scholarly journals Classical limits of scalar and tensor gauge operators based on the overlap Dirac matrix

2008 ◽  
Vol 78 (8) ◽  
Author(s):  
Andrei Alexandru ◽  
Ivan Horváth ◽  
Keh-Fei Liu
Keyword(s):  
Dirac Matrix

New Routines for Algebraic Programming of the Dirac Equation

1997 ◽  
Vol 08 (02) ◽  
pp. 273-286 ◽  
Author(s):  
Ion I. Cotăescu ◽  
Dumitru N. Vulcanov
Keyword(s):  
Dirac Equation ◽  
Main Part ◽  
Space Time ◽  
Curved Space ◽  
Algebraic Programming ◽  
Matrix Algebras ◽  
Dirac Matrix ◽  
New Procedures

We present new procedures in the REDUCE language for algebraic programming of the Dirac equation on curved space-time. The main part of the program is a package of routines defining the Pauli and Dirac matrix algebras. Then the Dirac equation is obtained using the facilities of the EXCALC package. Finally we present some results obtained after running our procedures for the Dirac equation on several curved space-times.

scholarly journals The Dirac matrix group and Fierz transformations

1970 ◽  
Vol 17 (4) ◽  
pp. 322-342 ◽  
Author(s):  
E. de Vries ◽  
A. J. van Zanten
Keyword(s):  
Matrix Group ◽  
Dirac Matrix

scholarly journals Lattice Clifford fractons and their Chern-Simons-like theory

2021 ◽  
Vol 4 (2) ◽  
Author(s):  
Weslei Fontana ◽  
Pedro Gomes ◽  
Claudio Chamon
Keyword(s):  
Clifford Algebra ◽  
Degrees Of Freedom ◽  
Quantum Hall ◽  
Effective Theory ◽  
Matrix Representations ◽  
Quantum Hall States ◽  
Dirac Matrix ◽  
Spatial Dimensions ◽  
K Matrix ◽  
Chern Simons

We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example, we build lattice fractons in odd D spatial dimensions and their (D+1) spacetime dimensional effective theory. The model possesses an anti-symmetric K matrix resembling that of hierarchical quantum Hall states. The gauge charges are conserved in sub-dimensional manifolds which ensures the fractonic behavior. The construction extends to any lattice fracton model built from commuting projectors and with tensor products of spin-1/2 degrees of freedom at the sites.

scholarly journals Hamiltonian analysis of Mimetic gravity with higher derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yunlong Zheng
Keyword(s):  
Hamiltonian Formalism ◽  
Ricci Scalar ◽  
Gravity Models ◽  
Jordan Frame ◽  
Cosmological Perturbation ◽  
Unitary Gauge ◽  
Dirac Matrix ◽  
Higher Derivatives ◽  
Mimetic Gravity ◽  
Hamiltonian Analysis

Abstract Two types of mimetic gravity models with higher derivatives of the mimetic field are analyzed in the Hamiltonian formalism. For the first type of mimetic gravity, the Ricci scalar only couples to the mimetic field and we demonstrate the number of degrees of freedom (DOFs) is three. Then in both Einstein frame and Jordan frame, we perform the Hamiltonian analysis for the extended mimetic gravity with higher derivatives directly coupled to the Ricci scalar. We show that different from previous studies working at the cosmological perturbation level, where only three propagating DOFs show up, this generalized mimetic model, in general, has four DOFs. To understand this discrepancy, we consider the unitary gauge and find out that the number of DOFs reduces to three. We conclude that the reason why this system looks peculiar is that the Dirac matrix of all secondary constraints becomes singular in the unitary gauge, resulting in extra secondary constraints and thus reducing the number of DOFs. Furthermore, we give a simple example of a dynamic system to illustrate how gauge choice can affect the number of secondary constraints as well as the DOFs when the rank of the Dirac matrix is gauge dependent.

Pauli-Dirac matrix generators of Clifford Algebras

1982 ◽  
Vol 12 (7) ◽  
pp. 719-738 ◽  
Author(s):  
Charles P. Poole ◽  
Horacio A. Farach
Keyword(s):  
Clifford Algebras ◽  
Dirac Matrix

scholarly journals Chronological inversion method for the Dirac matrix in hybrid Monte Carlo

1997 ◽  
Vol 484 (1-2) ◽  
pp. 353-374 ◽  
Author(s):  
R.C. Brower ◽  
T. Ivanenko ◽  
A.R. Levi ◽  
K.N. Orginos
Keyword(s):  
Monte Carlo ◽  
Inversion Method ◽  
Hybrid Monte Carlo ◽  
Dirac Matrix
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