) constrains a spinor basis representing opposite spins to preserve handiness (chirality); (5) the gauge phase allows to explicitly formalize irreversibility in spin measurement. In the two-particle case it (1) identifies entangled spin pairs as having opposite handiness and precise gauge phase relations; (2) doubles the dimensionality of the spin space due to variation of handiness; (3) the four maximally entangled states are naturally derived by pairing spins that are reflections (triplets) and inversions (singlet) of each-other. The cross-product terms in the expression for the squared total spin of two particles can be affected by experiment and they yield the standard expectation values after measurement. Here I directly define and transform spin in 3D orientation space, without invoking concepts like abstract Hilbert space and tensor product as in the standard formulation. The STA formalism allows working with whole geometric objects instead of only components, thereby helping keep a clear geometric picture of ‘on paper’ (controlled gauge phase) and ‘on lab’ (uncontrolled gauge phase) spin transformations.

scholarly journals Evaluation of the one electron expectation values for different wave function of Be atom

2007 ◽  
Vol 4 (3) ◽  
pp. 393-396
Author(s):  
Baghdad Science Journal
Keyword(s):  
Wave Function ◽  
Slater Determinant ◽  
Open Shell ◽  
Expectation Values ◽  
Electronic Density ◽  
Expectation Value ◽  
Hartree Fock ◽  
Shell System ◽  
Electronic Wave Function ◽  
The One

The aim of this work is to evaluate the one- electron expectation value from the radial electronic density function D(r1) for different wave function for the 2S state of Be atom . The wave function used were published in 1960,1974and 1993, respectavily. Using Hartree-Fock wave function as a Slater determinant has used the partitioning technique for the analysis open shell system of Be (1s22s2) state, the analyze Be atom for six-pairs electronic wave function , tow of these are for intra-shells (K,L) and the rest for inter-shells(KL) . The results are obtained numerically by using computer programs (Mathcad).

scholarly journals Cityspace, Cyberspace, and the Spatiology of Information

1970 ◽  
Vol 1 (1) ◽  
Author(s):  
Michael L. Benedikt
Keyword(s):  
Cellular Automata ◽  
Data Visualization ◽  
Virtual Worlds ◽  
Physical Space ◽  
Thought Experiments ◽  
William Gibson ◽  
Architectural Space ◽  
Spatial Framework ◽  
The One ◽  
The Universe

Published in 1996* but not widely read, this article argues that space and information are so deeply related that the universe at every moment is exactly and only as large as it needs to be to “contain” the information it in fact is. Using three thought experiments—one about data visualization, one about cellular automata and consciousness, and one about the analysis of architectural space using isovists, each experiment blurring (or rather, uniting) the phenomena of psychological and physical space, the article argues that what we experience as “space” is that set of dimensions which provides the largest capacity for the world’s other qualities, objects, and events to express their variety most fully. The natural universe is incompressible, expanding only as, and because, it becomes richer in information (i.e. cools and evolves). Imaginary and virtual worlds obey the same rule: they are “naturally” as big as they are rich in information. But the possibility exists in cyberspace—as it does not in nature—to choose which dimensions will serve as the spatial framework, and which will become/appear as properties of the things themselves. Data visualizers know this well. One wonders why virtual worlds to this day look so similar to ours, then, rather than to the one envisaged by William Gibson in 1984 and 1986 and which he called “cyberspace.” A failure of architectural nerve? A constraint upon computation? Or has cyberspace proper yet to evolve?

Building a ‘Lofty, Beloved People's Amusement Centre’: The socialist transformation of Shanghai's Great World (Dashijie) (1950–58)

2020 ◽  
pp. 1-42
Author(s):  
WENMING XIAO ◽  
YAO LI
Keyword(s):  
Physical Space ◽  
Cultural Transformation ◽  
Transformation Process ◽  
Early Years ◽  
Communist Regime ◽  
Republic Of China ◽  
Strong State ◽  
The People ◽  
Institutional Structures ◽  
The One

Abstract Based on a detailed case study of the socialist transformation of the Shanghai Great World Amusement Centre (Dashijie), this article documents state-building efforts during the early years of the People's Republic of China (PRC). Between 1950 and 1958, the Communist regime incrementally transformed the power configuration within Dashijie, promoting dramatic changes in its personnel, institutional structures, drama performances, and physical space. Over the course of this process, Dashijie seemed to become a ‘loftier’ cultural organization in accordance with the aims of its transformation. This transfigured Dashijie, however, fell out of favour with the people of Shanghai. This multifaceted transformation process reflects considerable state capacities on the one hand and illustrates the complexity of state capacities—their unevenness and the limitations of a strong state—on the other. The complexity of state capacities thus shaped and was embedded in the process and outcome of this socialist cultural transformation. Since the Chinese state is once again making strenuous efforts at culture-building, an overview of cultural transformation in the early PRC era has important contemporary implications.

