scholarly journals CARTAN CALCULUS VIA PAULI MATRICES

2003 ◽  
Vol 18 (28) ◽  
pp. 5231-5259
Author(s):  
D. MAURO
Keyword(s):  
Vector Field ◽  
Path Integral ◽  
Classical Mechanics ◽  
Tensor Products ◽  
Lie Derivative ◽  
Exterior Derivative ◽  
Integral Formalism ◽  
Jacobi Fields ◽  
Finite Dimensional ◽  
Pauli Matrices

In this paper we will provide a new operatorial counterpart of the path-integral formalism of classical mechanics developed in recent years. We call it new because the Jacobi fields and forms will be realized via finite dimensional matrices. As a byproduct of this we will prove that all the operations of the Cartan calculus, such as the exterior derivative, the interior contraction with a vector field, the Lie derivative and so on, can be realized by means of suitable tensor products of Pauli and identity matrices.

δ2-QUANTIZATION OF GAUGE FIELDS

1992 ◽  
Vol 07 (30) ◽  
pp. 2819-2826
Author(s):  
A. N. SISSAKIAN ◽  
I. L. SOLOVTSOV ◽  
O. Yu. SHEVCHENKO
Keyword(s):  
Vector Field ◽  
Phase Space ◽  
Configuration Space ◽  
Path Integral ◽  
Wilson Loop ◽  
Gauge Condition ◽  
Gauge Fields ◽  
Time And Space ◽  
Integral Formalism ◽  
Path Integral Formalism

On the basis of the path-integral formalism in the phase space, a new scheme of quantization of gauge fields is proposed. The path integral in the configuration space is shown to contain two functional δ-functions that reflect the gauge condition and the Gauss law. A new propagator is obtained for the vector field which, for instance, for gauges nμAμ=0 distinguishes choices between time- and space-like vectors nμ and does not lead to contradictions in the computation of the Wilson loop.

Some Properties of Symplectic Manifolds S on the Projective Tangent Bundle PTM

2011 ◽  
Vol 187 ◽  
pp. 483-486
Author(s):  
Yong He ◽  
Xiao Ying Lu ◽  
Wei Na Lu
Keyword(s):  
Vector Field ◽  
Symplectic Manifold ◽  
Tangent Bundle ◽  
Fiber Bundle ◽  
Symplectic Manifolds ◽  
Lie Derivative ◽  
The Relationship

In this paper, we show the relationship between 2-form of the two projective tangent bundle and the relationship between 2-form on projective tangent bundle and 1-form on by using the theory of fiber bundle and the properties of symplectic manifold of the projective tangent bundle . Moreover, we derived a simpler formula of Lie derivative of a special vector field, which is on the projective tangent bundle.

Application of path integral formalism in spectral line broadening: Lyman- in hydrogenic plasma

2005 ◽  
Vol 94 (3-4) ◽  
pp. 335-346 ◽  
Author(s):  
H. Bouguettaia ◽  
Is. Chihi ◽  
K. Chenini ◽  
M.T. Meftah ◽  
F. Khelfaoui ◽  
...  
Keyword(s):  
Spectral Line ◽  
Path Integral ◽  
Line Broadening ◽  
Integral Formalism ◽  
Path Integral Formalism ◽  
Spectral Line Broadening

Multi-instantons and exact results IV: Path integral formalism

2011 ◽  
Vol 326 (8) ◽  
pp. 2186-2242 ◽  
Author(s):  
Ulrich D. Jentschura ◽  
Jean Zinn-Justin
Keyword(s):  
Path Integral ◽  
Exact Results ◽  
Integral Formalism ◽  
Path Integral Formalism

The exterior derivative as a Killing vector field

1996 ◽  
Vol 93 (1) ◽  
pp. 157-170 ◽  
Author(s):  
J. Monterde ◽  
O. A. Sánchez-Valenzuela
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Exterior Derivative

scholarly journals The solar-interior equation of state with the path-integral formalism

2009 ◽  
Vol 505 (2) ◽  
pp. 735-742 ◽  
Author(s):  
A. Perez ◽  
K. Mussack ◽  
W. Däppen ◽  
D. Mao
Keyword(s):  
Equation Of State ◽  
Path Integral ◽  
Solar Interior ◽  
Integral Formalism ◽  
Path Integral Formalism

Entanglement criteria for the three-qubit states

2017 ◽  
Vol 15 (07) ◽  
pp. 1750049 ◽  
Author(s):  
Y. Akbari-Kourbolagh
Keyword(s):  
White Noise ◽  
Tensor Products ◽  
W State ◽  
Entangled States ◽  
Mean Values ◽  
W States ◽  
Pauli Matrices ◽  
The Mean ◽  
Simple Sets ◽  
Qubit States

We present sufficient criteria for the entanglement of three-qubit states. For some special families of states, the criteria are also necessary for the entanglement. They are formulated as simple sets of inequalities for the mean values of certain observables defined as tensor products of Pauli matrices. The criteria are good indicators of the entanglement in the vicinity of three-qubit GHZ and W states and enjoy the capability of detecting the entangled states with positive partial transpositions. Furthermore, they improve the best known result for the case of W state mixed with the white noise. The efficiency of the criteria is illustrated through several examples.

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