scholarly journals Particles within extended-spin space: Lagrangian connection

2015 ◽  
Vol 267-269 ◽  
pp. 199-206 ◽  
Author(s):  
J. Besprosvany ◽  
R. Romero
Keyword(s):  
Spin Space

New isotopic spin space and classification of elementary particles

1960 ◽  
Vol 18 (2) ◽  
pp. 209-228 ◽  
Author(s):  
P. Hillion ◽  
J. P. Vigier
Keyword(s):  
Elementary Particles ◽  
Isotopic Spin ◽  
Spin Space

Interaction theory in a new isobaric spin space

1961 ◽  
Vol 28 (1) ◽  
pp. 624-635
Author(s):  
Pierre Hillion ◽  
Jean-Pierre Vigier
Keyword(s):  
Spin Space ◽  
Interaction Theory

Computer Simulation Study of a Disordered Two-Dimensional Nematogenic Lattice Model with Long-Range Interactions Isotropic in Spin Space

1997 ◽  
Vol 11 (07) ◽  
pp. 919-928
Author(s):  
S. Romano
Keyword(s):  
Computer Simulation ◽  
Long Range ◽  
Temperature Phase ◽  
Two Dimensional ◽  
Spin Space ◽  
Pair Potentials ◽  
Long Range Interactions ◽  
Invariant Pair ◽  
Ordering Transition ◽  
Low Temperature Phase

We have considered a classical spin system, consisting of 3-component unit vectors, associated with a two-dimensional lattice {uk, k∈ Z2}, and interacting via translationally invariant pair potentials, isotropic in spin space, and of the long-range form [Formula: see text] Here ∊ is a positive constant setting energy and temperature scales (i.e. T*=k B T /∊), P2 denotes the second Legendre polynomial, and xj are dimensionless coordinates of the lattice sites. Available theorems entail the existence of an ordering transition at finite temperature when 0 < σ < 2, and its absence when σ ≥ 2. We have studied the border case σ=2, by means of computer simulation. Similarly to the nearest-neighbour counterpart of the present model, and to other long-range models, we found evidence suggesting a transition to a low-temperature phase with slow decay of correlations and infinite susceptibility, i.e. a Berezhinski[Formula: see text]–Kosterlitz–Thouless-like transition; the transition temperature was estimated to be Θ=1.112 ± 0.005.

COMPUTER SIMULATION STUDY OF A DISORDERED ONE-DIMENSIONAL NEMATOGENIC LATTICE MODEL WITH LONG-RANGE INTERACTIONS ISOTROPIC IN SPIN SPACE

1995 ◽  
Vol 09 (25) ◽  
pp. 3345-3354 ◽  
Author(s):  
S. ROMANO
Keyword(s):  
Computer Simulation ◽  
Long Range ◽  
Temperature Phase ◽  
Spin Space ◽  
Rigorous Results ◽  
One Dimensional ◽  
Pair Potentials ◽  
Long Range Interactions ◽  
Invariant Pair ◽  
Ordering Transition

We have considered a classical spin system, consisting of 3-component unit vectors, associated with a one-dimensional lattice {uk, k ∈ Z}, and interacting via translationally invariant pair potentials, isotropic in spin space, and of the long-range form [Formula: see text] where ∊ is a positive constant setting energy and temperature scales (i.e. T* = kBT/∊). Extending previous rigorous results, one can prove the existence of an ordering transition at finite temperature when 0 < σ < 1, and its absence when σ ≥ 1. We have studied the border case σ = 1, by means of computer simulation. Similarly to the magnetic counterparts of the present model, we found evidence suggesting a transition to a low-temperature phase with slow decay of correlations and infinite susceptibility, i.e. a Berezhinskiǐ–Kosterlitz–Thouless-like transition; the transition temperature was estimated to be Θ = 0.475 ± 0.005.

Spin gauge field theory of electric and magnetic spinors

1981 ◽  
Vol 377 (1768) ◽  
pp. 1-23 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Gauge Theory ◽  
Gauge Field Theory ◽  
Spin Space ◽  
Conjugation Operator ◽  
Vector Potentials ◽  
Covariant Derivatives ◽  
Component Theory ◽  
Curvature And Torsion ◽  
Derivatives Of

In the first section, a gauge theory of an unquantized generalized electron interacting with the electromagnetic field through two vector potentials is formulated, based on invariance of the Lagrangian under an algebra of spin space transformations. The covariant derivative is essentially expres­sed in terms of spin space operators. It is not possible to define dual monopole spinors in a four-component theory. However, a modified eight-component generalized electron gauge theory transforms into a dual monopole theory by using a square root of the charge conjugation operator. The covariant derivatives of the two spinors are members of a continuous set, and define curvature and torsion in spin space corresponding to the two spinors. Physically important ‘weak spin curvature’ is closely related to the total electromagnetic field. Possible physical interpretations and extensions of the theory are discussed.

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