scholarly journals PREPOTENTIALS OF N=2 SUPERSYMMETRIC GAUGE THEORIES AND SOLITON EQUATIONS

1996 ◽  
Vol 11 (02) ◽  
pp. 131-138 ◽  
Author(s):  
TOHRU EGUCHI ◽  
SUNG-KIL YANG
Keyword(s):  
Gauge Theories ◽  
Scalar Fields ◽  
Vector Multiplet ◽  
Coulomb Branch ◽  
Supersymmetric Gauge Theories ◽  
Expectation Values ◽  
Soliton Equations ◽  
Supersymmetric Gauge ◽  
Β Function ◽  
The One

Using recently proposed soliton equations we derive a basic identity for the scaling violation of N=2 supersymmetric gauge theories Σiai∂F/∂ai−2F=8πib1u. Here F is the prepotential, ai’s are the expectation values of the scalar fields in the vector multiplet, u=1/2 Tr<ϕ2> and b1 is the coefficient of the one-loop β-function. This equation holds in the Coulomb branch of all N=2 supersymmetric gauge theories coupled with massless matter.

scholarly journals Cultural Workers from the Paintbrush Factory. Between Institution-Building and Urban Development Challenges

2019 ◽  
Vol 64 (2) ◽  
pp. 85-106
Author(s):  
Marina Mironică
Keyword(s):  
Development Strategy ◽  
Contemporary Art ◽  
Physical Space ◽  
Institution Building ◽  
Cultural Workers ◽  
Cultural Policies ◽  
Art Scene ◽  
The One

Abstract The paper is an ethnography of cultural workers from the contemporary art centre from Cluj-Napoca, Romania – The Paintbrush Factory. The one-decade existence of the alternative space contributed to a range of changes in the local cultural scene and evolved from a physical space into a resource for the city’s culture-led development strategy. It also became affected and reshaped by wider changes in terms of applied cultural policies. Cultural workers’ perspective, their precarity and their involvement in the local art scene influenced the current commodification and entrepreneurialisation of the cultural offer. The Paintbrush Factory’s expansion and contraction are vividly presented through the reflexive lenses of the cultural workers and managers, whose case-study could easily be regarded as a signal and a symbol of the deficient cultural policies mostly oriented to profit and lacking any local and long term-vision.

scholarly journals Od groźnych po zagrożone Alpy — procesy zawłaszczania i tożsamość alpejskich obrońców środowiska w Tyrolu

2021 ◽  
Vol 14 ◽  
pp. 137-149
Author(s):  
Maria Buck
Keyword(s):  
European Union ◽  
Physical Space ◽  
The Other ◽  
The European Union ◽  
History Of ◽  
The Alps ◽  
History Of Culture ◽  
The One ◽  
Sports Arena ◽  
Resistance Movement

While in the early days of the European history of culture the Alps were seen as forbidding, since the 1970s environmental activists have used this description, turning it the other way round — now it is the Alps that are increasingly threatened by today’s environmental problems. Noise, air pollution, deforestation and problems relating to ozone depletion threaten the ecologically sensitive Alpine range. The problems affect not just the Alps, but owing to geographical and topographic conditions their consequences are particularly strong here. Thus the Alps constitute a reference framework as well as a point of origin for the thematisation of ecological problems. Defenders of the Alps were especially critical of the claims — or, more openly, designs — of the European Union in the area of transport, tourism and energy. The relations between the Alps and the European Union constituted a unique moment in the discussion of environmental activists. On the one hand they styled the Alps as a model ecological region in contrast to the economy-focused European Union, and on the other the European Union served as a common enemy, which turned the Alps into a political argument in declaring unity of this space. This unity was, according to the defenders of the Alps, important in the context of securing and forcing through the region’s internal needs. To sum up, the Alps were presented as a place where various, partly opposing, economic, ecological and political interest met, and a place appropriated, depending on the context, as a living, cultural and economic space, as Europe’s roof and water tower, or as a holiday idyll and sports arena. Given the collaboration of Alpine environmentalists crossing state borders south and north of the Brenner Pass, and within the extraordinarily politically and socially heterogenous resistance movement in North Tirol, a question arises: to what extent have the Alps generated unique forms of identification for these figures? The author of the article argues that for Alpine environmentalists the Alps are both a discursive and a physical space, used as an identity-building element and space of activity.

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