scholarly journals Construction of a unique metric in quasi-Hermitian quantum mechanics: Nonexistence of the charge operator in a 2×2 matrix model

2006 ◽  
Vol 640 (1-2) ◽  
pp. 52-56 ◽  
Author(s):  
Miloslav Znojil ◽  
Hendrik B. Geyer
Keyword(s):  
Quantum Mechanics ◽  
Matrix Model ◽  
Charge Operator

scholarly journals Areas and entropies in BFSS/gravity duality

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Tarek Anous ◽  
Joanna Karczmarek ◽  
Eric Mintun ◽  
Mark Van Raamsdonk ◽  
Benson Way
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theory ◽  
Matrix Model ◽  
Finite Temperature ◽  
The Matrix ◽  
Gravity Duality ◽  
General Connection ◽  
Ordinary Quantum

The BFSS matrix model provides an example of gauge-theory / gravity duality where the gauge theory is a model of ordinary quantum mechanics with no spatial subsystems. If there exists a general connection between areas and entropies in this model similar to the Ryu-Takayanagi formula, the entropies must be more general than the usual subsystem entanglement entropies. In this note, we first investigate the extremal surfaces in the geometries dual to the BFSS model at zero and finite temperature. We describe a method to associate regulated areas to these surfaces and calculate the areas explicitly for a family of surfaces preserving SO(8) symmetry, both at zero and finite temperature. We then discuss possible entropic quantities in the matrix model that could be dual to these regulated areas.

scholarly journals D-Brane Configurations and Nicolai Map in Supersymmetric Yang–Mills Theory

1997 ◽  
Vol 12 (03) ◽  
pp. 183-193 ◽  
Author(s):  
I. I. Kogan ◽  
R. J. Szabo ◽  
G. W. Semenoff
Keyword(s):  
Quantum Mechanics ◽  
Phase Transitions ◽  
Matrix Model ◽  
Short Distance ◽  
Dimensional Theory ◽  
Yang Mills ◽  
Large N ◽  
The Matrix ◽  
M Theory ◽  
Matrix Quantum

We discuss some properties of a supersymmetric matrix model that is the dimensional reduction of supersymmetric Yang–Mills theory in 10 dimensions and which has been recently argued to represent the short-distance structure of M-theory in the infinite momentum frame. We describe a reduced version of the matrix quantum mechanics and derive the Nicolai map of the simplified supersymmetric matrix model. We use this to argue that there are no phase transitions in the large-N limit, and hence that S-duality is preserved in the full 11-dimensional theory.

scholarly journals NON-ABELIAN BERRY PHASE, YANG–MILLS INSTANTON AND USp(2k) MATRIX MODEL

1999 ◽  
Vol 14 (13) ◽  
pp. 869-877 ◽  
Author(s):  
B. CHEN ◽  
H. ITOYAMA ◽  
H. KIHARA
Keyword(s):  
Quantum Mechanics ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Matrix Model ◽  
Berry Phase ◽  
Space Time ◽  
Dimensional Euclidean Space ◽  
Yang Mills ◽  
Time Points

The non-Abelian Berry phase is computed in the T dualized quantum mechanics obtained from the USp (2k) matrix model. Integrating the fermions, we find that each of the space–time points [Formula: see text] is equipped with a pair of su(2) Lie algebra valued pointlike singularities located at a distance m(f) from the orientifold surface. On a four-dimensional paraboloid embedded in the five-dimensional Euclidean space, these singularities are recognized as the BPST instantons.

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